Equal Opportunities

In this paper I will clarify the term † equivalent opportunities† according to early years practice. Investigate this with regards to the UN Convention on the Rights of the Child and clarify the effect the Convention on UK enactment. I am likewise going to recommend a few stages which in my thought can execute correspondence of chance for kids in UK. Equivalent open door is an illustrative term for a methodology expected to give equivalent access to a specific social condition or to guarantee individuals are not explicitly avoided from partaking in exercises, for example, training, work or human services based on unchanging characteristics. The absence of access may cause poor confidence, regard, mistaken assumptions, generalizing and separation. Bruce and Meggit, 2002) Also it implies opening up the universe for the youngster and family with the goal that they can take full profit of the youth exercises in school and in the public arena. Equivalent open door doesn't mean rewarding everybody the equivalent. The Common territories of segregation are race, monetary capacity, sex and the capacity of the kid. Each kid's future relies upon circumstances gave to it in his initial long stretches of life which for the most part characterizes the youngster's viewpoint towards life. This will be the window through which the kid will characterize race, sex, nationality, religion, family set-up, extraordinary necessities and sexual direction of guardians in their own specific manner. The educator and guardians will assume the most imperative job in the youngster's initial long periods of advancement and they will give all the fundamental components of this procedure to fabricate the kid's future. Instructors and guardians need to ensure that he is in the correct condition for this advancement to happen. To support them, the UN has assumed a significant job and contributed tremendously to this procedure. The UN general get together consented to embrace the shows on the privileges of the kid on November twentieth, 1989. It came into power in September 1990 after it was confirmed by 192 part countries. The show is kid driven and manages youngster explicit needs and right to instruction and care. It additionally takes care of the wellbeing of the youngster. Articles 2,3,6,7,8,11,12,13,23,28,29,30,31,32,34,35 are connected explicitly to the early years in regard to training and care. These articles of the approach express that the part countries will regard the rights set out in the current show to every youngster inside their purview without separation of any sort. (Show on the privileges of the youngster, 1990) The Convention on the Rights of the Child applies in the UK since confirmation in December 1991, when the administration consented to make all laws, strategy and practice perfect with the UN Convention. (http://www. unicef. organization) Every kid has certain fundamental rights, including the privilege to life, his/her own name and personality, and to be raised by his/her folks inside a family or social gathering and have a relationship with the two guardians, regardless of whether they are isolated. † (www. wikipedia. organization) The chiefs laid out in the worldwide human rights structure apply to the two youngsters and grown-ups. I am doing to focus on kids which are referenced particularly in a significant number of the human rights. Measures are extraordinarily adjusted or adjusted where the need and concerns encompassing are unmistakable for kids. http://www. kid misuse. com) The Convention on the Rights of the Child perceives and advances this extraordinary connection between children’s rights and obligations. The points of instruction characterized in the Article 29, incorporate supporting children’s regard for human rights, for their own and others social qualities and for the earth. This Article shows us how fundamental it is for each kid from birth to be thought resilience and endorsement for individuals of other social and have the option to gain admittance to a similar level and standard of instruction. Kids should be associated with procedure of finding out about different societies so as to comprehend them better. Along these lines kids become naturally with all the data, acknowledge them and discover that everyone has equivalent rights and merit endorsement and regard from Other individuals, regardless of how old they are. (UN Convention, Article 29) Other articles express children’s rights in wording that pressure how children’s exercise of those rights must be mindful and aware of the privileges of others. Article 15, expresses that youngsters reserve the privileges to meet with others and to join or set up affiliation, except if the reality of their doing so would damage the privileges of others. . Each youngster ought to be permitted to join those gatherings, along these lines kids find out about one another and develop their degree of resistance. Through public activity youngsters and youngsters meet and watch other kids and gain from one another. (UN Convention, Article 15) Another case of youngsters rights is Article 31 which again elevates the rights to rest and relaxation, play and recreational exercises fitting for the age of the kid. Youngsters need to have the opportunity to re-charge they vitality, rest and play with one another or, and all alone. By and large we find out about kids who need to work extended periods of time and all the time don't get enough rest around evening time. This is the point at which we could make reference to kids being investigated, dedicated kids who lack the capacity to deal with social, masterful or recreation exercises. (UN Convention, Article 31) In maintaining the privileges of kids, the Convention doesn't encroach on the privileges of guardians to choose what is best for their kids. Rather, it explicitly expresses that administrations will bend over backward to keep families unblemished and will offer help and help to guardians in satisfying their obligations with respect to the childhood and improvement of their youngsters. The advancement of youngsters' privileges doesn't involve setting kids in strife with the grown-up experts in their lives, yet of urging all residents to cooperate for a sheltered, solid and gainful future for kids. (http://www. unicef. organization) Guardians, carers, families and educators are the most significant effect on results for kids and youngsters. The Every Child Matters: Change for Children program means to guarantee that help for guardians gets normal, especially at key focuses in a youngster or youthful person’s life. (http://www. crin. ch) The UK government point is for each youngster, whatever their experience or their conditions, to have the help they should be sound, remain safe, appreciate and accomplish, cause a positive commitment, to accomplish monetary prosperity. The UK government point is for each youngster, whatever their experience or their conditions, to have the help they should be sound, remain safe, appreciate and accomplish, cause a positive commitment, to accomplish monetary prosperity. This implies the associations engaged with offering types of assistance to youngsters from medical clinics and schools, to police and intentional gatherings will collaborate in new manners, sharing data and cooperating, to shield kids and youngsters from mischief and help them accomplish what they need throughout everyday life. Youngsters and youngsters will have unmistakably more state about issues that influence them as people and on the whole. (http://www. cre. gov. uk) The Children’s Commissioner for England was named, to give kids and youngsters a voice in government and in open life. The Commissioner will give specific consideration to get-together and advancing the perspectives on the most helpless kids and youngsters in the public arena, and will advance their inclusion in crafted by associations whose choices and activities influence them. The Commissioner’s job is to watch each angle about little youngsters and respond quickly if something is acting against they runs and accepts. (http://www. cre. organization. uk) By consenting to embrace the commitment of the show, UK’s government have conceded to extend and guarantee children’s rights as they consented to consider themselves responsible for the responsibility before the universal network. State gatherings to the show are obliged to create and embrace all activities and polices to the greatest advantage of the youngster. The errand, be that as it may, must connect with governments as well as all citizenry. The guidelines and standards verbalized in the show can possibly turn into a reality when they are regarded by everybody inside the families, in school and other organization that offer support for youngsters, in networks and at all degrees of organizations. (MCI convention) The DfES (Department for Education and Slikks) works in organization with network establishments, provincial network chambers, committees for intentional assistance and award making trusts to give an accomplished store manager in every region. Directors guarantee that effort and backing are accessible to help candidates. Choices on designating subsidizing are made by evaluation boards involved individuals with information on the issues looked by youngsters in the networks served by the assets. (http://dfes. gov. uk) New kid noble cause have been perceived all over nation assisting with advancing and guarantee children’s rights, and screen how far their are being acknowledged and regarded. The foundations work together with government and common society to gain ground in acknowledging children’s rights. The UN advisory group invited various UK activities, particularly new enactment, for example, the Human Rights Act and Adoption and Children Bill, youth cooperation, the accessible methodology for youngsters, youngsters, and procedures on kid destitution and adolescent pregnancy. ( http://www. distribution. parliament. uk). All pieces of government have a duty to find out about, advance and actualize the show. The youngsters, youngsters and families directorate inside the division for instruction and aptitudes co-ordinates the government’s report to the council on the ri

Assessing Macro And Micro Environment Analysis Commerce Essay

Evaluating Macro And Micro Environment Analysis Commerce Essay Downturn in national or world economies and ascending of swelling which is being experienced current period, are the most widely recognized components that can influence organizations. On the other hand, what cause an antagonistic impact for some, organizations, has had a valuable impact for Dominos Pizza UK, Ireland, the most driving delievery establishment. Keeping in see the current financial circumstance Dominos Pizza deals had expanded up to 11% in the initial multi week of 2008 than that of same time of a year ago, due to, generally individuals favored for conveyance at home, rather than going for eat outs, Like-for-like deals rose 14.7% a year ago, in spite of a value ascend across Dominos menu last harvest time. (The Times, twentieth February 2008) As per Cheif Executive, The Chris Moore, The outcomes are confirmation that our value point is strong in these monetary occasions and that we are profiting by the downturn in the café area. Rather than eating out three or four times each week, we are seeing genuine signs that [people] have sliced that to on more than one occasion. They are topping off that hole with pizza. (The Times, 20 February 2008) His remarks came not long after the organization reported designs to climb to the primary market so as to acquire reserves it has been not able to pull in the nine years it has spent on the Alternative Investment Market (AIM). Dominos shares have climbed 14-overlap since the organization drifted in November 1999 and the gathering presently has 501 destinations over the UK and Ireland, with plans to open 50 more this year. Its point is to have 1,000 by 2017. (The Times, twentieth February 2008). Dominos stated, deals had been improved, because of these new pizzas, similar to astute, Meateor and the rugby-themed Scrummy, and by offering better approaches for requesting, similar to insightful web based business salesorders taken electronically either on the web or through instant messages, because of which deals have been strengthened to 60.5%. As indicated by Dominos expectation, the float for requesting in food would proceed with this year. At present the outside condition moving quickly. The outer condition comprises of everything outside the business. Indeed, even in the present crtical practical circumstance, dominos keeps on succeeding which is because of dominos callous accentuation on the nature of dominos pizzas, entering duty to support and by publicizing to dominos clients to at whatever point and any place they are eager to arrange. It is their frevency that has brought benefit development of 27.8% to  £29.9m (2008:  £23.4m) and that will endures to get-moving dominos business in years to come. Vermin ( Political, Economic, Social and Technological) I. Policy centered ISSUES: Policy centered issues incorporate administrative casing work working in legal framework which may trouble the business in assorted manners. In UK, there isnt as such factors that may grasp dominos business. While factors like, laws on business work, contamination and tax assessment apply on the association which it ought to adhere to as per rules. ii. Financial FACTORS: In the event that the countys economy is better so the GDP of the nation will be acceptable, it is the activity for business as the per capita pay builds individuals will go through more cash. As indicated by dominos study, it came to realize that generally individuals spend more and visit all the more regularly, during or start in on of months. In addition, ascend in expansion rate, prompts augmentation of cost of crude material which likewise leads towards more significant expenses for merchandise and the other way around iii. SOCIAL FACTORS: Dominos is a worldwide and it is fundamentally initiated from America, accordingly, the association is snowed under by dominos western culture. There are distinctive social types of society which comprises of, privileged, white collar class, center high society, and lower class. In addition, each and every country, state has their own social standards, convictions, religion, values which may influence the association around the world. iv. Innovative FACTORS: Right now, innovation is improving, so as preparing and warming stoves will be of new and effective innovation and will offer proficient support. Because of these creative innovation there are numerous most recent methods of publicizing like insightful, through web; telemarketing through which association can promote their items in considerably more quickly than at any other time. PC based client information that is MIS (overseeing data framework) helps in gathering client information, day by day exchanges, future guaging and dynamic. New vehicles will make their administration progressively productive. SWOT Analysis: Each association has its own qualities and shortcomings just as dangers and openings, As far as dominos swot is concerned its swot investigation is as under. Qualities: At present Dominos is the market head in giving wide scope of pizzas, in a way that there are no rival in this division. There admireble picture has made the association more worthfull. In addition, Dominos is render satisfying taste, quality items with qualified staff, mind blowing vibe and clean environmental factors. They are spent significant time in pizzas. Additionally Motivation level of staff is exceptionally high which make the association increasingly prosperous. They are ISO (International Standard Organization) guaranteed. They have outfitted with a lot of assets for working various exercises of the association. They are without giving home conveyance administration. They have made syndication in this area. Another large Strength and even a Competitive Advantageis the way that they have a full help eatery just as conveyance administrations. The majority of dominos contenders don't have cafés. Due to the café, Dominos can advertise such a large number of various fragment s that other pizza chains can't. For instance, Dominos can market to families a lot simpler than Dominos or Little Caesars. Dominos shortcomings: The way that Dominos has a café to run is additionally a shortcoming. Dominos has higher overhead expenses, because of the eatery that different contenders dont need to manage. Another aftereffect of higher overhead expenses is more significant expenses Dominos must charge. Clearly, Dominos isn't the minimal effort maker. They depend on their quality pizza and great assistance to represent their more significant expenses. They are furnishing less scope of items nearly with significant expenses. They are progressively centered around western taste rather than Eastern. Not many outlets have feast in offices The menu is constrained and expensive, and there are not very many spending things on the menu. Openings: New markets can be investigated and new open doors they can pick up. Dominos can concoct the new items considering the Eastern taste of the individuals as like McDonalds. Broadening of new items can build their piece of the overall industry. They can diminish their costs as a result of more dominos. Dangers: Dominos number one dangers are from their rivals. At present, their nearest rival is pizza cabin who is attempting to open their Branch quickly. Dominos principle upper hand over Pizza cottage is their Lower cost. Assess dominos organization systems with other various organizations: Dominos has prevailing with regards to extending over mainlands and watched marvelous accomplishments, however in endeavors to grow universally it has not had the option to deal with the local market with full proficiency and accordingly, is losing grounds in the household showcase. Dominos has increased the expectations of pizza industry to extraordinary statures, yet in current monetary circumstance, rising product costs and reduction in people groups buying power, it is battling to adjust among benefit and keeping up its norms. The expanding rivalry in the cheap food industry adds to its variety of difficulties. A basic factor in Pizza Huts achievement has been a menu that has continually developed and extended to take into account the changing needs and explicit inclinations of clients in various pieces of the world. In having comprehended the beat of the clients, Pizza Hut has unmistakably settled itself as a brand with a Britain heart and Dominos need to discover that. Benchmarking: For a long time as a privately owned business, Dominos truly benchmarked against itself, without taking a gander at the outside world. We were glad for the way that for a long time we had positive same-store deals, which is a major budgetary marker of development and accomplishment in the retail world. All things considered, that was the uplifting news. The awful news was that during those equivalent years our rivals were developing at a quicker rate. Dominos were really surrendering piece of the overall industry. Simultaneously, dominos were facilitating inward festivals of the way that against our own interior grid dominos were progressing admirably. Dominos not just needed to see what had been our past outcomes and accommodate how dominos were performing against that benchmark, yet in addition dominos expected to take a gander at our general surroundings, take a gander at our rivals, and in numerous occurrences, I truly needed us to take a gander at the absolute best in class. Who is out there doing the most ideal activity in this specific zone of business? Dominos need to discover what their outcomes are and begin to consider ourselves responsible for that specific degree of execution. Dominos acknowledge average quality since dominos can pick many individuals around us who are similarly as unremarkable as dominos seem to be. I need to locate the extremely, best, and I need to benchmark against them, and I need to show signs of improvement. I think on the off chance that I lead that desire and I get my group and my association to grasp it, that is the way dominos would become world-class entertainers. Takeaways At the point when an association is fruitful, individuals will in general accept that they can quit improving. However, things never remain the equivalent: it is possible that you show signs of improvement, or you deteriorate. The moment organizations become self-satisfied and emotionless is the moment they start to come up short. To have a superior association, you should cultivate a culture of persistent improvement. Dont acknowledge average quality. Rather, look to your rivals, and benchmark yourself against them to accomplish world-class execution. Association s

Essay Writing Companies - What Can They Do For You?

