Using Shaping to Mold Child Behavior

Utilizing Shaping to Mold Child Behavior Forming (otherwise called progressive estimation) is an instructing method that includes an educator remunerating a kid as she or he effectively improves the securing of an objective ability. Forming is viewed as a basic procedure in educating in light of the fact that conduct can't be remunerated except if it initially happens. Molding is expected to lead kids toward proper complex conduct, and afterward reward them as they complete each progressive advance. Best Practices for Behavior Shaping Initial, an educator needs to distinguish the understudies qualities and shortcomings around a particular ability, and afterward break the aptitude into a progression of steps that lead a kid toward that target. On the off chance that the focused on aptitude is having the option to compose with a pencil, a youngster may experience issues holding a pencil. A proper assistive advance savvy methodology may begin with the instructor putting their hand over the childs hand, showing to the kid the right pencil handle. When the kid accomplishes this progression, they are compensated and the following stage is attempted. The initial step for another understudy who is uninterested recorded as a hard copy however prefers to paint may be giving the understudy a paint brushâ and remunerating the work of art of a letter. For each situation, you are helping a kid rough the geology of the conduct you need with the goal that you can strengthen that conduct as the youngster develops and creates. Molding may require an educator to make an undertaking examination of the ability so as to make a guide for forming the conduct or meeting the last expertise objective. All things considered, it is additionally basic for the instructor to demonstrate the molding convention for homeroom para-experts (educators helpers) so they recognize what approximations are fruitful and which approximations should be cleared and retaught. Despite the fact that this may appear to be a careful and moderate procedure, the progression and prize procedure profoundly installs the conduct in the understudies memory, so the individual in question will probably rehash it. History Forming is a procedure that emerged from behaviorism, a field of brain science set up by B.F. Skinner and dependent on the connection among practices and their fortification. Skinner accepted that practices should be strengthened by explicit favored things or food, however can be additionally combined with social support like acclaim. Behaviorism and social speculations are the establishments of applied conduct analysis (ABA), which is utilized effectively with kids who fall some place on the medically introverted range. Albeit frequently thought to be robotic, ABA has the benefit of permitting the advisor, educator, or parent to investigate the particular conduct, as opposed to concentrate on an ethical part of the conduct (as in Robert should realize that its wrong!). Forming isn't confined to showing methods with mentally unbalanced kids. Skinner himself utilized it to instruct creatures to perform undertakings, and showcasing experts have utilized molding to set up inclinations in a clients shopping practices. Models Maria utilized molding to assist Angelica with figuring out how to take care of herself freely, by helping Angelica utilize the spoon hand over hand - moving to contact Angelicas wrist until Angelica was at long last ready to get her spoon and eat from her bowl independently.While training Robert to utilize the can autonomously to pee, his mom, Susan, saw that he experienced issues pulling up his jeans. She chose to shape this progression in her assignment investigation by applauding and strengthening his capacity to pull his jeans up to his knees, at that point loosening up the versatile abdomen to complete the progression, and afterward helping Robert by utilizing hand over hand to finish the pulling up pants step.One forming test that Skinner directed was the point at which he and his partners chose to show a pigeon to bowl. The objective errand was to get the winged animal to send a wooden ball down a small rear entryway toward a lot of toy pins, by swiping the ball with a sidewa rd development of its mouth. The analysts originally fortified any swipe that seemed as though what they had at the top of the priority list, at that point strengthened any that approximated what they needed, and inside a couple of moments, they had succeeded. One way present day advertisers utilize molding is to give a free example of an item and remember a coupon for the huge rebate for the price tag. In the primary buy, the customer would discover a coupon for a littler markdown, etc, until the purchaser no longer needs the motivating forces and has built up the ideal conduct. Sources Koegel, Robert L. Evaluating and Training Teachers in the Generalized Use of Behavior Modification with Autistic Children, Dennis C. Russo, Arnold Rincover, Journal of Applied Behavior Analysis, Wiley Online Library, 1977. Peterson, Gail B. A Day of Great Illumination: B. F. Skinners Discovery of Shaping. Diary of the Experimental Analysis of Behavior, 10.1901/jeab.2004.82-317, National Center for Biotechnology Information, U.S. National Library of Medicine, November 2004, Bethesda, MD. Rothschild, Michael L. Conduct Learning Theory: Its Relevance to Marketing and Promotions. Diary of Marketing, William C. Gaidis, Vol. 45, No. 2, Sage Publications, Inc., JSTOR, Spring 1981.

