-----anything you want------ Research Paper Example | Topics and Well Written Essays - 1750 words

-----anything you want------ - Research Paper Example However, this act has done more harm to the lives of American citizens than good. There is no doubt that the U.S. Patriot Act intrudes upon the privacy of Americans, promotes censorship, initiates racial profiling, and lastly takes the issue of national security too far. First, the U.S. Patriot Act is unconstitutional because it intrudes upon the privacy of American citizens by violating their First and Fourth Amendment rights. The nature of the U.S. Patriot Act is an issue that still remains a mystery as Congress quickly passed the bill without much debate (Cornhels 1). The bill itself contains four hundred laws and expands the definition of â€Å"terrorism† drastically (Cassell 13). The First Amendment rights of freedom of speech along with freedom to assemble are rights that most Americans hold dear to their lives, but now actions such as civil disobedience, and protests, are now being defined as domestic terrorism under this legislation (Cornhels 2). A sixty-two year old e lderly man found his rights to be jeopardized as he was arrested based on his beliefs about the bombings in Afghanistan (Cassell 6). Under the Patriot Act, a clause known as Section 215 terrorizes Americans because it breaks the 4th and 5th Amendment, which ensures the privacy of individuals (â€Å"Reform the Patriot Act† 2). ... It was clear that these initiatives were an â€Å"all-out attack† against the American public itself. Peter Swire, a professor at Ohio University, reports that FBI officials are putting pressure on telecommunication companies to turn over records (Chang 49). Already concerns have been raised by the public whether sharing the information with federal agencies and local police is legal (Cassell 26). As Jim Edwards puts it, â€Å"The Patriot Act is already having a chilling effect, even in the areas where it does not apply† (Edwards 1). This law, however, does not affect US citizens only; in fact, the Canadian government has also passed legislation to â€Å"protect† its citizens. In Canada, a law has been created that prevents any public institution to store any private information in the U.S. (â€Å"Reform the Patriot Act† 1). Even Universities in Canada are striving to protect their students’ private information from USA (â€Å"Reform the Patriot Ac t† 2). Nova Scotia and B.C. legislations have set strict guidelines on public institutions when it comes to sharing information with companies outside the USA (â€Å"Reform the Patriot Act† 1).Therefore, the U.S. Patriot Act is unconstitutional because it violates the constitutional given rights of Americans. Secondly, the Patriot Act is unconstitutional because it promotes censorship. Section 215 in the U.S. Patriot Act is a fatal blow on libraries because it allows government to see records of a person’s checkout list (Smith 96). What is even worse is that the individual has no clue whether Section 215 has been used on him since the libraries can not disclose any information (Smith 98). A survey conducted in December 2001 by University of

The Things They Carried Analysis Essay Example for Free

The Things They Carried Analysis Essay The purpose of this paper is to introduce, discuss, and analyze the novel The Things They Carried by Tim OBrien.   Specifically it will contain a brief analysis of the first chapter of the book.   OBriens use of metaphors of weight and lightness throughout the story develops the readers understanding of the situation the soldiers in the story find themselves in. Author OBrien fought in Vietnam and so he writes about the men and the war from experience, and it shows in this moving novel.    The opening chapter, The Things They Carried, introduces the men, and allows the reader a glimpse into the real, everyday war these young men fought in Vietnam.   Twice within the first few pages OBrien talks about the death of Ted Lavender while contrasting his death with the lightness of the things he carried with him in his rucksack. OBrien uses the metaphor of humped to show the weight of the things the soldiers carry, but he also uses it to show the emotional baggage they carry with them into the war, such as Jimmys Cross unreturned love for Martha back home.   OBrien writes of Jimmys love, Almost everyone humped photographs.   In his wallet, Lieutenant Cross carried two pictures of Martha (OBrien 4).   Later, he uses the metaphor again when he writes of Lieutenant Cross responsibility to his men. He writes, He carried a strobe light and the responsibility for the lives of his men (OBrien 5).   OBrien makes the weight of these responsibilities seem light, but uses the metaphor to show how weighty they really are.   Clearly, Cross quite understands the weight of his responsibility, and he does not take it lightly.   He knows his men trust him with their lives, and if he makes the wrong decision his men could pay the ultimate cost, they could give up their lives because he makes a mistake.   And that is the ultimate weight that rests on Lieutenant Cross, and it is much heavier than his rucksack. OBrien spends a lot of time on the guns and ammo they carried and the weight of these items.   That is because the soldiers lives depend on these items, which gives them additional weight in the story.   Showing the amount of ammo and other items they carry also shows their fear and some of the conditions they faced as soldiers in Vietnam.   Their situation is far from light, it is very heavy, and they know it. Any of them could die at any moment.   The Vietnamese knew the jungles and the terrain and the Americans did not.   They could be surprised and ambushed at any time.   OBrien shows the soldiers fear in the large amount of weapons and ammo they carry, and also shows they do not actually mean much.   Ted Lavender dies carrying more ammo than anyone else, so the weight of the ammo did nothing to help him save his own life.   That is the fear all the men face – that they have no control over the situation around them, and any of them could die, just like Lavender did. Most important of the things they carry is the weight of memory OBrien talks about in the chapter and notes that is one weight they share.   They cannot forget many of the horrible things they have seen, or that they could be the next one.   They cannot forget their situation because it is the only reality they know for now. That is also too weighty for some of them, so they make jokes about their predicament and try to escape by drinking, using drugs, or thinking about memories back home.   Jimmy Cross has his false memories of Martha that he carries with him, and all the others have memories of something, too.   These memories can weigh the men down if they let them.   Cross thinks his memories helped get Lavender killed because he was not paying attention. OBrien also uses descriptive language to show their surroundings.   He writes, They carried the sky.   The whole atmosphere, they carried it, the humidity, the monsoons, the stink of fungus †¦ (OBrien 15).   OBrien puts the reader right into the jungle with the men.   Using metaphor, description, and language, he makes the reader feel the fear of the men and feel as if they know and understand these men and the things they carry.    References OBrien Tim. The Things They Carried