Essay Writing Companies - What Can They Do For You?Essay writing companies have been one of the most popular services that businesses seek out. The majority of individuals have resorted to writing in order to better understand the world around them. This practice of writing allows you to choose what knowledge and experiences to bring to life for your reader.Writing is an important aspect of writing for a number of reasons. It can be said that writing is a way to communicate information to others. Whether you are writing for personal or business use, you are able to take the pieces of information that you have and create a whole piece of work.Professional essay writing companies are able to turn your thoughts into useful information for others. This works in many ways and one of the ways is to use your facts in such a way that you help others in their life. Professional essay writing companies use several different techniques that will allow you to write a great essay in a short amoun t of time.There are three main categories of topics that are used in essay writing. These are the general topic, the subject matter, and the thesis statement. Each category of essay writing will help you achieve the best results possible.The general topic can be easily discovered by doing a search for essay writing companies that are focused on researching and writing essays on a variety of topics. If you decide to write a general essay then you will write about anything and everything. The majority of people usually write a general essay about a wide range of subjects. The examples of topics that are written for our general topics for example, sports, movies, schools, political, and many more.The subject matter is something that will generally cover the specific ideas that you want to discuss. These ideas will usually contain your main point and a list of ideas that you will be discussing. Subject matter is not as broad as a general topic and it is something that has to be research ed and crafted accordingly. If you find that you have a great idea for your topic then you should not hesitate to write it down.The thesis statement is the main content of the essay and this statement is the foundation of your entire paper. Your thesis statement will include what you wish to discuss and how the information you provide will prove your argument. Most of the time you are required to follow a specific format for your thesis statement. However, there are a few writers who choose to use different formats.Writing a thesis statement is something that is essential when using professional essay writing companies. You want to make sure that you have a reason for writing a thesis statement, which is typically five to seven paragraphs long. This is not something that you should rush through and if you do this then you will not end up with the best finished essay.

The World s First 5th Generation Air Superiority Fighter

After taking 25 years to develop the F-22 Raptor from conception to operational certification, the United States Air Force (USAF) produced the world’s first 5th generation air superiority fighter. This revolutionary fighter plane leveraged its very low observable stealth (VLO), thrust-vectoring and digital fly-by wire capabilities, and other cutting edge technology to produce an extremely fast, agile and lethal air-to-air combatant. Less than five years after operational certification in 2009, Robert Gates, Secretary of Defense, (SECDEF) convinced the President (POTUS) and Congress to truncate the F22 program, leaving the USAF with fewer than 187 operational F-22 Raptors. This number was well short of the 381 aircraft the USAF’s†¦show more content†¦security. The collapse of the USSR reduced the threat to the US. as the USSR no longer produced or planned to produce 5th generation air superiority fighters. By 2009 the emerging threats of Russia and China p roducing a 5th generation air superiority fighter reappeared, but this time with a much reduced risk than associated with the Cold War. These changes in the US. strategic environment did not eliminate the F-22 Raptor’s primary purpose or adversary, but the late arrival and reduced number of potential rival 5th generation air combatants made the F-22 Raptor less vital to the US. Security Strategy. In Robert Gates’ July 2009 speech to the Economic Club of Chicago, he described the F-22 Raptor as a niche capability only designed to defeat other superpowers’ highly advanced fighter planes. When the Obama Administration limited the F-22 Raptor to 187 aircraft, they did so with the full expectation that the US. possessed enough 5th generation capabilities to meet the nation’s strategic and security requirements. Gates’ decision met with many critics, primarily representatives of states that produce the F-22 Raptor components. They argued the DoD assu med unreasonable and ill-advised operational risk and created a â€Å"dangerous capabilities gap† by halting the F-22 Raptor to just 187 operational aircraft. They maintained Russia and China remain significant and growing competitors in global strategic struggles, making the F-22 Raptor a necessary capabilityShow MoreRelatedA Picatrix Miscellany52019 Words   |  209 PagesTalismans Picatrix Astrological Magic Aphorisms Extracts on Planetary Ritual Clothing Twenty Two Benefic Astrological Talismans Astrology, Magical Talismans and the Mansions of the Moon Ritual of Jupiter An Astrological Election of Mercury in the First Face of Virgo for Wealth and Growth XIV. Invocation of Mercury On the Decans and Tarot XV. XVI. XVII. XVIII. A Brief History of Tarot The Decans in Astrology Overview of Recent Tarot Works That Reference the Picatrix Magical Uses of the Tarot ColophonRead MoreProject Mgmt296381 Words   |  1186 Pages21st Century, First Edition Benton, Purchasing and Sup ply Chain Management, Second Edition Bowersox, Closs, and Cooper, Supply Chain Logistics Management, Third Edition Brown and Hyer, Managing Projects: A Team-Based Approach, First Edition Burt, Petcavage, and Pinkerton, Supply Management, Eighth Edition Cachon and Terwiesch, Matching Supply with Demand: An Introduction to Operations Management, Second Edition Finch, Interactive Models for Operations and Supply Chain Management, First Edition Fitzsimmons

Life Styles Inventory - Free Essay Example

Sample details Pages: 4 Words: 1248 Downloads: 1 Date added: 2017/09/13 Category Advertising Essay Did you like this example? My LSI Styles Complex My â€Å"primary† personal thinking style as shown in my circumplex is The Humanistic-Encouraging Style. This style means that I am â€Å"accepting of myself, and accept others for who they are without question or criticism† (Human 2010). Humanistic-Encouraging individuals believe they can â€Å"assist others in fulfilling their potential by providing a supportive climate that inspires self-improvement† (Human 2010). I believe that this very accurate summation of myself. This can easily be seen at my previous job as a waiter. I was often asked to train new employees because I was considered sensitive to peoples needs, and was willing to devote energy to counseling and coaching others. I also consider this style accurate about my myself because during my time as a Kohls retail shift manager, I tried to inspire my coworkers to think, grow and take responsibility for themselves by demonstrating belief in what my coworkers could accomplish. I always tried to believe when a subordinate told me that they could accomplish setting up a display in a certain amount of hours. My â€Å"backup† personal thinking style is The Competitive Style. Don’t waste time! Our writers will create an original "Life Styles Inventory" essay for you Create order I believe my backup style of being competitive is what pushes me to be all I can be. Competition is my motivation to succeed. I think I have developed this style by the environment I grew up in. As a child, my friends and I had races to see who could run the fastest, hop scotch competitions, and contests for the best cheerleading routines. Sports also played a major part in my competitiveness. I was motivated to do my very best in everything I did and winning a game always got you a trophy and/or a pizza party afterwards. In the workforce, competition is also used. At my previous job, prizes were given for the individual that took the most phone calls, received the lowest average handle time, etc. The benefits of my healthy competition in the workplace help me produce greater results and better quality of work. I believe my greatest limiting style is being oppositional. Being oppositional, my intention is not to be an adversary. My purpose is to look for problems and prepare for the worst to avoid unpleasant surprises. This style usually appears in meetings when changes that are going to occur in the business are discussed. I am the individual who brings up the â€Å"what ifs†. By doing this, I am looked upon as pessimistic and unable to envision positive possibilities. My reason behind this behavior is to plan for trouble and find ways to prevent it. It is my way of being proactive, rather than reactive. I uncovered that I have a management style that tends to be structured while at the same time having confidence in my subordinates. My combination of humanistic and competitive styles has affected my planning in a very unusual way. While I strive to set clear, specific, short-term goals and do everything I can to work towards them, I also have faith that my subordinates will accomplish their tasks successfully so that we can succeed as a team. Having these skills assist with planning performance goals and delegating/organizing tasks. I like to organize projects so that the team can get them done as quickly as possible with everyone doing their fair share without much micromanagement. My leadership style tends to lead more towards inspirational and leading by example. If a certain project is due soon, I don’t necessarily require my subordinates to stay late but instead stay late and work hard myself, hopefully inspiring others to do the same. The blend of humanistic and competitive styles has led me to be a bit more controlling than I would like to be. Although I do have faith in my subordinates and try to lead by example, my competitive nature leads me to take charge of small logistical aspects myself without delegating. My understanding of immediate organizational needs assists with monitoring performance and prepares me to take corrective action as needed. Many factors have gone into shaping my personal styles. Growing up in a large Asian-Indian family, I have always been pushed by my parents to succeed in school. With many older cousins, I was consistently being compared to how they performed in various subjects. I was pushed to take on leadership roles in many different clubs and organizations as they would â€Å"look good† on college applications. I learned early on, however, that leading by example and having faith in others helps gets projects accomplished much more successfully than bullying people around. For example, in high school, I was appointed chairperson of a school-wide international fair. I was in charge of organizing all the various multicultural clubs and societies and putting on a variety food and dance show. Although my competetaive drive was there pushing me to put on the best show I could, I realized that there was only so much I could do myself and make others do by forcing them. Instead I assigned tasks to others clubs and had faith that they would get the job done. I believe that by watching how I did not procrastinate or avoid doing my jobs, other members were inspired to do the same. Taking the LSI survey has definitely shed some light on my thinking styles. There are definitely some changes that I could make in order to become a more successful manager with a high performing team. I have learned that while it is important to be interested in people, to care about others, and to encourage them to improve, it is also just as important to provide direction and set goals. As discussed in class, leading others truly sets a manager apart from their peers. After viewing my results, the learning styles I would like to improve on is overcoming being so competitive and oppositional. I understand that being competitive can increase productivity and improve the quality of my work, but I must also understand that my employees may see me as an insensitive manager who is only interested in results and not their wellbeing. I plan to encourage cooperation and sharing of information and resources between my subordinates in a healthy way. To overcome being oppositional, I plan on working on identifying positive possibilities in future work situations and consider the impact my pessimism has on my quality of life. Creative energy in healthy competition and being optimistic will result in cooperative teamwork that will make everyone in the organization exultant. I believe the value of taking the LSI survey is that it put me in touch with my strengths I neglected and forgot I had. It also explains my weaknesses and what I need to do to become a better manager. It definitely increased my sense of self-awareness and I have an idea of my self-worth. It reminded me about the things that really matter to me and my subordinates. Knowing that the better I know about myself, the better my chances are of having satisfied subordinates and better my chances of moving up the ladder in my organization. To this end I believe my work in GM591 will be beneficial. I believe that in order to be a successful manager, one my analyze everything they can about different management styles. A manager must also be able to identify with his subordinates and understand what motivates them and what makes them satisfied. References Human Synergistics, Inc. (2010). Life Styles Inventory. Retrieved September 11, 2010, from https://www. survey-server2. com/lsiuniversity-sso/part_menu. asp