Essentials Of Law For Health Professionals -Myassignmenthelp.Com

Question: Talk About The Essentials Of Law For Health Professionals? Answer: Introducation At the point when two gatherings want to go into an authoritative relationship then the equivalent should be possible by shaping an agreement. An agreement is an understanding which is enforceable in law. An understanding is the trading of offer and acknowledgment by the offeror and offeree.[1] In this manner, considering the idea of understanding and agreement the fundamental basics required for the arrangement of an agreement are: An understanding An understanding is framed when an offer is upheld by an acknowledgment. in this way, there are two prerequisites to settle on an understanding: An offer is the primary basic fixing in contract development. It is a proposition which is planned by the offeror and which he moves to an offeree orally or in composed structure. It is a guarantee to do or not to carry out specific responsibilities in return of guarantee with respect to the offeree[2]; An acknowledgment is the subsequent fixing and is the expectation of the offeree which is imparted for the offer that is gotten by him. An acknowledgment is the endorsement of the proposition which is responded to the offeror[3]. At the point when an offer and acknowledgment is made then the gatherings go into an understanding. This understanding gets the enforceability of law when it is upheld with some increase/advantage. The thought moves from the promisor to the promisee to help the guarantees that are traded in the midst of the parties[4]; The offeror and offeree when making the guarantees ought to have lawful sound. Legitimate expectation depicts that the gatherings are eager to go to the courtroom in instances of disputes[5]. The offeror and offeree ought to likewise be the gatherings who are competent to make an agreement, an individual is supposed to be able when he isn't experiencing any sort of mental inadequacy. Likewise, the gatherings ought to have achieved the time of greater part according to the rule that everyone must follow. Every one of these basics together make an agreement which is enforceable in law. Need of Written agreement An agreement is a report executed by private gatherings by following the components of agreement. In Australia, there are two sorts of agreements that can be made by the parties:[6] The agreement that is made by the gatherings orally or verbally are oral agreements and the agreement that are made by the gatherings on a bit of paper are composed agreements. Both oral and composed agreement are substantial in Australia, the main necessity is that both the agreement must consent to the components of agreement. Therefore, there is no law that an agreement must be recorded as a hard copy so as to be official. An oral agreement has equivalent holiness in law. In any case, it is seen that the composed agreements are constantly favored when contrasted and an oral agreement. The essential reasons are:[7] That it is anything but difficult to offered significance to the agreement terms if there is vagueness in the agreement; The genuine expectation of the gatherings can be resolved; Human psyche is very spot and gatherings will in general overlook the terms. In the event that the agreement will be in composed structure, at that point it is anything but difficult to decide the goal of the gatherings; Courts are progressively disposed to depend on composed standing when contrasted and oral terms. Thus, composed agreement are favored over oral agreements despite the fact that both are substantial in law. Formal Contract and its necessities Regularly when all the agreement components that is, offer, acknowledgment, goal, thought and limit of the gatherings are conform to then an agreement is detailed by the gatherings. An agreement can be oral or composed. Bit, aside from these two agreements there is likewise one sort of agreement which is called Formal Contract.[8] A conventional agreement is a sort of composed agreement yet to be exact a proper agreement is a sort of agreement which requires certain necessities to be satisfied so as to think about an agreement as a conventional agreement. In this manner, only one out of every odd composed agreement is a proper agreement and there are scarcely any necessities to change over an agreement into a conventional agreement. The necessities are: That all the agreement components are not required to be available in a conventional agreement; There is no requirement for the nearness of any sort good for make a conventional agreement, in this manner, nonappearance of thought will likewise make an agreement enforceable. There is no requirement for the common exchange of guarantee. A composed archive send as deed to another gathering is a sort of formal agreement; A proper agreement has the legitimacy of 12 years and after the time range the agreement become unenforceable; It is essential that each conventional agreement must be in composed structure; It is essential that a conventional agreement ought to be marked by the gatherings. The two instances of formal agreements are: Those agreements which are legitimate with no compelling reason to demonstrate the gatherings expectation and the court depend on the supporting records to set up the legitimacy of agreement. These are court of records. For instance, to be of acceptable conduct, be thoughtful and so forth. The agreement which are marked and as deed are agreement of seal and are formal agreements Lawful aim of the gatherings Lawful aim of the gatherings implies that the offeror and offeree should make offer and acknowledgment with the expectation they will maintain the guarantees in lawful way. Thus, on the off chance that any debates emerge, at that point they are eager to go to official courtroom. In any case, there is a fundamental assumption, that on the off chance that gatherings are in social relationship, at that point there is no goal however the equivalent is available when they are in business relationship. In any case, this assumption can be invalidated if proof are created. It was held in Simkins v pays [1955][9] that gatherings are authoritatively bound in any event, when they are in social relationship gave there is lawful aim to tie by the agreement. It is presented that each Friday night a gathering of companion meet for drink. $ 2 is contributed by each companion for a lottery ticket which is taken out throughout the end of the week. Just a single companion is approved to purchase the ticket. At the point when the gathering won the lottery, the buyer presented that since the relationship is social so there is no agreement. It is presented that the commitment was made by all the companions in normal way with the goal that on the off chance that they win, at that point they will share the cash. In this way, however they are companions yet the legitimate expectation to tie by the ticket together is common. Along these lines, by applying the law in Simkins v pays [1955], it is presented that proof is showed which counter the important that there is no legitimate expectation in social relationship. Along these lines, the prize must be disseminated in the midst of the considerable number of companions as there is a substantial agreement in the midst of the gatherings. Specialist or Independent temporary worker There is a need to make a qualification of an individual as a self employed entity and a specialist for the most part since it is their relationship with the important that examinations the obligation of the head. In the event that the individual is a specialist, at that point he is the approved agent of the head and is in the work contract with the head. Each demonstration of the operator is authoritative on the head as he is going about according to the bearing of the head. Yet, in the event that the individual is a self employed entity, at that point he isn't working under the heading and control of the head and there is no business contract. The demonstrations of the contractual worker are free and the chief isn't considered responsible for the same.[10] References Andy Gibson, Douglas Fraser (2013) Business Law 2014, Pearson Higher Education AU. Forrester, Kim , Griffiths, Debra (2014) Essentials of Law for Health Professionals eBook. Elsevier Health Sciences. Laryea, Emmanuel (2002) Paperless Trade:Oppertunities, Challenges and Solutions, Kluwer Law International. Latimer, Paul (2012). Australian Business Law 2012. CCH Australia Limited. Case laws Gibson v Manchester City Council[1979]. Hadley v Baxendale[1854]. Nissan UK Ltd v Nissan Motor ManufacturingUK Ltd [1994]. Simkins v pays [1955] Williams v RoffeyBros Nicholls (Contractors) Ltd [1989]. Online Material Findlaw (2017) Is a verbal understanding legitimately authoritative? https://www.findlaw.com.au/articles/5626/is-a-verbal-understanding lawfully binding.aspx. [1] Kim Forrester, Debra Griffiths, (2014) Essentials of Law for Health Professionals eBook. Elsevier Health Sciences. [2] Gibson v Manchester City Council[1979]. [3] Nissan UK Ltd v Nissan Motor ManufacturingUK Ltd [1994]. [4] Williams v RoffeyBros Nicholls (Contractors) Ltd [1989]. [5] Hadley v Baxendale[1854]. [6] Emmanuel Laryea (2002) Paperless Trade:Oppertunities, Challenges and Solutions, Kluwer Law International. [7] Findlaw (2017) Is a verbal understanding legitimately authoritative? https://www.findlaw.com.au/articles/5626/is-a-verbal-understanding lawfully binding.aspx. [8] Paul Latimer (2012). Australian Business Law 2012. CCH Australia Limited. [9] Simkins v pays [1955], [10] Andy Gibson, Douglas Fraser (2013) Business Law 2014, Pearson Higher Education AU.