The Lymphatic System Essay - 881 Words

The lymphatic system is very similar, and works with and directly at the side of the cardiovascular system. The lymphatic system has a network of vessels like the circulatory system which pump a plasma-like fluid called lymph around it’s own lymph vessels, and are found in most other tissues of the body, except the central nervous system. Lymph is the name given to the fluid of plasma proteins that escape the circulatory system at the sites of the capillary network and diffuse into the cells around the capillaries. To enable the body to maintain a homeostatic fluid level and pressure, the lymph must be returned to the circulatory system. The way this happens is for the the network of lymph vessels to pick up the fluid which has escaped,†¦show more content†¦The act of breathing alters the pressure within the thoracic cavity and as the pressure drops, this also helps to force the lymph through the network of lymph vessels which have smooth muscle to aid the circulation. The structure of the lymph vessels are very similar to those of the circulatory system vessels. A protective outer layer, a muscular central core and a smooth inner lining to aid the free flow of lymph. Failure to circulate lymph back to the circulatory system results in swelling of the tissues, or oedema. Examples of this can be the result of infection through tropical disease where the lymph vessels are destroyed or blocked, or mild, temporary cases such as pregnancy where the weight of a foetus can press against the lymph vessels and prevent the return of lymph to the subclavian ducts. The lymphatic system works in three ways. It helps to control the balance of the body’s fluids by draining and cleansing fluid that seeps from the circulatory system during normal cardiovascular circulation. As fluid leaves the circulatory system it enters the tissue cells and whilst the majority of it diffuses back into the vessels of the circulatory system, the remainder enters the open ends of the lymph vessels. The lymphatic system also works with the villi in the digestive system to help deliver fats and absorbed nutrients in the digested food we eat, back to the circulatory system. This fluid is not calledShow MoreRelatedThe Lymphatic System862 Words   |  4 Pagesof our lymphatic system is vital to the health of our whole body. This system is critical to our body’s ability to detoxify and regenerate tissues, filter out toxins and foreign substances, recover crucial substances that have escaped from the blood, and maintain a healthy immune system. [pic] The Lymphatic system keeps the water of the body clean, and the pumping of the nodes during Lymphatic massage stimulates the production of various white blood cells and thus boosts the immune system. It isRead MoreEssay about The Lymphatic System491 Words   |  2 Pages The Lymphatic System nbsp;nbsp;nbsp;nbsp;nbsp;The Lymphatic System is very important. It helps with the Cardiovascular system, and our immune systems. The Lymphatic System is made up of two semi-independent parts. One is a network of lymphatic vessels. The other part is various lymphoid tissues and organs all over the body. The functions of the Lymphatic System transporting fluids that have escaped from the blood vascular system, and the organs house phagocytic cells and lymphocytes. nbsp;nbsp;nbsp;nbsp;nbsp;LymphaticRead MorePa 7 - Johnford. 1. Topic: Lymphatic Systems Assists In1200 Words   |  5 PagesPA 7 - Johnford 1. TOPIC: Lymphatic Systems Assists in Fluid Circulation A. How are lymph capillaries structurally and functionally SIMILAR to blood capillaries? ANSWER: The structures between the two are similar in a way that they look like a web or roots, and they both function to collect and return blood to the heart from the blood cycle (1 p. 399). B. How are lymph vessels structurally and functionally SIMILAR to veins which carry blood. ANSWER: The lymph vessels and the veins both have valvesRead MoreThe Lymphatic And Immune System859 Words   |  4 Pages The organs that make up the lymphatic and immune system are the tonsils, spleen, thymus gland, lymph nodes, and lymphatic vessels. White blood cells (leukocytes), red blood cells (erythrocytes), plasma, and platelets (thrombocytes) make up the blood. Lymphocytes are leukocytes (white blood cells) that help the body fight off diseases. Two types of lymphocytes are B cells and T cells. Lymphocytes recognize antigens, or foreign substances/matter, in the body. 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(The Spleen and Lymphatic System, Teens Health) The lymphatic system as a whole is similar to the cardiovascular system and has three specific functions. The vessels for one pick up extra fluid and return it to the bloodstream. Secondly, the lacteals receive lipoproteins andRead MoreLymphatic Disease : A General Overview Essay888 Words   |  4 PagesLymphatic Filarial Disease: A General Overview Lymphatic filarial disease is a disease that is caused by a parasitic infection of the lymphatic system. The parasites that cause this disease are found in the roundworm nematode family -- there are three types that cause it. The primary one is Wuchereria bancrofti; the other two are Brugia malayi, and Brougia timori (Centers for Disease Control and Prevention [CDC], 2013). The severity of infection ranges from asymptomatic, acute clinical, to chronicRead MoreThe Lymphatic System Lab Essay1048 Words   |  5 PagesAP-2 Lab 06 – Lab Report Name: Section: Unit 4 Lab Report: Exercise 6: The Lymphatic System Purpose: What was the purpose of doing this exercise? The purpose of this exercise is to learn about the lymphatic system and how it works and helps the human body. Why we need it and the components associated with the lymphatic system. Activity 1: Microscopic Anatomy of Lymphatic Structures Observations: Sketch of Reticular Connective Tissue Slide (Lymph Node). Describe the structuresRead MoreClinical Manifestations Of Hiv Infections1545 Words   |  7 Pagespertinent to the examination of this patient? HIV is manifested clinically as the development of recurrent, often severe, opportunistic infections, such as respiratory infections, and oral candidiasis (white patches), due to their compromised immune system. Parotid enlargement is another common finding in person with HIV, and the use of illicit drugs, especially by injections positions the patient at high risk of acquiring HIV infection. Then, the history of present illness, past medical history, familyRead MoreRegistered Nurses And Members Of Various Professions Exchange Knowledge1107 Words   |  5 PagesThe agenda was organized from the most general concepts and then proceeded to most specific concept. Initially, there was a review of the cardiovascular system and the lymphovascular system. It was at this point where there exists the connection between the two systems. Further instruction on the anatomy and physiology of the lymphovascular system was discussed. Detailed discussion ensued on the microvascular fluid exchange at the capillary level, the Starlings law of fluid exchange of 1896 and how

SWOT Analysis of the Organization.

Question: Discuss about the SWOT Analysis of the Organization. Answer: Introduction The aim of the following report is to make a profound and fruitful analysis of an organizations competitors along with its strength and weakness. For the distinct purpose, the present paper has considered one of the world-renowned and best-selling luxury car manufacturing organizations BMW. In order to accomplish the aim, the assignment would inaugurate with providing brief background information about the chosen organization and thereafter will attempt to make a competitor and SWOT analysis of the organization. Background of the Organization Bayerische Motoren Werke AG (BMW) is known as one of best selling luxury automobile production company that has been founded in the year 1916. The organization is known as the predecessor of Rapp Motorenwerke and headquartered in Munich, Bavaria of Germany. The organization is chiefly celebrated for manufacturing and selling luxury vehicles, sport cars, motor cycles and bicycles around the world. According to the last year production and profit report, BMW has earned a gross figure of 92.175 billion euro. Presently, the organization is running with more than 122,244 employees whose combine efforts have supported the organization to manufacture and sell near about 2,430,507 vehicles in the year 2015 (Kumar 2016). The impressive aspect about the organization is, BMW belongs to the membership of the National Environmental Achievement Track of U.S Environmental Protection Agency. The organization is praised for being one of the top most organizations for stewardship as well as performance. The organizations responsibility to maintain high environmental sustainability should be granted as one of the potential aspects of strength for BMW (Styles and Goddard 2014). However, it is unfortunate that Mercedes-Benz and Lexus are two potential rivals whom the considered organization is finding hard to compete in the front of North America. Nevertheless, BMW still has its unique capability of innovation and the distinct power of technological advancement through which it can maintain the status of being one of the market leaders in the domain of automobile production and selling. Competitor Analysis In order to understand the strength of the competitors along with to have a cohesive understanding about the strategies of the rival organizations of BMW, an in depth analysis of four key aspects objectives, assumptions, strategies and capabilities of the competitors of BMW is required to be done. The main competitors of BMW are Mercedes-Benz, Audi, Honda Motors, Porshe Automobile and Volkswagen (Csizmazia 2015). Competitors Objectives The objective of Mercedes-Benz is to accomplish a sustainable growth with an impressive profit margin through constantly increasing its value. The objective of Audi is found out to become the best brand for selling premium brand in the world (audi.com 2017). However, the corporate objectives of Honda motors are to have an impressive international growth by innovation and by making the target market happy. The goal of Volkswagen is to acquire a long-term return on its sale along with to generate the sale of the unit of near about 10 million vehicles a year. The organization desires to deploy innovation and technologies for accomplishing the motive. Competitors Assumptions The assumption or expectation of Volkswagen regarding its business aims is becoming one of the most attractive employers in the industry of automobile whereas Audi aspires to change the lifestyles of the customers by introducing unique design and incorporating innovative features in the vehicles. On the other hand, Honda Motors has expectation to develop business plans by assuming that the global economy and market situation will decline in the following year. However, rival organizations like Mercedes Benz and Porche desires to understand the changing demands of the target markets and fulfill their demands by doing thorough market research and product modification. Competitors Strategies and their Capabilities Mercedes Benz The four key business strategies of Mercedes Benz are strengthening the core capabilities, growing globally, leading the field of technology and driving one-step ahead of the digitalization. The strategies of the organization are accompanied by the organizations capabilities like continuous product innovation, financial stability, and worldwide facility of manufacturing and strong product portfolio (daimler.com 2017). Volkswagen The core capabilities of the organization are widest automotive portfolio and a firm synergy among its brands. The strategy, which supports the capabilities of the organization is the strategy of diversification (volkswagenag.com 2017). Audi The latest strategy that the organization is having is the TOGHETHER - strategy 2025, which is believed to assists the organizations core competencies like brand name, unique design and technical innovation. Honda Motors However, Honda motors, which is one of the potential competitors of BMW has strong position in the automobile market of Asia and has strong dominance in the engine industry (Csizmazia 2015). The distinct strategy that the organization holds to become successful is the Joy of selling by creating encouraging experiences for the customers, fulfill the complicated demand and improve customer relationship. SWOT Analysis Prior to evaluate the strength, weakness, threat and opportunities of BMW, it is required to mention here that the group of BMW consists of three particular brands BMW, MINI and Rolls Royce. Most importantly, the organization is not only known for manufacturing luxurious cars as BMW has also mastered in manufacturing aircraft and marine engines. However, the following analysis will give a precise understanding about the strength and weakness along with the possible premises of threats and future opportunities for BMW. Strength The power to manufacture cars in sophisticated style with unique and elegant interiors (Lee and Yang 2015) Diversification in business operations through having brands like MINI, Motorrad and Husqvarna Competent in producing hybrid as well as electric cars Early move in selling luxurious cars in the developing countries of South East Asia Production strength with more than 100,000 employees Weakness Disappointing automotive brand portfolio Disappointing number of strategic alliances (Jussani et al. 2015) In comparison with other organizations, BMW has few product differentiation The organization is suffering with increasing amount of debt A huge monetary loss for the controversy of recalling cars due to non-abidance to the governmentOpportunity Opportunity Opportunity to modify its current automotive portfolio Opportunity to improve its existing strategic alliances (Santos 2014) Opportunity to expand business into new business markets Opportunity to have revenue hike due to the rising demand for premium cars The organization has the opportunity to increase product differentiation Threat Tough competition in the market with Mercedes-Benz, Honda and Volkswagen Rate of fuels are increasing, therefore there are high chances to lose customers The price consciousness of the target market Chances to inferior quality imitation Negative impact of the fluctuations in the exchange rate From the above SWOT analysis, it can be contemplated that BMW can have a revenue hike in the coming future if the organization would increase its competency in producing hybrid as well as electric cars. Fortunately, the organization has already planned to launch models, which would run on various alternative fuels like natural gas. Most significant to contemplate here that BMWs more than 100,000 employees, who are responsible for a production of 1.5 million cars, should be considered to be the organizations key strength (Styles and Goddard 2014). However, as per the SWOT, BMW has unimpressive product diversification as they are only having brands like MINI, Motorrad and Husqvarna. However, it can be said that in order to stay potential in the competition, the organization should work on one of its major competence, which is product innovation and technological advancement. However, the SWOT is indicative of the fact that BMW immediately needs to work on its automotive brand portfolio as well as should attempt to decrease the rate of present debt. Nevertheless, one of the predominant threats of BMW is understandably the increasing rate of fuel. At the same time, it has been identified that younger generation are less bothered with brands and prefers to spend money on various electronic appliances. Conclusion: From the above report, it can be deduced that the chief rival organizations those can edge over BMW are Mercedes Benz, Audi, Honda motor and Volkswagen. However, from the above paper, it is understandable that the core capabilities of BMW are technical innovation, employee strength and diversified product range, through which the enterprise can dominate its competitors. References: Corporate strategy. 2017. [online] Audi.com. Available at: https://www.audi.com/corporate/en/company/corporate-strategy.html [Accessed 16 Feb. 2017]. Csizmazia, R.A., 2015. Sharing Economy-Downstream Extension of the Value Chain of German Automotive Manufacturers and of their Competitors. Jussani, A.C., Heer, A., Ibusuki, U. and de Moura Crtes, C., 2015.Electric car and Porters five Forces: Marketing Positioning in the Automotive Industry(No. 2015-36-0486). SAE Technical Paper. Kumar, K., 2016. Strategic Management On BMW. Lee, H.J. and Yang, H., 2015, December. Potential competitor identification and competitor analysis by monitoring patent information. InISPIM Innovation Symposium(p. 1). The International Society for Professional Innovation Management (ISPIM). Santos, L.M.D., 2014.Efficiency optimization of the transportation supply chain activity: the maritime option for Volkswagen Autoeuropa(Doctoral dissertation). Strategic focus areas. 2017. [online] Available at: https://www.daimler.com/company/strategy/objectives.html [Accessed 16 Feb. 2017]. Strategy. 2017. [online] Volkswagenag.com. Available at: https://www.volkswagenag.com/en/group/strategy.html [Accessed 16 Feb. 2017]. Styles, C. and Goddard, J., 2014. Spinning the wheel of strategic innovation.Business Strategy Review,25(4), pp.76-80. Zhang, J., Liang, Q. and Huang, J., 2016. Forward advertising: A competitive analysis of new product preannouncement.Information Economics and P

How to Use Emojis in Your Content

Emojis have become a fixture in almost every form of written communication from texts to emails to social media posts. In 2015, the Oxford Dictionary chose the â€Å"LOL† emoji as their Word of the Year and there’s even a World Emoji Day, celebrated on July 17th. Free Actionable Bonus: Free Actionable Bonus: Want to create better content for social media? Get the complete guide to building a social media strategy and creating content for social, plus 6 awesome examples to inspire your next post. With emojis showing no signs of fading, it’s no surprise that many businesses have made them a key addition to their content. If you’ve been on the fence about using emojis in your content, there’s no better time to start experimenting. Here’s a peak at what makes emojis such a powerful marketing tool and how some brands have used that in their content. Understanding Emoji Power What’s behind our love affair with emojis? A number of factors come into play. Emojis represent a purely visual form of communication that transcends language barriers. They also make your written content feel more friendly, convey the right tone and can help you better establish a connection with your audience. Best of all, they manage to say a lot in a single character. That brevity is perfect for push notifications, where messages of 24 characters or less have proven to perform the best. Emoji Marketing 101 More and more brands have been adding emojis to their marketing messages. A few memorable examples include: Domino’s Pizza: There are times when you’re so hungry, you can’t bear the thought of picking up your phone to place a pizza order. Sure, you could order online, but that’s too much typing. Enter Domino’s Pizza and their â€Å"tweet to order† system. Customers who have registered with the company’s Easy Order system can simply tweet a pizza emoji to Domino’s and their order will be on its way. Taco Bell: For quite some time, there were emojis for burgers, pizza, hot dogs and a number of other fast food treats but not for tacos. Taco Bell sought to remedy this oversight by launching a petition on Change.org, lobbying the Unicode Consortium to give users a long-awaited taco emoji. The petition was signed by over 33,000 taco lovers and the Unicode Consortium consented to the taco emoji. Taco Bell immediately put this new emoji to good use by unveiling their Taco Emoji Engine. Users who tweeted the taco emoji to Taco Bell’s Twitter account would be rewarded with one of 600 random â€Å"taco-inspired† sounds, images or gifs. Chevrolet: This example pushes the envelope and is memorable for it. The automaker introduced their 2016 Chevy Cruze by putting out a press release written almost entirely in emojis. Chevrolet challenged audiences to figure out the message on their own, but they eventually released a translation for readers who weren’t interested in deciphering the symbols. Over 6 billion emojis are sent via mobile messaging each day making it clear that these smileys are here to stay. Don’t miss out on a unique way to be creative with your content. Have fun experimenting with emoji marketing and enjoy this new way of connecting with your audience.

Hooray, hooray! It’s Presidents Day!

Hooray, hooray! It’s Presidents Day! Hooray, Hooray! It’s Presidents Day! Whether you think of  Presidents Day as a patriotic celebration of our country’s political leadership, or just a day off from work and/or school, it’s surely a good time to reflect on the educational legacy of President Washington and his successors. By â€Å"educational legacy† here, we don’t mean the policies they introduced while in office or donations made to colleges; we’re interested in what our presidents were like as students. Harry Truman, College Dropout Not every president has been a â€Å"classic† educational role model, with many not graduating at all. The most recent was Harry Truman, who dropped out of business school after only one semester. To be fair, he did drop out because of his family’s financial problems rather than a lack of interest in learning. And he did later become president. So he must have been doing something right. A Very Different Playbook Would history have differed much had Gerald Ford accepted one of the two offers he received from NFL clubs after graduating from the University of Michigan? Courtesy Gerald R. Ford Library. It’s hard to say, but he managed to help the Wolverines to national titles in 1932 and 1933, as well as winning the team’s MVP award in his senior year. Whether his skills as a linebacker were at all useful in office, we can only guess. Skull and Bones Yale University’s â€Å"Skull and Bones† society is notorious for its secrecy and elitism, inviting only the most powerful students to join. This has so far included three future presidents: William Howard Taft, George H. W. Bush, and George Bush Jr. Apparently, the initiation ritual for new members involves divulging â€Å"intimate personal details, including their full sexual histories.† Sounds fine to us. After all, there’s no way giving away sensitive personal information could possibly pose a terrible blackmail risk. If there was, they wouldn’t do it, right? Right? Go Team President! On a lighter note, four future presidents have spent their college days cheerleading, including Franklin D. Roosevelt, Dwight D. Eisenhower, Ronald Reagan and George W. Bush. Wait, George Bush Jr was a cheerleader and a member of Skull and Bones? When did the man find time to study? Maybe he just didn’t bother. That’s â€Å"Dr. Woodrow,† Thank You Out of the 43 people who’ve been president, one stands out for his educational achievements: Dr. Woodrow Wilson, PhD. The only president to have a college doctorate, Wilson earned a PhD in political science from John Hopkins University, producing a dissertation called â€Å"Congressional Government: A Study in American Politics.† He later went on to teach at Bryn Mawr College. So although Woodrow might be better known for his achievements as 28th President of the United States, from now on we’ll think of him first as an academic high-achiever. Happy Presidents Day!

MANAGEMENT FOR CLINICIANS Essay Example | Topics and Well Written Essays - 1250 words

MANAGEMENT FOR CLINICIANS - Essay Example asks that the healthcare industry re-align itself in such a way as to provide a team that is multi-disciplinary and works together for the good of the patient, that care become more patient centered, and an effort to determine how to use clinical support staff in such a way as to reduce the pressure on the healthcare professionals that are already overwhelmed (Garling report, 2008). This paper will discuss recommendations made by the commission and how shared patient centered care teams can provide much needed care. The patient provider relationship has been changing for some time and with new initiatives will continue to change. Today healthcare is electronic and highly regulated and healthcare workers are faced with increased amounts of accountability in their practice. Consumers are more interested in becoming part of their own healthcare and are reasonably able to contribute when that option is available (Smith, & Barefiled, 2007),. The shortage of professionals in healthcare is not expected to get better anytime soon and may, in fact, get worse. Every possibility of expanding the methods we presently use in supporting those professionals becomes important. This is the time for true patient centered care. This is a growing trend and empowers healthcare consumers and their families with the adaption of patient centered initiatives. Caring Together has determined to create a focus on the patient. In doing that, they have set a goal to make healthcare more efficient as well as more sustainable. They have clearly stated that â€Å"everything must be about the patient.† (Caring Together, pg. 5). This has not been true in the last few years as the amount of paperwork grows and the supervision of support staff has waned. Now, however, is the time to move forward and solve these problems for the betterment of patient care. According to Smith and Barefield (2007), there are seven aspects of patient centered care. Those include, respect for patient’s values,

Musical theatre Essay Example | Topics and Well Written Essays - 1500 words

Musical theatre - Essay Example Musical is the art of musical theater and it is a combination of dialogue and singing. Usually musical has several authors and they are rarely written by one script writer. The writing of the musical involves composer, lyricist and script. Every musical tends to be unique and specific. It tends to be remembered by the audience in the theatre. The melody in most cases inspires the authors to write a musical. It is apparent that aspiration is the main point in creating a masterpiece for musical theatre. Musical theatre sometimes adopts books and plays and reinterprets them in a new way. The Black Crook was the first theatre musical which adapted the modern principles of this genre. The musical lasted for five hours. And musical theatres became rather popular among people. Musical theatres created a new world full of mystery and admiration. Once visited musical theatre it is difficult to part with it. Musicals became like a fairy tales. (Kresner 1995) Nowadays musical theater became like a melody, which is being listened by everybody in the whole world. Foe many yeares theatre musica included popular music. For our parents and grandparents music theatre was something like musical channels on TV for younger generation. The older generation was inspired by musical theatre and such famous composers as Cole Porter, Jerome Kern, Irving Berlin and Richard Rodgers will be always remembered and honoured. But for young generation these composers are unknown. Some musical combine, for example, pop trends with classical tradition and libretto. As an example it is possible to mention musical Mama Mia, which is told to be the most entertaining modern musical. The lexicon of musical theatre was mentioned to be like a hybrid. (Lodge 2005) It is apparent that nowadays musical theatre is artistical and practical venue fot modern composers. Many of composers are aspired to write musicals, because they were brough uo with Porter, Kern and Rodgers. Randy Newman is also markable exmple of composer who tried to create modern pop musicals for musical theatres. Some admitted that musical theatre is like "smorgasbord", you can choose everything you like: singing, dancing, greatest hits and sad motives. Some people believe that musical is rather dissident form of theatre which referred to the theory of Brecht. (Kresner 1995) But it is necessary to observe the reaction of the audience of the musical theatre. The grown-ups sit stark in their sits and children look line they are burning fireworks. Everybody is impressed and full of admiration and delight. Musical theaters are really exciting and interesting. (Kresner 1995) The power of musical theatre was told to move people intuitively and emotionally to another world of songs and dances - to the wonderful fairy world. That power appealed to many people and they actually stuck to musical theatre. The people's love in the musical theatre is always storytelling, dancing and singing. In musical theatre people are always greatly attracted by gorgeous

Ethics Scholarship Essay Essay Example for Free

Ethics Scholarship Essay Essay One ethical issue to which I became aware of while in college mainly involved cases illegal drugs, bribery, and cheating. Although there is an existing law against illegal drugs and most schools and universities are very stringent in imposing penalties for illegal activities and other things that are criminal in nature, sadly there are still some students who find ways to break those rules, especially outside the campus. While I am not the one involved in these illegal activities, I felt that I had a moral obligation because two of my classmates were involved. These classmates of mine were actually good people, but unfortunately, they ended up with the wrong company. It took place not very long ago, during a house party held by one of the rich students in the university. This certain student, whom I personally know, constantly held parties in his/her lavish house. My two classmates were not invited because the host of the party didn’t like their introvert nature. They were very shy, had very little friends, and were only interested in playing video games and the like. Nevertheless, as I have mentioned above, they were people who possessed values. The problem is they just lacked social skills. One day in class, I noticed that they were talking to a guy who was a notorious rule breaker in the university and was one of the friend of the rich person mentioned earlier. Later, I found out that they were invited to one of the parties held by the rich person and they were both very excited to go as it was their first time to have the change to mingle with a lot of people. On the night of the party, I was to see them talking to a couple of girls and boys. Although I do not wish to judge them, I was a bit confused because, as mentioned above, they were very shy and were not the type of people who would approach someone for a casual conversation. I felt happy for my two classmates but I noticed that certain things about them started to change in the succeeding months. There were instances that they were absent from class, which was something they never did, and there were also times that they were asleep during a lecture or an exam. After some time, I spoke with one of the two and found out that the reason behind their unusual behavior was because of illegal drugs. This person further revealed that they were invited to the rich student’s party on the condition that they would do the assignments of a group of people who were close to of him/her (rich student). This classmate of mine also told me that they were doing drugs because it was considered â€Å"cool† among their new circle of friends. However, the main problem was that both these classmates of mine were nearly failing a lot of their subjects due to their absences and neglect. Because I was concerned for them, I sought the help of fellow students who were also concerned and together we notified the university officials on condition of anonymity. Although it was the right thing to do, I had an ethical dilemma because as a result of my actions, my two classmates were indefinitely suspended from school and were taken to a rehabilitation facility. I was very bothered at first because in a way, I cost them a lot by revealing their secret illegal activities. But after several months, I realized that it was the only thing to do because I didn’t want their future to be ruined by drugs. Basically, this event has impacted me in such a way that I carefully choose whom I associate with. Although I have a lot of friends, I only trust people whom I am sure would not give in to negative influences and to peer-pressure from the wrong ground. It also made me more vigilant and more careful of people who are trying to be nice to me but actually have ulterior motives. On the business perspective, it made me more cautious in dealing with alleged â€Å"easy money† gimmicks and deals which are perpetrated by people who have questionable backgrounds. In short, it made me wiser and clever in terms of business dealings because now I am more aware of the capabilities of certain people who only claim to offer good deals but in truth, do not offer anything of value at all.

Education at a Year-Round School Essay -- essays papers

Education at a Year-Round School Consider the following situation: A car is driving past the local elementary school on a hot and sunny July afternoon. As the car approached the school the driver notices some unusual things. Students are outside with the teachers for recess, and it looks as if school is in session. The school is on a year-round schedule. The driver is intrigued and decides to do some research. From the research, this person found that students are achieving more academically and the teachers are well rested. Year-round schooling is beneficial to school systems because: it alleviates overcrowding, offers remedial opportunities, decreases teacher burnout, increases retention rates, assists English as a Second Language (ESL) and low-poverty students, and improves the entire school community. Wildavsky (1999) says, â€Å"[The National Association for Year-Round Education] defines a year-round school as an institution with fewer than eight weeks of summer vacation† (para. 7). According to another article (1997), â€Å"In 1986, there were about 400 year-round schools in 16 states. By 1997, the number increased to 2400 in 41 states† (National Association for Year-Round Education, para. 4). Additionally, Hunter (1998) adds, â€Å"†¦the U.S. National Association for Year-Round Schools stated that year-round schooling has grown by 500 percent in the past decade† (para. 4). These schools are capable of meeting the needs of our students, teachers, and administrators. Overcrowding Schools that follow a year-round schedule can help alleviate overcrowded schools. The number of students is growing, as studied by Hellerman, Schriffen, D., Colenso-Semple, Spiner, and Schriffen, J. (1997), at 30,000 to 40,000 per year and distric... ...Summer in class. Macleans, 111 (32), 47. Retrieved March 3, 2005 from Academic Search Premier/EBSCO database. Learning that lasts year-round (1997). NEA Today, 15 (7), 19. Retrieved March 3, 2005 from Academic Search Premier/EBSCO database. Rivera, E. (2003). It’s August, but for some, vacation’s over; Arlington Elementary pupils begin test of year-round school. The Washington Post, B.01. Retrieved March 3, 2005, from Proquest database. Shields, C. M., & Oberg, S. L. (2000). Year-round schooling: Promises and pitfalls. Lanham, MD: Scarecrow Press. Wildavsky, B. (1999). Scholars of summer. U.S. News & World Report, 127 (5), 52-55. Retrieved March 3,2005 from Academic Search Premier/EBSCO database. Year-round schools can stimulate learning. (2000).USA Today Magazine, 129 (2663), 7. Retrieved March 3, 2005 from Academic Search Premier/EBSCO database.