Work Experience for a College Admission Application TKG

Work Experience for a College Admission Application These days, there’s a lot of pressure on students to cultivate the right suite of extra-curriculars. Often times, kids join too many clubs or take on too many volunteer opportunities and miss the mark on demonstrating that they’ve committed to one area of expertise. But developing depth in an area doesn’t have to be limited to unpaid activity. In this post, we talk about how work experience can be a great addition to the resume. Should I Get a Job?A lot of people who come through our doors ask about whether or not paid work experience is a good idea. After all, kids are basically told that if they don’t have an internship with Bill Gates by the time they’re 10, they won’t be getting into the Ivy League. That’s only partially true. When applying to college, one of your primary objectives should be to connect with the person reading your application. Even though there’s not a whole lot you can assume about the anonymous admissions counselor assigned to your application, there are a few things you can infer. For one, they’re probably underpaid. As such, they will likely be sympathetic to a young person who is working to make some money. In terms of what looks good on the resume, we actually rank paid work right up there with taking a research position under a professor.   Scores of privileged kids who have gone on fancy “service” trips and high-end prep schools apply to top-tier colleges will submit applications. Working hard to earn money shows that you’re not, well, spoiled. Leveling the Playing Field  The other thing about working is that it’s not optional for a lot of students. Although more kids from various socio-economic backgrounds are attending college than they did in decades past, sharp rises in tuition, coupled with insanely competitive application rates, have widened the gap between kids from different income brackets. The kids who can afford fancy SAT tutors, and yes, private college counselors like us, have an advantage. B ut admissions counselors know that some students just don’t have those luxuries and actually have to work hard to help their families pay the bills. Students who do have to work typically gain real-world wisdom not available to them through joining clubs with their peers. That’s all good news. Showing growth and development through an extra-curricular is key. It also makes for great material to discuss in essays down the line. So, our advice is to get a job if you can. It will warm the admissions officer up to you and you will learn a lot of valuable lessons.  Need some help with your resume? Reach out to us here. We know what we’re doing when it comes to strategizing about extra-curriculars.