Flight Control Systems

Flight Control Systems W. -H. Chen Department of Aeronautical and Automotive Engineering Loughborough University 2 Flight Control Systems by W. -H. Chen, AAE, Loughborough Contents 1 Introduction 1. 1 Overview of the Flight Envelope 1. 2 Flight control systems . . . . . . 1. 3 Modern Control . . . . . . . . . . 1. 4 Introduction to the course . . . . 1. 4. 1 Content . . . . . . . . . . 1. 4. 2 Tutorials and coursework 1. 4. 3 Assessment . . . . . . . . 1. 4. 4 Lecture plan . . . . . . . 1. 4. 5 References . . . . . . . . . 7 7 8 8 9 9 10 10 10 11 13 13 16 16 17 17 18 19 19 20 20 20 20 20 24 25 25 25 25 26 27 27 29 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Longitudinal response to the control 2. 1 Longitudinal dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 2. 2 State space description . . . . . . . . . . . . . . . . . . . . . . . . . 2. 2. 1 State variables . . . . . . . . . . . . . . . . . . . . . . . . 2. 2. 2 General state space model . . . . . . . . . . . . . . . . . . . 2. 3 Longitudinal state space model . . . . . . . . . . . . . . . . . . . . 2. 3. 1 Numerical example . . . . . . . . . . . . . . . . . . . . . . . 2. 3. 2 The choice of state variables . . . . . . . . . . . . . . . . . . 2. 4 Aircraft dynamic behaviour simulation using state space models . 2. 4. 1 Aircraft response without control . . . . . . . . . . . . . . . 2. 4. 2 Aircraft response to controls . . . . . . . . . . . . . . . . . 2. 4. 3 Aircraft response under both initial conditions and controls 2. 5 Longitudinal response to the elevator . . . . . . . . . . . . . . . . 2. 6 Transfer of state space models into transfer functions . . . . . . . . 2. 6. 1 From a transfer function to a state space model . . . . . . . 2. 7 Block diagram representation of state space models . . . . . . . . . 2. 8 Static stability and dynamic modes . . . . . . . . . . . . . . . . . . 2. 8. 1 Aircraft stability . . . . . . . . . . . . . . . . . . . . . . . . 2. 8. 2 Stability with FCS augmentation . . . . . . . . . . . . . . . 2. 8. 3 Dynamic modes . . . . . . . . . . . . . . . . . . . . . . . . . 2. 9 Reduced models of longitudinal dynamics . . . . . . . . . . . . . . 2. 9. Phugoid approximation . . . . . . . . . . . . . . . . . . . . 2. 9. 2 Short period approximation . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3 Lateral response to the controls 3. 1 Lateral state space models . . . . . . . . . . . . 3. 2 Transient response to aileron and rudder . . . . 3. 2. 1 Numerical example . . . . . . . . . . . . 3 . 2. 2 Lateral response and transfer functions 3. 3 Reduced order models . . . . . . . . . . . . . . 3. 3. 1 Roll subsidence . . . . . . . . . . . . . . 3. 3. Spiral mode approximation . . . . . . . 3. 3. 3 Dutch roll . . . . . . . . . . . . . . . . . 3. 3. 4 Three degrees of freedom approximation 3. 3. 5 Re-formulation of the lateral dynamics . CONTENTS 31 31 33 33 33 35 38 38 39 39 40 43 43 46 46 46 46 48 49 49 55 55 55 58 58 60 60 61 62 65 66 66 67 68 68 68 69 69 69 70 70 71 71 73 73 73 73 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Stability Augmentation Systems 4. 1 State space design techniques . . . . . . . . . . . 4. 2 Longitudinal stability augmentation systems . . . 4. 2. 1 The choice of feedback variables . . . . 4. 2. 2 SAS for short period dynamics . . . . . . 4. 3 Lateral stability augmentation systems . . . . . . 4. 3. 1 Yaw rate feedback for rudder control . . . 4. 3. 2 Roll feedback for aileron control . . . . . 4. 3. 3 Integration of lateral directional feedback 5 Autopilots 5. 1 Pitch holding autopilot . . . . . . . . . . . . . . . . . . . . . . . 5. 1. 1 phugoid suppress . . . . . . . . . . . . . . . . . . . . . . 5. 1. 2 Eliminate the steady error with integration . . . . . . . 5. 1. 3 Improve transient performance with pitch rate feedback 5. 2 Height holding autopilot . . . . . . . . . . . . . . . . . . . . . . 5. . 1 An intuitive height holding autopilot . . . . . . . . . . . 5. 2. 2 Improved height holding systems . . . . . . . . . . . . . 5. 3 Actuator dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 6 Handling Qualities 6. 1 Handing qualities for aircraft . . . . . . . . . . . . 6. 2 Pilot-in-loop dynamics . . . . . . . . . . . . . . . . 6. 2. 1 Pilot as a controller . . . . . . . . . . . . . 6. 2. 2 Frequency response of a dynamic system . . 6. 2. 3 Pilot-in-loop . . . . . . . . . . . . . . . . . 6. 3 Flying qualities requirements . . . . . . . . . . . . 6. 4 Aircraft role . . . . . . . . . . . . . . . . . . . . . . 6. . 1 Aircraft classi? cation . . . . . . . . . . . . . 6. 4. 2 Flight phase . . . . . . . . . . . . . . . . . . 6. 4. 3 Levels of ? ying qualities . . . . . . . . . . . 6. 5 Pilot opinion rating . . . . . . . . . . . . . . . . . . 6. 6 Longitudinal ? ying qualities requirements . . . . . 6. 6. 1 Short perio d pitching oscillation . . . . . . 6. 6. 2 Phugoid . . . . . . . . . . . . . . . . . . . . 6. 6. 3 Flying qualities requirements on the s-plane 6. 7 Lateral-directional ? ying qualities requirements . . 6. 7. 1 Roll subsidence mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CONTENTS 6. 7. 2 6. 7. 3 6. 7. 4 5 Spiral mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Dutch roll mode . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Lateral-directional mode in s-plane . . . . . . . . . . . . . . . . . 75 77 . . . . . . . . . . . control derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 79 79 79 79 79 7 Fly-by-Wire ? ight control 8 Appendices 8. Boeing 747-100 data . . . . . . . . . . . 8. 2 De? nitions of Aerodynamic stability and 8. 3 Root Locus . . . . . . . . . . . . . . . . 8. 4 Frequency response . . . . . . . . . . . . appendices 6 CONTENTS Chapter 1 Introduction 1. 1 Overview of the Flight Envelope †¢ Flight planing †¢ Aircraft checking †¢ Taxi †¢ Take-o? – Rotate, â€Å"select† an attitude – Clean up (gear, ? aps, etc) – Emergencies (engine failure, ? re, etc) †¢ Climb – Speed control – Procedure (manual, autopilot) †¢ Mission Tasks – Cruise – Combat (air to air) – Strike (air to earth) – General handling (stalling, spinning, aerobatics) – Formation ? ing (Navigation, procedure etc) – Emergencies – Con? guration (weapons, tanks, fuel load) †¢ Recovery – Descent – Instrument approach – Landing – Overshoot 7 8 CHAPTER 1. INTRODUCTION Stick – Linkage 6 Trim ? -? Servo Actuator – Aircraft dynam ics Figure 1. 1: Manual pilot control aircraft – Formation – Procedures – Emergencies †¢ Taxi Longitudinal and lateral dynamics thus Flight control systems are involved in Take o? , Climb, Mission tasks and Recovery. †¢ Di? erent aircraft (aircraft class) †¢ Di? erent ? ight phase Manual– handling qualities/? ight qualities Improve the handling qualities of airplane; Autopilot 1. 2Flight control systems Objectives †¢ To improve the handling qualities †¢ To release the operation burden of pilots partly or fully †¢ To increase the performance of aircraft or missiles Types of Flight Control Systems (FCS) 1. Open-loop control 2. Stability augmentation systems 3. Autopilot 4. Integrated Navigation systems and Autopilots (? ight management systems) 1. 3 Modern Control †¢ Classic control– transfer function – frequency domain †¢ Limitation of classic design method: single input, single output (SISO), only conc ern the output behaviour, linear systems (saturation) †¢ System description in state space form. 1. 4.INTRODUCTION TO THE COURSE 9 Stick Trim – Aircraft dynamics – + ? + -Linkage – ? – ? – Servo Actuator 6 6  Stability Aug. Systems  Sensor  ? Figure 1. 2: Stability Augmentation Systems Reference Command + -? Autopilot – 6 6 + -? 6 – SAS – Actuators – Aircraft dynamics – Sensor  6  Navigation Systems ? ? Figure 1. 3: Autopilot con? guration †¢ Describe aircraft or other dynamics systems in a set of ? rst order di? erential equations. Expressed in a matrix form †¢ State space analysis and design techniques– very powerful technique for control systems †¢ Matrix manipulation knowledge required 1. 4 1. 4. 1 Introduction to the courseContent This course will cover †¢ state space analysis and design techniques for aircraft †¢ simple ? ight control systems including stability aug mentation systems, and simple autopilots †¢ handling qualities 10 CHAPTER 1. INTRODUCTION Flight Management 6 Systems/Autopilot 6 + -? 6 – SAS – Actuators – Aircraft dynamics – Sensor  6 Navigation Systems ? ? Figure 1. 4: Autopilot con? guration †¢ Fly-By-Wire (FBW) 1. 4. 2 Tutorials and coursework †¢ Tutorials will start from Week 3 †¢ One tutorial section in each week †¢ One coursework based on MATLAB/Simulink simulation, must be handed in before 4:00 PM Thursday, Week 11 1. 4. 3Assessment †¢ Coursework: 20%; †¢ Examination: 2 hours; attempt 3 from 5 questions; 80% of the ? nal mark. 1. 4. 4 Lecture plan †¢ Overall ? ight envelope †¢ Flight control systems †¢ Modern control design methodology †¢ The introduction of the course– structure, assessment, exercises, references 1. Introduction 2. Response to the controls (a) State space analysis (b) Longitudinal response to elevator and throttle (c) Transient response to aileron and rudder 3. Aircraft stability augmentation systems 1. 4. INTRODUCTION TO THE COURSE (a) Performance evaluation †¢ †¢ †¢ †¢ stability Time domain requirements Frequency domain speci? ations Robustness 11 (b) Longitudinal Stability Augmentation Systems †¢ Choice of the feedback variables †¢ Root locus and gain determination †¢ Phugoid suppress (c) Lateral stability augmentation systems †¢ Roll feedback for aileron control †¢ Yaw rate feedback for rudder control 4. Simple autopilot design †¢ Augmented longitudinal dynamics †¢ Height hold systems 5. Handling Qualities (a) Time delay systems (b) Pilot-in-loop dynamics (c) Handling qualities (d) Frequency domain analysis (e) Pilot induced oscillation 6. Flight Control system implementation Fly-by-wire technique 1. 4. 5 References 1. Flight Dynamics Principles.M. V. Cook. 1997. Arnold. Chaps. 4,5,6,7,10,11 2. Automatic Flight Control Systems. D. McL ean. 1990. Prentice Hall International Ltd. Chaps. 2, 3,6,9. 3. Introduction to Avionics Systems. Second edition. R. P. G. Collinson. 2003. Kluwer Academic Publishers. Chap. 4 12 CHAPTER 1. INTRODUCTION Chapter 2 Longitudinal response to the control 2. 1 Longitudinal dynamics From Flight Dynamics course, we know that the linearised longitudinal dynamics can be written as mu ? ? ? X ? X ? X ? X u? w? ? w + (mWe ? )q + mg? cos ? e ? u ? w ? ?w ? q ? Z ? Z ? Z ? Z ? u + (m ? )w ? ? w ? (mUe + )q + mg? sin ? e ? u ? w ? ?w ? q ?M ? M ? M ? M u? w? ? w + Iy q ? ? q ? ?u ? w ? ?w ? q = = = ? X ? t ? Z ? t ? M ? t (2. 1) (2. 2) (2. 3) The physical meanings of the variables are de? ned as u: Perturbation about steady state velocity Ue w: Perturbation on steady state normal velocity We q: Pitch rate ? : Pitch angle Under the assumption that the aeroplane is in level straight ? ight and the reference axes are wind or stability axes, we have ? e = We = 0 (2. 4) The main controls in longitudina l dynamics are the elevator angle and the engine trust. The small perturbation terms in the right side of the above equations can be expressed as ? X ? t ?Z ? t ? M ? t where 13 = = = ? X ? X ? e + ? e ?Z ? Z ? e + ? e ?M ? M ? e + ? e (2. 5) (2. 6) (2. 7) 14 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL ? e : the elevator de? ection (Note ? is used in Appendix 1) ? : engine thrust perturbation Substituting the above expression into the longitudinal symmetric motion yields ? X ? X ? X ? X u? w? ? w? q + mg? ?u ? w ? ?w ? q ? Z ? Z ? Z ? Z ? u + (m ? )w ? ? w ? (mUe + )q ? u ? w ? ?w ? q ? M ? M ? M ? M u? w? ? w + Iy q ? ? q ? ?u ? w ? ?w ? q mu ? ? = = = ? X ? X ? e + ? e ?Z ? Z ? e + ? e ?M ? M ? ?e + e (2. 8) (2. 9) (2. 10)After adding the relationship ? ? = q, (2. 11) Eqs. (2. 8)- (2. 11) can be put in a more concise vector and matrix format. The longitudinal dynamics can be written as ? m ? 0 ? ? 0 0 ? ?X ? w ? ?Z m ? ?w ? ? ? M ? w ? 0 0 0 Iy 0 u ? 0 0 w ? ? 0 q ? ? 1 ? ? ? = ? ? ? ? ? ? ? ? ? ?X ? u ? Z ? u ? M ? u ? X ? w ? Z ? w ? M ? w ? Z ? q ? X ? q + mUe ?M ? q 0 0 ?X e ? Z e ? M e 0 ?X ?Z ?M ? ? ? ? 1 ?mg u 0 w 0 q ? 0 ? ? ?+ ? ?e ? (2. 12) 0 Put all variables in the longitudinal dynamics in a vector form as ? ? u ? w ? ? X=? ? q ? ? and let m ? ?X ? w ? ? 0 m ? ?Z ? ?w ? = ? 0 ? ?M ? w ? 0 ? ?X ? X ? = ? ? ? B ? = ? ? ? u ? Z ? u ? M ? u ? w ? Z ? w ? M ? w ? Z ? q (2. 13) ? M 0 0 Iy 0 ?X ? q ? 0 0 ? ? 0 ? 1 (2. 14) ? ?mg 0 ? ? 0 ? 0 A + mUe ?M ? q (2. 15) 0 0 ?X e ? Z e ? M e 0 ?X ?Z ?M ? ? ? ? 1 (2. 16) 0 U= ?e ? (2. 17) 2. 1. LONGITUDINAL DYNAMICS Equation (2. 12) becomes 15 ? MX = A X + B U (2. 18) It is custom to convert the above set of equations into a set of ? rst order di? erential equations by multiplying both sides of the above equation by the inverse of the matrix M , i. e. , M ? 1 . Eq. (2. 18) becomes ? ? ? ? ? ? u ? xu xw xq x? x? e x? u ? w ? ? zu zw zq z? ? ? w ? ? z? z? ? ? e ? ? ? =? ? ? ? ( 2. 19) ? q ? ? mu mw mq m? ? ? q ? + ? m? e m? ? ? ? ? ? 0 0 1 0 0 0 ? Let xu ? zu A = M ? 1 A = ? ? mu 0 ? ? xw zw mw 0 xq zq mq 1 ? x? z? ? ? m? ? 0 (2. 20) and x? e ? z? e B = M ? 1 B = ? ? m ? e 0 ? x? z? ? ? m? ? 0 (2. 21) It can be written in a concise format ? X = AX + BU (2. 22) Eq. (2. 22) with (2. 20) and (2. 21) is referred as the state space model of the linearised longitudinal dynamics of aircraft. Appendix 1 gives the relationship between the new stability and control derivatives in the matrix A and B, i. e. xu , so on, with the dimensional and non-dimensional derivatives, where ?X ? Xu = ? u (2. 23) denotes dimensional derivative and Xu its corresponding non-dimensional derivative. These relationships are derived based on the Cramer’s rule and hold for general body axes. In the case when the derivatives are referred to wind axes, as in this course, the following simpli? cations should be made Ue = Vo , We = 0, sin ? e = 0, cos ? e = 1 (2. 24) The description of the longitudinal dynamics in the matrix-vector format as in (2. 19) can be extended to represent all general dynamic systems. Consider a system with order n, i. e. , the system can be described by n order di? rential equation (as it will be explained later, this is the same as the highest order of the denominator polynomial in the transfer function is n). In the representation (2. 22), A ? Rn? n is the system matrix ; B ? Rn? m is the input matrix ; X ? Rn is the state vector or state variables and U ? Rm the input or input vector. The equation (2. 22) is called state equation. For the stability augmentation system, only the in? uence of the variation of the elevator angle, i. e. the primary aerodynamic control surface, is concerned. The above equations of motion can be simpli? ed. The state space representation remains the 6 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL same format as in eq. (2. 22) with the same matrix A and state variables but with a di? erent B and input U as given below ? ? x ? e ? z ? B = M ? 1 B = ? ?e ? (2. 25) ? m? e ? 0 and U = ? e (2. 26) Remark: It should be noticed that in di? erent textbooks, di? erent notations are used. For the state space representation of longitudinal dynamics, sometime widetilded derivatives are used as follows ? ? 1 ? X 1 ? X ? ? 1 ? X ? ? 0 ? g u ? u m ? u m ? w m e 1 ? Z 1 ? Z 1 ? Z ? w ? ? 0 ? ? w ? ? m e ? ?+? ? ? ? = ? m ? u m ? w Ue ? ? e (2. 27) ? q ? Mu ? Mw Mq 0 ? ? q ? ? M? e ? ? ? ? 0 0 1 0 0 where Mu = Mw = 1 ? M 1 ? Z 1 ? M + ? Iyy ? u m ? u Iyy ? w ? 1 ? M 1 ? Z 1 ? M + ? Iyy ? w m ? w Iyy ? w ? 1 ? M 1 ? M + Ue ? Iyy ? q Iyy ? w ? (2. 28) (2. 29) (2. 30) (2. 31) Mq = M? e = 1 ? M 1 ? Z 1 ? M + ? Iyy e m e Iyy ? w ? The widetilded derivatives and the other derivatives in the matrices are the same as the expression of the small letter derivatives under certain assumptions, i. e. using stability axis. 2. 2 2. 2. 1 State space description State variables A minimum set of variables which, when known at time t0 , together with the input, are su? ient to describe the behaviours of the system at any time t > t0 . State variables may have no any physical meanings and may be not measurable. For the longitudinal dynamic of aircraft, there are four state variables, i. e, ? ? u ? w ? ? X=? (2. 32) ? q ? ? and one input or control variable, the elevator de? ection, U = ? e (2. 33) 2. 3. LONGITUDINAL STATE SPACE MODEL Thus n=4 m=1 17 (2. 34) The system matrix and input matrix of the longitudinal dynamics are given by ? ? xu xw xq x? ? z zw zq z? ? ? A = M ? 1 A = ? u (2. 35) ? mu mw mq m? ? 0 0 1 0 and ? x? e ? z ? B = M ? 1 B = ? ?e ? ? m ? e ? 0 ? (2. 36) respectively. . 2. 2 General state space model w Ue When the angle of attack ? is of concern, it can be written as ? = which can be put into a general form as y = CX where y=? = and C= 0 1/Ue 0 0 (2. 40) Eq. (2. 38) is called Output equation; y the output variable and C the output matrix. For more general case where there are more than one output and has a direct path from input to output variable, the output equation can be written as Y = CX + DU (2. 41) w Ue (2. 38) (2. 39) (2. 37) where Y ? Rr ,C ? Rr? n and D ? Rr? m . For motion of aerospace vehicles including aircraft and missiles, there is no direct path between input and output.In this course only the case D = 0 is considered if not explicitly pointed out. Eq. (2. 22) and (2. 38) (or (2. 41)) together represent the state space description of a dynamic system, which is opposite to the transfer function representation of a dynamic system studied in Control Engineering course. 2. 3 Longitudinal state space model When the behaviours of all the state variables are concerned, all those variables can be chosen as output variables. In addition, there are other response quantities of interest including the ? ight path angle ? , the angle of attack ? and the normal acceleration az (nz ).Putting all variables together, the output vector can be written a s 18 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL ? ? ? ? ? Y =? ? ? ? ? Invoking the relationships ? = ? ? ? ? ? ? ? ? ? ? u w q ? ? ? az w Ue (2. 42) (2. 43) w Ue (2. 44) the ? ight path angle ? = = and the normal acceleration az (nz ) az = = = ?Z/m = ? (Zu u + Zw w + Zq q + Zw w + Z? e ? e )/m ? ? ? (w ? qUe ) ? ?zu u ? zw w ? zq q ? z? e ? e + Ue zq (2. 45) where the second equality substituting the expression matrix is given by ? ? ? u 1 ? w ? ? 0 ? ? ? ? q ? ? 0 ? ? ? Y =? ? ? =? 0 ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? 0 az ? zu ollows from (2. 9) and the last equality is obtained by of w in its concise derivative format. Hence the output ? 0 1 0 0 1/Ue ? 1/Ue ? zw 0 0 1 0 0 0 ? zq + Ue 0 0 0 1 0 1 0 ? ? ? ? ? ? ? ? ? ? u ? ? ? w ? ? +? q ? ? ? ? ? 0 0 0 0 0 0 ? z? e ? ? ? ? ? ? ? e ? ? ? ? (2. 46) There is a direct path between the output and input! The state space model of longitudinal dynamics consists of (2. 22) and (2. 46). 2. 3. 1 Numerical example Boeing 747 jet transpor t at ? ight condition cruising in horizontal ? ight at approximately 40,000 ft at Mach number 0. 8. Relevant data are given in Table 2. 1 and 2. 2.Using tables in Appendix 1, the concise small derivatives can be calculated and then the system matrix and input matrix can be derived as ? ? ? 0. 006868 0. 01395 0 ? 32. 2 ? ?0. 09055 ? ?0. 3151 774 0 ? A=? (2. 47) ? 0. 0001187 ? 0. 001026 ? 0. 4285 ? 0 0 0 1 0 ? ? ? 0. 000187 ? ?17. 85 ? ? B=? (2. 48) ? ?1. 158 ? 0 Similarly the parameters matrices in output equation (2. 46) can be determined. It should be noticed that English unit(s) is used in this example. 2. 4. AIRCRAFT DYNAMIC BEHAVIOUR SIMULATION USING STATE SPACE MODELS19 Table 2. 1: Boeing 747 transport data 636,636lb (2. 83176 ? 106 N) 5500 ft2 (511. m2 ) 27. 31 ft (8. 324 m) 195. 7 ft (59. 64 m) 0. 183 ? 108 slug ft2 (0. 247 ? 108 kg m2 ) 0. 331 ? 108 slug ft2 (0. 449 ? 108 kg m2 ) 0. 497 ? 108 slug ft2 (0. 673 ? 108 kg m2 ) -0. 156 ? 107 slug ft2 (-0. 212 ? 107 kg m2 ) 774 ft /s (235. 9m/s) 0 5. 909 ? 10? 4 slug/ft3 (0. 3045 kg/m3 ) 0. 654 0. 0430 W S c ? b Ix Iy Iz Izx Ue ? 0 ? CL0 CD Table 2. 2: Dimensional Derivatives– B747 jet X(lb) Z(lb) M(ft. lb) u(f t/s) ? 1. 358 ? 102 ? 1. 778 ? 103 3. 581 ? 103 w(f t/s) 2. 758 ? 102 ? 6. 188 ? 103 ? 3. 515 ? 104 q(rad/sec) 0 ? 1. 017 ? 105 ? 1. 122 ? 107 2 w(f t/s ) ? 0 1. 308 ? 102 -3. 826 ? 103 5 ? e (rad) -3. 17 ? 3. 551 ? 10 ? 3. 839 ? 107 2. 3. 2 The choice of state variables The state space representation of a dynamic system is not unique, which depends on the choice of state variables. For engineering application, state variables, in general, are chosen based on physical meanings, measurement, or easy to design and analysis. For the longitudinal dynamics, in additional to a set of the state variables in Eq. (2. 32), another widely used choice (in American) is ? u ? ? ? ? X=? ? q ? ? ? (2. 49) Certainly, when the logitudinal dynamics of the aircraft are represented in terms of the above state variab les, di? rent A, B and C are resulted (see Tutorial 1). 2. 4 Aircraft dynamic behaviour simulation using state space models State space model developed above provides a very powerful tool in investigate dynamic behavious of an aircraft under various condition. The idea of using state pace models for predicting aircraft dynamic behavious or numerical simulation can be explained by 20 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL the following expression X(t + ? t) = X(t) + dX(? ) ? |? =t ? t = X(t) + X(t)? t d? (2. 50) ? where X(t) is current state, ? t is step size and X(t) is the derivative calculated by the state space equation. . 4. 1 Aircraft response without control ? X = AX X(0) = X0 (2. 51) 2. 4. 2 Aircraft response to controls ? X = AX + BU ; X(0) = 0 (2. 52) where U is the pilot command 2. 4. 3 Aircraft response under both initial conditions and controls ? X = AX + BU ; X(0) = X0 (2. 53) 2. 5 Longitudinal response to the elevator After the longitudinal dynamics are descri bed by the state space model, the time histories of all the variables of interests can be calculated. For example, the time responses of the forward velocity u, normal velocity w (angle of attack) and ? ight path angle ? under the step movement of the levator are displayed in Fig 2. 1–2. 5 Discussion: If the reason for moving the elevator is to establish a new steady state ? ight condition, then this control action can hardly be viewed as successful. The long lightly damped oscillation has seriously interfered with it. A good operation performance cannot be achieved by simply changing the angle of elevator. Clearly, longitudinal control, whether by a human pilot or automatic pilot, demands a more sophisticated control activity than open-loop strategy. 2. 6 Transfer of state space models into transfer functions Taking Laplace transform on both sides of Eq. (2. 2) under the zero initial assumption yields sX(s) = Y (s) = where X(s) = L{X(t)}. AX(s) + BU (s) CX(s) (2. 54) (2. 55) 2. 6. TRANSFER OF STATE SPACE MODELS INTO TRANSFER FUNCTIONS21 Step response to elevator: Velocity 90 80 70 60 Velocity(fps) 50 40 30 20 10 0 0 1 2 3 4 5 Time(s) 6 7 8 9 10 Figure 2. 1: Longitudinal response to the elevator Step response to evelator: angle of attack 0 ?0. 005 ?0. 01 Angle of attack(rad) ?0. 015 ?0. 02 ?0. 025 ?0. 03 0 1 2 3 4 5 Time(s) 6 7 8 9 10 22 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL Step respnse to elevator: Flight path angle 0. 1 0. 08 0. 06 0. 04 Flight path angle (rad) 0. 02 0 0. 02 ?0. 04 ?0. 06 ?0. 08 ?0. 1 0 1 2 3 4 5 Time(s) 6 7 8 9 10 Figure 2. 2: Longitudinal response to the elevator Step Response to elevator: long term 90 80 70 60 Velocity (fps) 50 40 30 20 10 0 0 100 200 300 Time (s) 400 500 600 Figure 2. 3: Longitudinal response to the elevator 2. 6. TRANSFER OF STATE SPACE MODELS INTO TRANSFER FUNCTIONS23 Step response to elevator: long term 0 ?0. 005 ?0. 01 Angle of attack (rad) ?0. 015 ?0. 02 ?0. 025 ?0. 03 0 100 200 300 Time (s) 400 50 0 600 Figure 2. 4: Longitudinal response to the elevator Step response to elevator: long term 0. 1 0. 08 0. 06 0. 04 Flight path angle (rad) 0. 02 0 ?0. 2 ?0. 04 ?0. 06 ?0. 08 ?0. 1 0 100 200 300 Time (s) 400 500 600 Figure 2. 5: Longitudinal response to the elevator 24 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL Y (s) = C[sI ? A]? 1 BU (s) Hence the transfer function of the state space representation is given by G(s) = C[sI ? A]? 1 B = C(Adjoint(sI ? A))B det(sI ? A) (2. 56) (2. 57) Example 1: A short period motion of a aircraft is described by ? ? q ? = ? 0. 334 ? 2. 52 1. 0 ? 0. 387 ? q + ? 0. 027 ? 2. 6 ? e (2. 58) where ? e denotes the elevator de? ection. The transfer function from the elevator de? ection to the angle of attack is determined as follows: ? (s) ? 0. 27s ? 2. 6 = 2 ? e (s) s + 0. 721s + 2. 65 (2. 59) # The longitudinal dynamics of aircraft is a single-input and multi-output system with one input ? e and several outputs, u, w, q, ? , ? , az . Using the techniq ue in Section (2. 6), the transfer functions between each output variable and the input elevator can be derived. The notation u(s) Gue = (2. 60) ? ?e (s) is used in this course to denote the transfer function from input ? e to output u. For the longitudinal dynamics of Boeing 747-100, if the output of interest is the forward velocity, the transfer function can be determined using formula (2. 56) as u(s) ? e (s) ? 0. 00188s3 ? 0. 2491s2 + 24. 68s + 11. 6 s4 + 0. 750468s3 + 0. 935494s2 + 0. 0094630s + 0. 0041959 (2. 61) Gue ? = = Similarly, all other transfer functions can be derived. For a system with low order like the second order system in Example 1, the derivation of the corresponding transfer function from its state space model can be completed manually. For complicated systems with high order, it can be done by computer software like MATLAB. It can be found that although the transfer functions from the elevator to di? erent outputs are di? erent but they have the same denominat or, i. e. s4 + 0. 750468s3 + 0. 935494s2 + 0. 0094630s + 0. 041959 for Beoing 747-100. Only the numerators are di? erent. This is because all the denominators of the transfer functions are determined by det(sI ? A). 