Eveline - 3513 Words

Historical background: Irish Social Conditions and Emigration Ireland has endured waves of emigration, particularly after1848. Many left their native land to seek a better life elsewhere. The Irish were second-class citizens within their own nation; Ireland was a British colony and the Northern Protestants controlled the economy of the country. Catholic families often faced hardship. Alcoholism and abuse, as portrayed in â€Å"Eveline† were rampant. As a result, many of the Irish sought to escape James Joyce represents everyday life of Dublin in the early twentieth century in his collection of short stories, Dubliners. Dubliners consists of 15 stories and each of them unfolds lives of many different Dubliners vividly. By describing details of†¦show more content†¦A bell clangs, and Frank tries to pull her on board, but Eveline clutches an iron railing on shore, feeling that he will drown her in the seas of the world. She cries out and grasps the railing tighter while Frank calls to her, and she turns her helpless face to him without a glimpse of love or farewell or recognition, staying on shore as the boat pulls away. Characters Frank 2 Frank is a sailor planning to move to Buenos Aires and take his lover Eveline with him. He has told Eveline he intends to marry her, which may well be the case, but Frank is a mysterious character and there is some implication that his intentions are devious. He started his sailing career on a trade route associated with exile and full of stories about infamously savage tribes from Argentina. Also, going to Buenos Aires was a slang term for prostitution, and the night boat to Liverpool may have been a reference to the mythological journey over the Styx river to the pagan underworld—both of which are implications that Frank might have no intention of marrying his lover, but instead is planning bring her into a situation she will find immoral. However, Frank is also described as kind, manly, open-hearted and is set up as Evelines only way to happiness, so he may indeed have only the best intentions in helping his lover to escape from her abusive household and difficult job. In fact, theShow MoreRelated Empty Spaces in James Joyces Eveline from Dubliners Essay1080 Words   |  5 Pagesclearly delineating his characters every feature, Joyce concentrates on hinting at the emotional meanings of his depictions with a rich thick dab of paint here and there. Although Joyce flexes his descriptive muscles in the Dubliners short story Eveline (1914,) he leaves much to the imagination of the reader through calculated omissions and suggestive phrases.    Such omissions begin at the opening of the story; She sat at the window watching the evening invade the avenue (Joyce 37). JoyceRead MoreEveline s Struggles By Eveline944 Words   |  4 PagesStruggles Although Eveline has to be the central life and the caretaker of her family’s home, she dwells on the past and fearing her life ahead of her. Eveline is seen as the woman in charge of the household. The narrator states, â€Å"Of course she had to work hard, both in the house and at business,† implying that she not only works hard around the home but also has a job where she earns her own money (Joyce). Eveline takes care of the home and has to keep it clean and together. Also, Eveline had been â€Å"treatedRead MoreEveline1643 Words   |  7 PagesIn â€Å"Eveline,† James Joyce uses the juxtaposition of the ever-changing setting and the unchanging stoic character of Eveline in order to exemplify the character’s reluctance and inability to move forward. James Joyce is known for his juxtaposition of light and dark throughout his short stories, specifically in his story â€Å"Araby.† I would argue that Joyce is using the contrast of opposing forces described above between the setting and the character in a similar way as he was light and dark. â€Å"Araby†Read MoreReflection Of Eveline1135 Words   |  5 PagesEveline In the short story â€Å"Eveline† by James Joyce, talks about a young woman who is around nineteen years of age that deals with a lot in life. As Eveline sits and gazes out the window one evening, she begins to think about her past and how it has been painful to her.   Growing up Eveline didn’t have the best family life. She had an abusive father who would always terrorize the family.   Before Eveline’s mother died, she told Eveline to make sure she watched after her brothers and to keep them safeRead MoreEveline Essay578 Words   |  3 Pagesthe short story Eveline by James Joyce, the title character Eveline is fearful of making a change in her life by moving with her boyfriend Frank from her homeland of Ireland and making a life with him in Buenos Ayres. Joyce illustrates that one of our most inherent qualities as humans and one that Eveline displays is that we are resistant to change. Through Evelines relationships with her father, Frank and various peripheral relationships, Joyce demonstrates to us how Eveline has come to haveRead MoreLiterary Analysis Of Eveline1019 Words   |  5 PagesJames Joyce’s â€Å"Eveline† is a short story about a nineteen-year-old Eveline, who contemplates abandoning a life she is accustomed to and moving to a distant land with a man she hardly knows. In one hand she holds the weight of uncertain happiness, in the other, inevitable misery. Eveline needs to make a choice between two contrasting lives; one in which she is a servant to her father, in other, a respected wife. Following her mother’s death, Eveline assumes the role of a parent and inherits all the Read MoreAnalysis Of The Novel Eveline 1069 Words   |  5 PagesIn Joyce’s, â€Å"Eveline†, most of the story is situated in the mind of the main character, Eveline. Eveline is characterized as passive, easily-influenced, and indecisive. Joyce highlights Eveline’s indecisiveness as she struggles with her immediate predicament; should she leave her abusive father and disobey her duty as a daughter, or pursue a new life with her potential husband Frank, to be free? As she contemplates, readers are taken inside Eveline’s mind to discover factors from her past and presentRead MoreChildhood Abuse In Eveline1128 Words   |  5 Pages James Joyces short story Eveline is set in Dublin, Ireland during the turn of the 20th century. The suffering was of the Irish was immense during this time in history, due to the struggle of against the English occupation of Ireland. An observation made about Dublin during the early 1900s was that â€Å"the Irish capita l is paralysed by Catholicism, by the English imperialism, by grave poverty and social injustice† (Boyson). Ireland was still reeling from the famine the occurred fifty yearsRead MoreCharacter Analysis Of Eveline1123 Words   |  5 PagesJames Joyce’s Eveline is a story of a woman dealing with the decision to stay at home with her father and the children she cares for while enduring abuse, or going out across the sea with her boyfriend Frank, who wishes to make Eveline his wife. Although Eveline s father had caused her strife through his abusiveness, she reflects on a time when she was younger and her mother was still alive and he was not that way. Eveline wonders what what they would say about her in the stores if she were to goRead MoreEveline Essay examples721 Words   |  3 Pages2012 Comparison of Eveline and Connie â€Å"Eveline† and â€Å"Where Are You Going, Where Have You Been† are similar stories set in different eras. â€Å"Eveline† is a short story written by James Joyce. â€Å"Where are you going, Where have you been† is a short story written by Joyce Carol Oates. Eveline and Connie are two teenage girls who are ultimately trapped by the influences of their cultures. The church plays a heavy influence on Eveline throughout the story. Eveline is conflicted on whether she