2. 6. 1 From a transfer function to a state space model The number of the state variable is equal to the order of the transfer function, i. e. , the order of the denominator of the transfer function. By choosing di? erent state variables, for the same transfer function, di? erent state space models are given. 2. 7. BLOCK DIAGRAM REPRESENTATION OF STATE SPACE MODELS 25 2. 7 Block diagram representation of state space models 2. 8 2. 8. 1 Static stability and dynamic modesAircraft stability Consider aircraft equations of motion represented as ? X = AX + BU (2. 62) The stability analysis of the original aircraft dynamics concerns if there is no any control e? ort,whether the uncontrolled motion is stable. It is also referred as openloop stability in general control engineeri ng. The aircraft stability is determined by the eigenvalues of the system matrix A. For a matrix A, its eigenvalues can be determined by the polynomial det(? I ? A) = 0 (2. 63) Eigenvalues of a state space model are equal to the roots of the characteristic equation of its corresponding transfer function.An aircraft is stable if all eigenvalues of its system matrix have negative real part. It is unstable if one or more eigenvalues of the system matrix has positive real part. Example for a second order system Example 1 revisited 2. 8. 2 Stability with FCS augmentation When a ? ight control system is installed on an aircraft. The command applied on the control surface is not purely generated by a pilot any more; it consists of both the pilot command and the control signal generated by the ? ight control system. It can be written as ? U = KX + U (2. 64) ? where K is the state feedback gain matrix and U is the reference signal or pilot command.The stability of an aircraft under ? ight co ntrol systems is refereed as closed-loop stability. 26 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL Then the closed-loop system under the control law is given by ? ? X = (A + BK)X + B U (2. 65) Stability is also determined by the eigenvalues of the system matrix of the system (2. 65), i. e. , A + BK. Sometimes only part of the state variables are available, which are true for most of ? ight control systems, and only these measurable variables are fed back, i. e. output feedback control. It can be written as ? ? U = KY + U = KCX + B U where K is the output feedback gain matrix.Substituting the control U into the state equation yields ? ? X = (A + BKC)X + B U (2. 67) (2. 66) Then the closed-loop stability is determined by the eigenvalues of the matrix A+BKC. Boeing Example (cont. ) Open-loop stability: ? 0. 3719 + 0. 8875i ? 0. 3719 ? 0. 8875i eig(A) = ? 0. 0033 + 0. 0672i ? 0. 0033 ? 0. 0672i (2. 68) Hence the longitudinal dynamics are stable. The same conclusion can be drawn from the the transfer function approach. Since the stability of an open loop system is determined by its poles from denominator of its transfer function, i. e. , s4 +0. 750468s3 + 0. 935494s2 + 0. 0094630s + 0. 041959=0. Its roots are given by s1,2 = ? 0. 3719  ± 0. 8875i s3,4 = ? 0. 0033  ± 0. 0672i (2. 69) (This example veri? es that the eigenvalues of the system matrix are the same as the roots of its characteristic equation! ) 2. 8. 3 Dynamic modes Not only stability but also the dynamic modes of an aircraft can be extracted from the stat space model, more speci? cally from the system matrix A. Essentially, the determinant of the matrix A is the same as the characteristic equation. Since there are two pairs of complex roots, the denominator can be written in the typical second order system’s format as 2 2 (s2 + 2? ? p s + ? p )(s2 + 2? s ? s s + ? s ) (2. 70) (2. 71) (2. 72) where ? p = 0. 0489 for Phugoid mode and ? s = 0. 3865 for the short period mode. ?s = 0. 9623 ? p = 0. 0673 2. 9. REDUCED MODELS OF LONGITUDINAL DYNAMICS B 747 Phugoid mode 1. 5 27 1 93. 4s 0. 5 Perturbation 0 ? 0. 5 ? 1 0 300 600 Time (s) Figure 2. 6: Phugoid mode of Beoing 747-100 The ? rst second order dynamics correspond to Phugoid mode. This is an oscillad d tion with period T = 1/? p = 1/(0. 0672/2? ) = 93. 4 second where ? p is the damped frequency of the Phugoid mode. The damping ratio for Phugoid mode is very small, i. e. , ? p = 0. 489. As shown in Figure 2. 6, Phugoid mode for Boeing 747-100 at this ? ight condition is a slow and poor damped oscillation. It takes a long time to die away. The second mode in the characteristic equation corresponds to the short period mode in aircraft longitudinal dynamics. As shown in Fig. 2. 7, this is a well damped response with fast period about T = 7. 08 sec. (Note the di? erent time scales in Phugoid and short period response). It dies away very quickly and only has the in? uence at the beginning of the response. 2. 9 Reduced mode ls of longitudinal dynamics Based on the above example, we can ? d Phugoid mode and short period mode have di? erent time scales. Actually all the aircraft have the similar response behaviour as Boeing 747. This makes it is possible to simplify the longitudinal dynamics under certain conditions. As a result, this will simplify following analysis and design. 2. 9. 1 Phugoid approximation The Phugoid mode can be obtained by simplifying the full 4th order longitudinal dynamics. Assumptions: †¢ w and q respond to disturbances in time scale associated with the short period 28 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL Beoing 747 Short period mode From: U(1) 0. 7 0. 6 0. 5 0. 4Perturbation To: Y(1) 0. 3 0. 2 0. 1 0 ?0. 1 ?0. 2 0 5 10 15 Time (sec. ) Figure 2. 7: Short Period mode of Beoing 747-100 mode; it is reasonable to assume that q is quasi-steady in the longer time scale associated with Phugoid mode; q=0; ? †¢ Mq , Mw , Zq , Zw are neglected since both q and w are rel atively small. ? ? ? Then from the table in Appendix 1, we can ? nd the expression of the small concise derivatives under these assumptions. The longitudinal model reduces to ? ? ? Xu Xw ? ? X? e ? 0 ? g u ? u m m m Zw ? w ? ? Zu Ue 0 ? ? w ? ? Z? e ? m m ? ? ? =? M ? + ? M ? ?e (2. 73) ? m ? ? 0 ? ? u Mw 0 0 ? q ? ? ? e ? Iyy Iyy Iyy ? ? ? 0 0 1 0 0 This is not a standard state space model. However using the similar idea in Section 2. 6, by taking Laplace transform on the both sides of the equation under the assumption that X0 = 0, the transfer function from the control surface to any chosen output variable can be derived. The characteristic equation (the denominator polynomial of a transfer function) is given by ? (s) = As2 + Bs + C where A = ? Ue Mw Ue B = gMu + (Xu Mw ? Mu Xw ) m g C = (Zu Mw ? Mu Zw ) m (2. 75) (2. 76) (2. 77) (2. 74) 2. 9. REDUCED MODELS OF LONGITUDINAL DYNAMICS 29 This corresponds to the ? st mode (Phugoid mode) in the full longitudinal model. After substit uting data for Beoing 747 in the formula, the damping ratio and the natural frequency are given by ? = 0. 068, ? n = 0. 0712 (2. 78) which are slightly di? erent from the true values, ? p = 0. 049, ? p = 0. 0673, obtained from the full 4th longitudinal dynamic model. 2. 9. 2 Short period approximation In a short period after actuation of the elevator, the speed is substantially constant while the airplane pitches relatively rapidly. Assumptions: †¢ u=0 †¢ Zw (compared with m) and Zq (compared with mUe ) are neglected since they ? are relatively small. w ? q ? Zw m mw Ue mq w q + Z ? e m m ? e ?e (2. 79) The characteristic equation is given by s2 ? ( Zw 1 1 Mq Zw + (Mq + Mw Ue ))s ? (Ue Mw ? )=0 ? m Iyy Iyy m (2. 80) Using the data for B747-100, the result obtained is s2 + 0. 741s + 0. 9281 = 0 with roots s1,2 = ? 0. 371  ± 0. 889i The corresponding damping ratio and natural frequency are ? = 0. 385 wn = 0. 963 (2. 83) (2. 82) (2. 81) which are seen to be almost same as t hose obtained from the full longitudinal dynamics. Actually the short period approximation is very good for a wide range of vehicle characteristics and ? ight conditions. Tutorial 1 1. Using the small concise derivatives, ? d the state equations of longitudinal dynamics of an aircraft with state variables ? ? u ? ? ? ? X=? (2. 84) ? q ? ? 30 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL Normal acceleration at the pilot seat is a very important quantity, de? ned as the normal acceleration response to an elevator measured at the pilot seat, i. e. aZx = w ? Ue q ? lx q ? ? (2. 85) where lx is the distance from c. g. to the pilot seat. When the outputs of interest are pitch angle ? and the normal acceleration at the pilot seat, ? nd the output equations and identify all the associated parameter matrices and dimension of variables (state, input and output). . The motion of a mass is governed by m? (t) = f (t) x (2. 86) where m is mass, f (t) the force acting on the mass and x(t) the di splacement. When the velocity x(t) and the velocity plus the position x(t) + x(t) are chosen ? ? as state variables, and the position is chosen as output variable, ? nd the state space model of the above mass system. Determine the transfer function from the state space model and compare it with the transfer function directly derived from the dynamic model in Eq. (2. 86). 3. Find the transfer function from elevator de? ection ? e to pitch rate q in Example 1.Determine the natural frequency and damping ratio of the short period dynamics. Is it possible to ? nd these information from a state space model directly, instead of using the transfer function approach? 4. Suppose that the control strategy ? ?e = ? + 0. 1q + ? e (2. 87) ? is used for the aircraft in Example 1 where ? e is the command for elevator de? ection from the pilot. Determine stability of the short period dynamics under the above control law using both state space method and Routh stability criterion in Control Engineeri ng (When Routh stability criterion is applied, you can study the stability using the transfer function from ? to q or that from ? e to ? (why? )). Compare and discuss the results achieved. Chapter 3 Lateral response to the controls 3. 1 Lateral state space models mv ? ?Y v ? ( ? Y + mWe )p ? ?v ? p ? mUe )r ? mg? cos ? e ? mg? sin ? e ? L ? L ? L ? v + Ix p ? ? p ? Ixz r ? ? r ? v ? p ? r ? N ? N ? N v ? Ixz p ? ? p + Iz r ? ? r ? ?v ? p ? r = = = ? Y ? A + A ? L ? A + A ? N ? A + A ? Y ? R R ? L ? R R ? N ? R R (3. 1) (3. 2) (3. 3) Referred to body axes, the small perturbed lateral dynamics are described by ? ( ? Y ? r where the physical meanings of the variables are de? ed as v: Lateral velocity perturbation p: Roll rate perturbation r: Yaw rate perturbation ? : Roll angle perturbation ? : Yaw angle perturbation ? A : Aileron angle (note that it is denoted by ? in Appendix 1) ? R : Rudder angle (note that it is denoted by ? in Appendix 1) Together with the relationships ? ?= p and ? ? = r, (3. 4) (3. 5) the lateral dynamics can be described by ? ve equations, (3. 1)-(3. 5). Treating them in the same way as in the longitudinal dynamics and after introducing the concise notation as in Appendix 1, these ? ve equations can be represented as ? ? ? ? ? ? v ? p ? r ? ? ? ? ? ? yv lv nv 0 0 yp lp np 1 0 yr lr nr 0 1 y? 0 0 0 0 y? 0 0 0 0 v p r ? ? ? ? y? A l? A n ? A 0 0 y? R l? R n ? R 0 0 ? ? ? ? ? ? ? A ? R (3. 6) ? ? ? ? ?=? ? ? ? ? ? ? ? ? ?+? ? ? ? ? 31 32 CHAPTER 3. LATERAL RESPONSE TO THE CONTROLS When the derivatives are referred to airplane wind axes, ? e = 0 (3. 7) from Appendix 1, it can be seen that y? = 0. Thus all the elements of the ? fth column in the system matrix are zero. This implies that ? has no in? uence on all other variables. To simplify analysis, in most of the cases, the following fourth order model is used ? ? ? ? ? v ? v y? A y? R yv yp yr y? ? p ? ? lv lp lr 0 ? ? p ? ? l? A l? R ? ?A ? ? ? ? ? ? =? (3. 8) ? r ? ? n v n p n r 0 ? ? r ? + ? n ? A n ? R ? ? R ? ? ? 0 1 0 0 0 0 ? (It should be noticed that the number of the states is still ? ve and this is just for the purpose of simplifying analysis). Obviously the above equation can also be put in the general state space equation ? X = AX + BU with the state variables ? v ? p ? ? X=? ? r ? , ? ?A ? R yp lp np 1 yr lr nr 0 ? (3. 9) (3. 10) the input/control variables U= the system matrix yv ? lv A=? ? nv 0 and the input matrix ? ? , ? y? 0 ? ? 0 ? (3. 11) (3. 12) y ? A ? l? A B=? ? n ? A 0 ? y? R l? R ? ? n ? R ? 0 (3. 13) For the lateral dynamics, another widely used choice of the state variables (American system) is to replace the lateral velocity v by the sideslip angle ? and keep all others. Remember that v (3. 14) Ue The relationships between these two representations are easy to identify. In some textbooks, primed derivatives, for example, Lp , Nr , so on, are used for state space representation of the lateral dynamics. The primed derivatives ar e the same as the concise small letter derivatives used in above and in Appendix 1.For stability augmentation systems, di? erent from the state space model of the longitudinal dynamics where only one input elevator is considered, there are two inputs in the lateral dynamic model, i. e. the aileron and rudder. 3. 2. TRANSIENT RESPONSE TO AILERON AND RUDDER Table 3. 