Alcohol Is Bad, But Prohibition Is Worst - 848 Words

Forbidden Fruit Alcohol is bad, but prohibition is worst. Why did not we learn that lesson during the 1920s? The consumption of alcohol is part of many reasons, mostly is used to celebrate, sometimes it can also be used in a melancholic state. Alcohol can be used to share with your food or being in a social environment sharing, or also it can be part of a religion. Drinking is fun, but it should be considered to do it in moderation. Alcohol drinking age limit should be lowered to the age of 18, because having a high age limit can cause many problem thinking that they’re actually being solved. The law of 21 and over drinking is seemed as a useless law, because the average American starts drinking under the age of 21. Most teenager’s drink alcohol as an act of rebellion, because as a young age alcohol is seen as the â€Å"forbidden fruit†. The prohibition for young adults to consume alcoholic beverages is the one causing the problem. The drinking age limit have many consequences for young adults. If at the age of 18 going to war and voting is allowed, drinking a beer should be allowed as well. The prohibition of alcohol drinking before 21 has led to rebellion, binge drinking and breaking the law with fake ID’s, building more problems, rather than solving the problem of â€Å"immature† drinking. The history of the United States in the 1920s shows that when alcohol was banned led to many street wars, crimes and many other illegal activities, if this did not work in the past, it should notShow MoreRelatedThe Volstead Act of 1920775 Words   |  3 Pagesadopted. They tried to convince people to stop drinking alcohol. It didn’t take much long after this, that the Woman’s Christian Temperance Union said that they would support the ban on drugs as well as alcohol. Then in 1893, the anti-Saloon League was formed. Not too much longer, they were a political power at making this ban on alcoh ol reality. Women were a major driving force on the prohibition of alcohol. Many of them stated that alcohol was a major driving force in ending lots of marriagesRead MoreEssay about Prohibition in the USA in 19191038 Words   |  5 PagesProhibition in the USA in 1919 Prohibition was introduced in 1919; however it is impossible to find one simple reason for why it was introduced. It was not a new idea as the movement had already begun in 1830. By 1914 over half of Americas states were dry. At one minute past midnight on January 16th 1920 the law against the sale and transportation of alcohol in America became law; however in 1917 the law had been passed by congress due to the eighteenth amendmentRead MoreProhibitionin the Twenties1600 Words   |  7 PagesProhibition In the roaring twenties the idea of a dry age was crossing the minds of many citizens in the states. During this time, the economy was starting to boom. As society was booming, the temperance movement started to cause problems in the system. Most people went along with the idea that drinking was bad and needed to be put to an end but they still wanted to drink. Other problems are brought up about all of the job loss that this prohibition would cause. Prohibition was created to reformRead More Prohibition Essay1362 Words   |  6 PagesHonors P. 1 Mrs. Robinson 4 May 2004 â€Å"Prohibition: The Noble Experiment† nbsp;nbsp;nbsp;nbsp;nbsp;â€Å"Prohibition, sometimes referred to as the noble experiment, did not achieve its goals. It did the exact opposite by adding to the problems that it was intended to solve† (Thorton). It is also considered to be the thirteen years that damaged America. On January 16, 1920 one of the most disobeyed laws was put into effect. The 18th amendment, also known as Prohibition, was ineffective and caused more corruptionRead MoreHow Prohibition Affected Russia s Financial Crisis During Russian Revolution1228 Words   |  5 PagesKetevan Kemoklidze Mr. Hermansen English Composition 06/01/2016 How Prohibition affected Russia’s Financial Fiasco During Russian Revolution? Amid Russian Revolution years there is the chance to watch the Russian economy experiencing a few basic moves, including a portion of the most exceedingly bad things that can happen to a nation. There was war and civil war. The economy endured monetary breaking down, separation, and starvation. There was a breakdown of state limit: government prohibited VodkaRead MoreEssay on Life Changes of Americans in the 1920s568 Words   |  3 PagesChanges of Americans in the 1920s In the 1920s many American lives were improved greatly, but some lives were as bad as they had been before. The economy was booming, with cars being mass produced, and many other consumer goods such as radios, were widely available. Also more jobs became available, and many people recieved a par rise. However there were bad things such as racism about. Many ethnic minority groups were treated poorly. The most racist group around was theRead MoreEssay about Marijuana Should Be Legalized1628 Words   |  7 Pages   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   In a country where tobacco products and alcohol are legal, I have always wondered, why not cannabis?   Why did this plant still have the stigma of being illegal when it does not cause any deaths, is not nearly as physically addicting, nor as harmful as its legal counterparts?   Clearly, the law of marijuana prohibition is one that is up for debate and one that is up for change.  Ã‚   Currently, many state laws have been passed that are either decriminalizing marijuana or allowing it forRead More Cultural Context: Alcohol Essay2143 Words   |  9 PagesCultural Context: Alcohol Alcohol has always been a controversial topic in the United States for social, political, and religious reasons. The negative effects of drinking came to the foreground of American concern during the early twentieth century. This was a time of great prosperity followed by the Great Depression. Both of these eras led Americans to turn to or against liquor as the cause or demise of their success. Prohibition marked a change in the American way of life and is bestRead MoreThe Start of Gangsterism/ Organized Crime because of Prohibition1984 Words   |  8 PagesProhibition, the greatest thing that has happened, was what most â€Å"dry† people thought. Yes, prohibition did stop a lot of people from consuming alcohol. Prohibition helped turn some â€Å"wets†, people who consumed alcohol, into â€Å"drys†, which were individuals that did not consume alcohol. Unfortunately, there was a huge downside to prohibition. Throughout the times of prohibition, the rate of ga ng activity that was involved in daily life rose dramatically due to the desire to obtain alcohol despite theRead MoreThe Great Depression And Dust Bowl2250 Words   |  9 Pagesthese two bookend events. During the best of the decade there was economic boom, the Harlem Renaissance, improved women s rights, and the ending of the captains of industry era. On the other hand, there was the Great Depression, Dust Bowl, and Prohibition which were viewed very negatively due to the intense effect they had on the entire country. The decades leading up to the 1920s set the ground work for a lot of the best parts of the 20s, specifically the economic boom. Starting with the creation