1: Dimensional Derivatives– B747 jet Y(lb) L(ft. lb) N(ft. lb) v(ft/s) ? 1. 103 ? 103 ? 6. 885 ? 104 4. 790 ? 104 p(rad/s) 0 ? 7. 934 ? 106 ? 9. 809 ? 105 r(rad/sec) 0 7. 302 ? 106 ? 6. 590 ? 106 ? A (rad) 0 ? 2. 829 ? 103 7. 396 ? 101 ? R (rad) 1. 115 ? 105 2. 262 ? 103 ? 9. 607 ? 103 33 3. 2 3. 2. 1 Transient response to aileron and rudderNumerical example Consider the lateral dynamics of Boeing 747 under the same ? ight condition as in Section 2. 3. 1. The lateral aerodynamic derivatives are listed in Table 3. 1. Using the expression in Appendix 1, all the parameters in the state space model can be calculated, gi ven by ? ? ? 0. 0558 0. 0 ? 774 32. 2 ? ?0. 003865 ? 0. 4342 0. 4136 0 ? ? A=? (3. 15) ? 0. 001086 ? 0. 006112 ? 0. 1458 0 ? 0 1 0 0 and 0. 0 ? ?0. 1431 B=? ? 0. 003741 0. 0 ? ? 5. 642 0. 1144 ? ? ? 0. 4859 ? 0. 0 (3. 16) Stability Issue ? 0. 0330 + 0. 9465i ? 0. 0330 ? 0. 9465i eig(A) = ? 0. 5625 ? 0. 0073 (3. 17)All the eigenvalues have negative real part hence the lateral dynamics of the Boeing 747 jet transport is stable. 3. 2. 2 Lateral response and transfer functions ? v p ? ?+B r ? ? State space model of lateral dynamics ? ? ? v ? ? p ? ? ? ? ? = A? ? r ? ? ? ? ? ?A ? R (3. 18) This is a typical Multi-Input Multi-Output (MIMO) system. For an MIMO system like the lateral dynamics, similar to the longitudinal dynamics, its corresponding transfer function can be derived using the same technique introduced in Chapter 2. However, in this case the corresponding Laplace transform of the state space model, 34 CHAPTER 3.LATERAL RESPONSE TO THE CONTROLS G(s) ? Rr? m is a complex functi on matrix which is referred as a transfer function matrix where m is the number of the input variables and r is the number of the output variables. The ijth element in the transfer function matrix de? nes the transfer function between the ith output and jth input, that is, Gyij (s) = u yi (s) . uj (s) (3. 19) For example, GpA (s) denotes the transfer function from the aileron, ? A , to the roll ? rate, p. Its corresponding transfer function matrix is given by ? ? ? ? v G? A (s) GvR (s) v(s) ? ? p(s) ? ? Gp (s) Gp (s) ? ?A (s) ? R ? ? ? ? ?A (3. 20) ? r(s) ? ? Gr (s) Gr (s) ? ?R (s) ? A ? R ? p ? (s) G? A (s) G? R hi(s) With the data of Boeing 747 lateral dynamics, these transfer functions can be found as ? 2. 896s2 ? 6. 542s ? 0. 6209 GvA (s) = 4 fps/rad (3. 21) ? s + 0. 6344s3 + 0. 9375s2 + 0. 5097s + 0. 003658 ? 0. 1431s3 ? 0. 02727s2 ? 0. 1101s rad/s/rad, or deg/s/deg s4 + 0. 6344s3 + 0. 9375s2 + 0. 5097s + 0. 003658 (3. 22) 0. 003741s3 + 0. 002708s2 + 0. 0001394s ? 0. 004534 GrA (s) = rad/s/rad, deg/s/deg ? s4 + 0. 6344s3 + 0. 9375s2 + 0. 5097s + 0. 003658 (3. 23) ? 0. 1431s2 ? 0. 02727s ? 0. 1101 ? rad/rad, or deg/deg (3. 24) G? A (s) = 4 s + 0. 6344s3 + 0. 9375s2 + 0. 097s + 0. 003658 and GpA (s) = ? GvR (s) = ? 5. 642s3 + 379. 4s2 + 167. 5s ? 5. 917 fps/rad s4 + 0. 6344s3 + 0. 9375s2 + 0. 5097s + 0. 003658 (3. 25) GpR (s) = ? 0. 1144s3 ? 0. 1991s2 ? 1. 365s rad/s/rad, or deg/s/deg s4 + 0. 6344s3 + 0. 9375s2 + 0. 5097s + 0. 003658 (3. 26) ? 0. 4859s3 ? 0. 2321s2 ? 0. 008994s ? 0. 05632 rad/s/rad, or deg/s/deg s4 + 0. 6344s3 + 0. 9375s2 + 0. 5097s + 0. 003658 (3. 27) 0. 1144s2 ? 0. 1991s ? 1. 365 rad/rad, or deg/deg (3. 28) s4 + 0. 6344s3 + 0. 9375s2 + 0. 5097s + 0. 003658 GrR (s) = ? G? R (s) = ? The denominator polynomial of the transfer functions can be factorised as (s + 0. 613)(s + 0. 007274)(s2 + 0. 06578s + 0. 896) (3. 29) 3. 3. REDUCED ORDER MODELS 35 It has one large real root, -0. 5613, one small real root, -0. 0073 (very close to origin) and a pair of complex roots (-0. 0330 + 0. 9465i, -0. 0330 – 0. 9465i). For most of the aircraft, the denominator polynomial of the lateral dynamics can be factorized as above, ie. , with two real roots and a pair of complex roots. That is, 2 (s + 1/Ts )(s + 1/Tr )(s2 + 2? d ? d s + ? d ) = 0 (3. 30) where Ts Tr is the spiral time constant (for spiral mode), Tr is the roll subsidence time constant (for roll subsidence), and ? d , ? are damping ratio and natural frequency of Dutch roll mode. For Boeing 747, from the eigenvalues or the roots, these parameters are calculated as: Spiral time constant Ts = 1/0. 007274 = 137(sec); (3. 31) Roll subsidence time constant Tr = 1/0. 5613 = 1. 78(sec) and Dutch roll natural frequency and damping ratio ? d = 0. 95(rad/sec), ? d = 0. 06578 = 0. 0347 2? d (3. 33) (3. 32) The basic ? ight condition is steady symmetric ? ight, in which all the lateral variables ? , p, r, ? are identically zero. Unlike the elevator, the lateral controls are not used individually to produce changes in steady state.That is because the steady state values of ? , p, r, ? that result from a constant ? A and ? R are not of interest as a useful ? ight condition. Successful movement in the lateral channel, in general, should be the combination of aileron and rudder. In view of this, the impulse response, rather than step response used in the lateral study, is employed in investigating the lateral response to the controls. This can be considered as an idealised situation that the control surface has a sudden move and then back to its normal position, or the recovering period of an airplane deviated from its steady ? ght state due to disturbances. The impulse lateral responses of Boeing 747 under unit aileron and rudder impulse action are shown in Figure 3. 1 and 3. 2 respectively. As seen in the response, the roll subsidence dies away very quickly and mainly has the in? uence at the beginning of the response. The spiral mode has a large time constant a nd takes quite long time to respond. The Dutch roll mode is quite poorly damped and the oscillation caused by the Dutch roll dominates the whole lateral response to the control surfaces. 3. 3 Reduced order models Although as shown in the above ? gures, there are di? rent modes in the lateral dynamics, these modes interact each other and have a strong coupling between them. In general, the approximation of these models is not as accuracy as that in the longitudinal dynamics. However to simplify analysis and design in Flight Control Systems, reduced order models are still useful in an initial stage. It is suggested that the full lateral dynamic model should be used to verify the design based on reduced order models. 36 CHAPTER 3. LATERAL RESPONSE TO THE CONTROLS Lateral response to impluse aileron deflection 0. 1 Lateral velocity (f/s) 0. 05 0 ? 0. 05 ? 0. 1 ? 0. 5 0 10 20 30 Time(s) 40 50 60 0. 05 Roll rate (deg/sec) 0 ? 0. 05 ? 0. 1 ? 0. 15 0 x 10 ?3 10 20 30 Time (s) 40 50 60 5 Yaw rate(deg/sec) 0 ? 5 ? 10 ? 15 0 10 20 30 Time (s) 40 50 60 0 Roll angle (deg) ? 0. 05 ? 0. 1 ? 0. 15 ? 0. 2 ? 0. 25 0 10 20 30 Time (s) 40 50 60 Figure 3. 1: Boeing 747-100 lateral response to aileron 3. 3. REDUCED ORDER MODELS 37 Lateral response to unit impluse rudder deflection 10 Lateral velocity (f/s) 5 0 ? 5 ? 10 0 10 20 30 Time (s) 40 50 60 2 Roll rate (deg) 1 0 ? 1 ? 2 0 10 20 30 Time (s) 40 50 60 0. 4 Yaw rate (deg) 0. 2 0 ? 0. 2 ? 0. 4 ? 0. 6 0 10 20 30 Time (s) 40 50 60 Roll angle (deg) 0 ? 1 ? 2 ? 3 ? 4 0 10 20 30 Time (s) 40 50 60 Figure 3. 2: Boeing 747-100 lateral response to Rudder 38 CHAPTER 3. LATERAL RESPONSE TO THE CONTROLS 3. 3. 1 Roll subsidence Provided that the perturbation is small, the roll subsidence mode is observed to involve almost pure rolling motion with little coupling into sideslip and yaw. A reduced order model of the lateral-directional dynamics retaining only roll subsidence mode follows by removing the side force and yaw moment equations to giv e p = lp p + l? A ? A + l? R ? R ? (3. 34) If only the in? uence from aileron de? ction is concerned and assume that ? R = 0, taking Laplace transform on Eq. (3. 34) obtains the transfer function p(s) l ? A kp = = ? A s ? lp s + 1/Tr where the gain kp = l? A and the time constant Tr = 1 Ix Iz ? Ixz =? lp Iz Lp + Ixz Np (3. 36) (3. 37) (3. 35) Since Ix Ixz and Iz Ixz , then equation (3. 37) can be further simpli? ed to give the classical approximation expression for the roll mode time constant Tr = ? Ix Lp (3. 38) For the Boeing 747, the roll subsidence estimated by the ? rst order roll subsidence approximation is 0. 183e + 8 Tr = ? = 2. 3sec. (3. 39) ? 7. 934e + 6 It is close to the real value, 1. sec, given by the full lateral model. 3. 3. 2 Spiral mode approximation As shown in the Boeing 747 lateral response to the control surface, the spiral mode is very slow to develop. It is usual to assume that the motion variables v, p, r are quasi-steady relative to the time scale of the mo de. Hence p = v = r = 0 and the ? ? ? lateral dynamics can be written as ? ? ? 0 yv ? 0 ? ? lv ? ? ? ? 0 ? = ? nv ? 0 ? yp lp np 1 yr lr nr 0 y? v 0 p 0 r 0 ? ? y? A ? ? l ? A ? +? ? ? n ? A 0 ? ? y ? R l? R ? ? n ? R ? 0 ?A ? R (3. 40) If only the spiral mode time constant is concerned, the unforced equation can be used.After solving the ? rst and third algebraic equations to yield v and r, Eq. (3. 40) reduces to lp nr ? l n l np ? lp n 0 p yv lr nv ? lr np + yp + yr lv nv ? lv nv y? v r r r (3. 41) ? = ? ? 1 0 3. 3. REDUCED ORDER MODELS 39 Since the terms involving in yv and yp are assumed to be insigni? cantly small compared to the term involving yr , the above expression for the spiral mode can be further simpli? ed as ? y? (lr nv ? lv nr ) ? = 0 ? + (3. 42) yr (lv np ? lp nv ) Therefore the time constant of the spiral mode can be estimated by Ts = yr (lv np ? lp nv ) y? (lr nv ? lv nr ) (3. 43)Using the aerodynamic derivatives of Boeing 747, the estimated spiral mode time c onstant is obtained as Ts = 105. 7(sec) (3. 44) 3. 3. 3 Dutch roll ? p=p=? =? =0 ? v ? r ? = yv nv yr nr v r + 0 n ? A y? R n ? R ? A ? R (3. 45) (3. 46) Assumptions: From the state space model (3. 46), the transfer functions from the aileron or rudder to the lateral velocity or roll rate can be derived. For Boeing 747, the relevant transfer functions are given by GvA (s) = ? GrA (s) = ? GvR (s) = ? GrR (s) = ? ?2. 8955 s2 + 0. 2013s + 0. 8477 0. 003741(s + 0. 05579) s2 + 0. 2013s + 0. 8477 s2 5. 642(s + 66. 8) + 0. 013s + 0. 8477 (3. 47) (3. 48) (3. 49) (3. 50) ?0. 4859(s + 0. 04319) s2 + 0. 2013s + 0. 8477 From this 2nd order reduced model, the damping ratio and natural frequency are estimated as 0. 1093 and 0. 92 rad/sec. 3. 3. 4 Three degrees of freedom approximation Assume that the following items are small and negligible: 1). The term due to gravity, g? 2). Rolling acceleration due to yaw rate, lr r 3). Yawing acceleration as a result of roll rate, np p Third order Dutch roll approximation is given by ? ? ? ? ? ? v ? yv yp yr v 0 y ? R ? p ? = ? lv lp 0 ? ? p ? + ? l? A l? R ? ? r ? nv 0 nr r n? A n?R ?A ? R (3. 51) 40 CHAPTER 3. LATERAL RESPONSE TO THE CONTROLS For Boeing 747, the corresponding transfer functions are obtained as GvA (s) = ? GpA (s) = ? GrA (s) = ? ?2. 8955(s + 0. 6681) (s + 0. 4511)(s2 + 0. 1833s + 0. 8548) ? 0. 1431(s2 + 0. 1905s + 0. 7691) (s + 0. 4511)(s2 + 0. 1833s + 0. 8548) 0. 003741(s + 0. 6681)(s + 0. 05579) (s + 0. 4511)(s2 + 0. 1833s + 0. 8548) 5. 642(s + 0. 4345)(s + 66. 8) (s + 0. 4511)(s2 + 0. 1833s + 0. 8548) 0. 1144(s ? 4. 432)(s + 2. 691) (s + 0. 4511)(s2 + 0. 1833s + 0. 8548) ? 0. 4859(s + 0. 4351)(s + 0. 04254) (s + 0. 4511)(s2 + 0. 1833s + 0. 8548) (3. 52) 3. 53) (3. 54) and GvR (s) = ? GpR (s) = ? GrR (s) = ? (3. 55) (3. 56) (3. 57) The poles corresponding to the Dutch roll mode are given by the roots of s2 + 0. 1833s + 0. 8548 = 0. Its damping ratio and natural frequency are 0. 0995 and 0. 921 rad/sec. Compared wit h the values given by the second order Dutch roll approximation, i. e. , 0. 1093 and 0. 92 rad/sec, they are a little bit closer to the true damping ratio ? d = 0. 0347 and the natural frequency ? d = 0. 95 (rad/sec) but the estimation of the damping ratio still has quite poor accuracy. 3. 3. 5 Re-formulation of the lateral dynamicsThe lateral dynamic model can be re-formulated to emphasise the structure of the reduced order model. ? ? v ? yv ? r ? ? nv ? ? ? ? ? p ? = ? lv ? ? 0 ? ? yr nr lr 0 yp np lp 1 g v 0 r 0 p 0 ? ? 0 ? ? n ? A ? +? ? ? l? A 0 ? ? y? R n ? R ? ? l? R ? 0 ? A ? R (3. 58) The system matrix A can be partitioned as A= Directional e? ects Directional/roll coupling e? ects Roll/directional coupling e? ects Lateral or roll e? ects (3. 59) Tutorial 2 1. Using the data of Boeing 747-100 at Case II, form the state space model of the lateral dynamics of the aircraft at this ? ight condition.When the sideslip angle and roll angle are of interest, ? nd the output equa tion. 2. Find the second order Dutch roll reduced model of this airplane. Derive the transfer function from the rudder to the yaw rate based on this reduced order model. 3. 3. REDUCED ORDER MODELS 41 3. Using MATLAB, assess the approximation of this reduced order model based on time response, and the damping ratio and natural frequency of the Dutch roll mode. 4. Based on the third order reduced model in (3. 51), ? nd the transfer function from the aileron to the roll rate under the assumption y? A = yp = 0.