The Universal Human Rights Of The United Nations - 873 Words

The Universal Human Rights: From Paper to Reality According to the Office of High Commissioner of Human Rights of the United Nations, â€Å"human rights are rights inherent to all human beings, whatever our nationality, place of residence, sex, national or ethnic origin, color, religion, language, or any other status. We are all equally entitled to our human rights without discrimination. These rights are all interrelated, interdependent and indivisible† (United Nations Human Rights). In other words, universal Human Rights are basic rights and â€Å"fundamental freedom,† which are widely acceptable, that every individual should have. The detailed list of human rights is the Universal Declaration of Human Rights adopted by the United Nations in 1948. The list has a preamble and 30 articles, including several fundamental rights and freedom of human such as right to life, liberty, and security; right to be equal before law; right to marriage; right to education; right to nationality; and right to property. As stated on th e United Nations’ website, the concept of human rights was formally developed in 1946, right after the Word War II and the creation of the United Nations. From that time to December 10, 1948, the world leaders discussed and made a list of basic human rights which they believe should be guarantee for every individual everywhere. The first draft of the list of Human Rights, or the Universal Declaration of Human Rights was conducted by leaders of countries thatShow MoreRelatedThe United Nations Universal Human Rights Essay1657 Words   |  7 PagesThe United Nations’ Universal Declaration of Human Rights stands as the current gold standard for every individual’s rights. Focusing on culture, one may see that cultural rights are not clearly defined and are oftentimes in conflict with other types of rights. In this paper, I will first discuss the United Nations’ use of ‘cultural’ in its universal human rights in relation to the concept of cultura l relativism. Then, using South African and American practices, such as virginity testing and discriminatoryRead MoreThe Rights Of The United Nations Universal Declaration Of Human Rights870 Words   |  4 PagesAll human beings are born with rights no matter a person’s race, religion, or gender. There are 30 of rights found in the Universal Declaration of Human Rights (UDHR). Under the UDHR there are 30 rights given to humans that were created to stop war from happening among people. These rights should have the power to prevent war from happening by giving every human life importance. Everyone has the same human rights shows all lives matter and are important and should be respected. Three human rightsRead MoreThe United Nations Universal Declaration Of Human Rights1805 Words   |  8 PagesIn accordance with the United Nations Universal Declaration of Human Rights (UDHR) it is proclaimed by the General Assembly that â€Å"all human beings are born free and equal in dign ity and rights† (The United Nation [UN], 1948). But what are human rights? While they might be a substantially contemporary subject, the worlds first charter of human rights is now identified in 593 B.C when Cyrus the Great; freed the slaves, established racial equality and freedom to choose one’s own religion (Fleiner, 1999)Read MoreThe United Nations Universal Declaration Of Human Rights1854 Words   |  8 PagesThere are many arguments that there will soon be a Third World War. World Wars I and II have been instigated by nations wanting to rule parts of the world. The Islamic State in Iraq and Syria (ISIS) has caused many fights and controversy all around the world, possibly igniting World War III. 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My Romeo and Juliet Essay Example For Students

My Romeo and Juliet Essay Romeo and Juliet Married Happily Ever-After?!?Many will speculate about this question, others may guess., but you have to look at the facts in order to correctly judge these two young lovers fate. Let us start with the basics in solving this equation and some information about the characters. Romeo and Juliet have married, but what are the chances that they will live happily ever-after? RomeoJulietMONTAGUE- his father CAPULET- her fatherLADY MONTAGUE- his motherLADY CAPULET- her motherBENVOLIO- their kinsman NURSE to JulietABRAM- a Montague servingmanTYBALT- kinsman to the CapuletsBALTHASAR- Romeos servingmanPERCRUTIO- Tybalts companionMontagues and CapuletsBoth have their differencesBoth really hate each otherBut you know what they say about opposites dont you? Well this is a good example of that never forgotten theory. They were like a magnet and a paperclip when they first met each other, both have never seen anyone more beautiful than each other in their lives! It was love at first site. But Romeo has had his troubles with girls in the past. He has just gotten out of a terrible relationship with a Montague named Rosaline, she told him that she didnt loved him any more. This, of coarse, broke his heart. Romeos friends try to get him to find another girl and be free of this depression, so they go to a Capulets masquerade party disguised with their masks. There he meets the ever-so beautiful Juliet. Aahh yes, Juliet, she is as beautiful as the sun as Romeo says. Oh, but Juliet is having a little bit of trouble too. She is getting pressured by his family to start thinking about marrying someone and doing this, and doing that.she feels very confused right now. Her mom wants her to marry a man named Paris, but she really doesnt know yet Anyways, they meet in a masquerade party and they really like each other. They like each other so much that they really dont care that they are from different households. Later after the party, they meet each other again under Juliets balcony and decide to secretly get married the next day by a man named Friar Lawrence. Lawrence thinks that this marriage will finally bring the feuding families togetherThere, now you know the facts, but you must understand the hate that these two families have for each other. They have had many fights in the streets of Verona that Prince Escalus says that if they fight again, that he will kill them. Tybalt wants to kill Romeo and Juliet doesnt want to marry Paris, but Paris doesnt know that, so if he finds out about this secret love of hers, he will be outraged. Tybalt doesnt want Romeo around any more, and this hate may cause a conflict that might get someone killed. Friar Lawrence thinks that this is a good idea for them to get married because he thinks that this will end the feud between the families. So much can happen in a short amount of time that may end the relationship quicker than it started.Words/ Pages : 513 / 24

Flight Control Systems free essay sample

Assessment †¢ 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 contr ol 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. McLean. 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 longitudinal 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 ? rs t 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 stabilit y 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 gt; 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 as 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. 2 2) and (2. 46). 2. 3. 1 Numerical example Boeing 747 jet transport 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 Derivativesà ¢â‚¬â€œ 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 variables, di? rent A, B and C are resulted (see Tutorial 1). 2. 4 Aircraft dynamic behaviour simulation using state space models State space model develo ped 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 described 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) 400 500 600 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 technique 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 denominator, 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 de nominators 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 modes Aircraft 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 engineering. 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 control 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 th e 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 models 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 CHAP TER 2. LONGITUDINAL RESPONSE TO THE CONTROL Beoing 747 Short period mode From: U(1) 0. 7 0. 6 0. 5 0. 4 Perturbation 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 relatively 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 o f 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 substituting 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 those 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 ? an d 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 displacement. 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 Engineering (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 are 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 rudder Numerical 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, given 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 function 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. 5 613, 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 and takes quite long time to respond. The Dutch rol l 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 give 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 mode. Hence p = v = r = 0 and the ? ? ? lateral dyna mics 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 constant 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 with 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 dynamics The 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 equation. 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.

American Revolution - Early Campaigns of the American Revolution

American Revolution - Early Campaigns of the American Revolution Previous: Causes of Conflict | American Revolution 101 | Next: New York, Philadelphia, Saratoga Opening Shots: Lexington Concord Following several years of rising tensions and the occupation of Boston by British troops, the military governor of Massachusetts, General Thomas Gage, began efforts to secure the colonys military supplies to keep them from the Patriot militias. These actions received official sanction on April 14, 1775, when orders arrived from London commanding him to disarm the militias and to arrest key colonial leaders. Believing the militias to be hoarding supplies at Concord, Gage made plans for part of his force to march and occupy the town. On April 16, Gage sent a scouting party out of the city towards Concord which gathered intelligence, but also alerted the colonials to British intentions. Aware of Gages orders, many key colonial figures, such as John Hancock and Samuel Adams, left Boston to seek safety in the country. Two days later, Gage ordered Lieutenant Colonel Francis Smith to prepare a 700-man force to sortie from the city. Aware of British interest in Concord, many of the supplies were quickly moved to other towns. Around 9:00-10:00 that night, Patriot leader Dr. Joseph Warren informed Paul Revere and William Dawes that the British would be embarking that night for Cambridge and the road to Lexington and Concord. Departing the city by separate routes, Revere and Dawes made their famous ride west to warn that the British were approaching. In Lexington, Captain John Parker gathered the towns militia and had them form into ranks on the town green with orders not to fire unless fired upon. Around sunrise, the British vanguard, led by Major John Pitcairn, arrived in the village. Riding forward, Pitcairn demanded that Parkers men disperse and lay down their arms. Parker partially complied and ordered his men to go home, but to retain their muskets. As his men began to move, a shot rang out from an unknown source. This led to an exchange of fire which saw Pitcairns horse hit twice. Surging forward the British drove the militia from the green. When the smoke cleared, eight of the militia were dead and another ten wounded. One British soldier was injured in the exchange. Departing Lexington, the British pushed on towards Concord. Outside of the town, the Concord militia, unsure of what had transpired at Lexington, fell back and took up a position on a hill across the North Bridge. The British occupied the town and broke into detachments to search for the colonial munitions. As they began their work, the Concord militia, led by Colonel James Barrett, was reinforced as other towns militias arrived on the scene. A short time later fighting broke out near the North Bridge with the British being forced back into the town. Gathering his men, Smith began the return march to Boston. As the British column moved, it was attacked by colonial militia which took up concealed positions along the road. Though reinforced at Lexington, Smiths men continued to take punishing fire until they reached the safety of Charlestown. All told, Smiths men suffered 272 casualties. Rushing to Boston, the militia effectively placed the city under siege. As news of the fighting spread, they were joined by militia from neighboring colonies, ultimately forming an army of over 20,000. The Battle of Bunker Hill On the night of June 16/17, 1775, colonial forces moved onto the Charlestown Peninsula with the goal of securing high ground from which to bombard British forces in Boston. Led by Colonel William Prescott, they initially established a position atop Bunker Hill, before moving forward to Breeds Hill. Using plans drawn by Captain Richard Gridley, Prescotts men began constructing a redoubt and lines extending northeast towards the water. Around 4:00 AM, a sentry on HMS Lively spotted the colonials and the ship opened fire. It was later joined by other British ships in the harbor, but their fire had little effect. Alerted to the American presence, Gage began organizing men to take the hill and gave command of the assault force to Major General William Howe. Transporting his men across the Charles River, Howe ordered Brigadier General Robert Pigot to directly attack Prescotts position while a second force worked around the colonial left flank to attack from behind. Aware that the British were planning an attack, General Israel Putnam dispatched reinforcements to Prescotts aid. These took up a position along fence which extended to the water near Prescotts lines. Moving forward, Howes first attack was met my massed musket fire from the American troops. Falling back, the British reformed and attacked again with the same result. During this time, Howes reserve, near Charlestown, was taking sniper fire from the town. To eliminate this, the navy opened fire with heated shot and effectively burned Charlestown to the ground. Ordering his reserve forward, Howe launched a third attack with all of his forces. With the Americans nearly out of ammunition, this assault succeeded in carrying the works and forced the militia to retreat off the Charlestown Peninsula. Though a victory, the Battle of Bunker Hill cost the British 226 killed (including Major Pitcairn) and 828 wounded. The high cost of the battle caused British Major General Henry Clinton to remark, A few more such victories would have shortly put an end to British dominion in America. Previous: Causes of Conflict | American Revolution 101 | Next: New York, Philadelphia, Saratoga Previous: Causes of Conflict | American Revolution 101 | Next: New York, Philadelphia, Saratoga The Invasion of Canada On May 10, 1775, the Second Continental Congress convened in Philadelphia. A month later on June 14, they formed the Continental Army and chose George Washington of Virginia as its commander-in-chief. Traveling to Boston, Washington took command of the army in July. Among Congress other goals was the capture of Canada. Efforts had been made the previous year to encourage French-Canadians to join the thirteen colonies in opposing British rule. These advances were rebuffed, and Congress authorized the formation of the Northern Department, under Major General Philip Schuyler, with orders to take Canada by force. Schuylers efforts were made easier by the actions of Colonel Ethan Allen of Vermont, who along with Colonel Benedict Arnold, captured Fort Ticonderoga on May 10, 1775. Located at the base of Lake Champlain, the fort provided an ideal springboard for attacking Canada. Organizing a small army, Schuyler fell ill and was forced to turn command over to Brigadier General Richard Montgomery. Moving up the lake, he captured Fort St. Jean on November 3, after a 45-day siege. Pressing on, Montgomery occupied Montreal ten days later when Canadian governor Major General Sir Guy Carleton withdrew to Quebec City without a fight. With Montreal secured, Montgomery departed for Quebec City on November 28 with 300 men. While Montgomerys army had been attacking through the Lake Champlain corridor, a second American force, under Arnold moved up the Kennebec River in Maine. Anticipating the march from Fort Western to Quebec City to take 20 days, Arnolds 1,100-man column encountered problems shortly after departing. Leaving September 25, his men endured starvation and disease before finally reaching Quebec on November 6, with around 600 men. Though he outnumbered the citys defenders, Arnold lacked artillery and could not penetrate its fortifications. On December 3, Montgomery arrived and the two American commanders joined forces. As the Americans planned their attack, Carleton reinforced the city raising the number of defenders to 1,800. Moving forward on the night of December 31, Montgomery and Arnold assaulted the city with the latter attacking from the west and the former from the north. In the resulting Battle of Quebec, American forces were repulsed with Montgomery killed in action. The surviving Americans retreated from the city and were placed under the command of Major General John Thomas. Arriving on May 1, 1776, Thomas found American forces weakened by disease and numbering fewer than a thousand. Seeing no other choice, he began retreating up the St. Lawrence River. On June 2, Thomas died of smallpox and command devolved to Brigadier General John Sullivan who had recently arrived with reinforcements. Attacking the British at Trois-Rivià ¨res on June 8, Sullivan was defeated and forced to retreat to Montreal and then south towards Lake Champlain. Seizing the initiative, Carleton pursued the Americans with the goal of reclaiming the lake and invading the colonies from the north. These efforts were blocked on October 11, when a scratch-built American fleet, led by Arnold, won a strategic naval victory at the Battle of Valcour Island. Arnolds efforts prevented a northern British invasion in 1776. The Capture of Boston While Continental forces were suffering in Canada, Washington maintained the siege of Boston. With his men lacking supplies and ammunition, Washington turned down several plans for assaulting the city. In Boston, conditions for the British worsened as winter weather approached and American privateers hampered their re-supply by sea. Seeking advice to break the stalemate, Washington consulted artilleryman Colonel Henry Knox in November 1775. Knox proposed a plan for transporting the guns captured at Fort Ticonderoga to the siege lines at Boston. Approving his plan, Washington immediately dispatched Knox north. Loading the forts guns on boats and sledges, Knox moved 59 guns and mortars down Lake George and across Massachusetts. The 300-mile journey lasted 56 days from December 5, 1775 to January 24, 1776. Pressing through severe winter weather, Knox arrived at Boston with the tools to break the siege. On the night of March 4/5, Washingtons men moved onto Dorchester Heights with their newly acquired guns. From this position, the Americans commanded both the city and the harbor. The next day, Howe, who had taken command from Gage, decided to assault the heights. As his men prepared, a snow storm rolled in preventing the attack. During the delay, Howes aids, remembering Bunker Hill, convinced him to cancel the assault. Seeing that he had no choice, Howe contacted Washington on March 8 with the message that the city would not be burned if the British were allowed to leave unmolested. On March 17, the British departed Boston and sailed for Halifax, Nova Scotia. Later in the day, American troops triumphantly entered the city. Washington and the army remained in the area until April 4, when they moved south to defend against an attack on New York. Previous: Causes of Conflict | American Revolution 101 | Next: New York, Philadelphia, Saratoga

Research Paper on the Beatles Example | Topics and Well Written Essays - 750 words

On the Beatles - Research Paper Example In November of 1960, they met the rock and roller Tony Sheridan, and they became friends. The next year, they met again and this time they performed a song together, â€Å"My Bonnie†, which was really, their coming-out song, so to speak, because performing this song brought them to the attention of Brian Epstein. He was a music entrepreneur and he became their manager. Epstein worked on getting them a record deal and label, but they got rejected by almost every British record company (Spitz, 15-20). One day, Epstein persuaded George Martin to listen to a recording the Beatles had done, and after convincing him that they would one day become very famous, he signed them on with Parlophone. They released their first eight albums with Parlophone. In August of 1962, Pete Best left the Beatles and he was replaced by Ringo Starr as the drummer. He also contributed as a vocalist on a number of successful songs. In January 11, 1963, The Beatles released â€Å"My Bonnie† which wa s an instant hit, and Beatlemania began in England (The Beatles, 23-35). After this, there was almost a non-stop series of concerts and tours for about a year. This was the year for the Beatles. Everybody was talking about them, they were everywhere. They got intense media interest. They had TV shows, press interviews, and a weekly radio show. They appeared on ABC’s TV show â€Å"Thank Your Lucky Stars†, they were on BBC’s Here We Go, and many others. They were literally on the show every day. That year, they had four nationwide tours; they would finish one show and leave immediately for another, or even do two shows in one day. Two of the four tours were led by American Stars, but at almost every show during them, the crowd was wild for the Beatles, which made the Beatles to be embarrassed for the American singers (The Beatles, 37-39). The Beatles hit the United States the next year, early 1964. However, weeks before their arrival, the fateful assassination of President John F. Kennedy took place, and the nation was in grief. This was a critical time in American history, and it affected many Americans, many of whom were the youth. The Beatles wanted to be able to reach out to them through their music. In the span of the next few days they flew over Miami, where they spent time with Ed Sullivan again and got to catch up with him. On the 22nd of February, they left America victorious and arrived at Heathrow Airport, where again they were met by thousands of fans. The same year, the Beatles went back again to America for yet another tour, this time much longer. They performed thirty concerts in twenty three cities, attracting thousands of fans, making millions of dollars, and paving the way for other British groups to wow America (Davies, 15-19). The next year, 1965, Beatlemania still continued on and after having attending a premiere of their film, â€Å"Help†, they went back to America to Shea Stadium where they had their biggest co ncert, attended by fifty five thousand fans. After that successful concert, they met with Elvis Presley and after, flew back to the UK (Miles, 24-25). The next year was one that proved to be rough for the Beatles. Lead singer John Lennon was interviewed where he said â€Å"We are bigger than Jesus. Christianity will vanish and shrink; I don’t know what will go first, rock and roll or Christianity.† The British people didn’t say much of it, but the Americans were shocked. It ignited a lot of anger and hostility and the Beatles were