The History Of Lsd And Its Effects On The American Counterculture Essay

After World War II ended, the age of baby-booming and urban sprawling began. During this time, many American soldiers came home from the war; married, and had five or six children. This created the largest generation ever. Could this new generation change the social world of America? In 1964, most of the baby-boomer's children were in their late teens. This was the beginning of a major social change in the United States. With the birth of rock-n-roll not far in the past, and a growing liberalism of the normally conservative American Society, it is no wonder that a powerful hallucinogenic drug called LSD gained so much popularity. LSD-25 was first created in 1938 by Albert Hoffmann in the Sandoz chemical-pharmaceutical laboratories in Basle, Switzerland. It was synthesized from the twenty-fifth compound of Iysergic acid. When first tested on animals, scientists had no idea that the powerful chemical had such psychedelic properties until Albert Hoffmann himself, involuntarily tested the new chemical. This "involuntary" testing of the LSD is the first time it was ever tested on a human subject; it was a result of Hoffmann accidentally intoxicating himself with LSD-25 during a routine purification process with the chemical.(3) After the experience, Hoffmann wrote: "Last Friday, April 16, 1943, I was forced to stop my work in the laboratory in the middle of the afternoon and to go home, as I was seized by a peculiar restlessness associated with a sensation of mild dizziness. On arriving home, I lay down and sank into a kind of drunkenness, which was not unpleasant and which was characterized by extreme activity of the imagination. As I lay in a dazed condition with my eyes closed, (I experienced daylight as disa... ...lso considered to be very inspirational to the hippies. Alan Ginsberg, a popular beat poet was a favorite of many hippies. Rock and folk music were also big contributors to this new movement. (2) In my opinion, the one thing that gave the most inspiration to the counterculture movement, beyond everything else, is the nationwide recreational use of LSD. LSD opened up the minds of the American youth, prompting them to explore life beyond the norms of society. It made people think critically about the information that is fed to us by the establishment. LSD was the tool to see through all the propaganda of the American capitalist's, and see the truths. The truth is what sparked many young people of this time period to stand up for their beliefs. Drugs like LSD seemed to be a good way to cure ones self from the brainwashing of American media and corporate bureaucracies. The History Of Lsd And Its Effects On The American Counterculture Essay After World War II ended, the age of baby-booming and urban sprawling began. During this time, many American soldiers came home from the war; married, and had five or six children. This created the largest generation ever. Could this new generation change the social world of America? In 1964, most of the baby-boomer's children were in their late teens. This was the beginning of a major social change in the United States. With the birth of rock-n-roll not far in the past, and a growing liberalism of the normally conservative American Society, it is no wonder that a powerful hallucinogenic drug called LSD gained so much popularity. LSD-25 was first created in 1938 by Albert Hoffmann in the Sandoz chemical-pharmaceutical laboratories in Basle, Switzerland. It was synthesized from the twenty-fifth compound of Iysergic acid. When first tested on animals, scientists had no idea that the powerful chemical had such psychedelic properties until Albert Hoffmann himself, involuntarily tested the new chemical. This "involuntary" testing of the LSD is the first time it was ever tested on a human subject; it was a result of Hoffmann accidentally intoxicating himself with LSD-25 during a routine purification process with the chemical.(3) After the experience, Hoffmann wrote: "Last Friday, April 16, 1943, I was forced to stop my work in the laboratory in the middle of the afternoon and to go home, as I was seized by a peculiar restlessness associated with a sensation of mild dizziness. On arriving home, I lay down and sank into a kind of drunkenness, which was not unpleasant and which was characterized by extreme activity of the imagination. As I lay in a dazed condition with my eyes closed, (I experienced daylight as disa... ...lso considered to be very inspirational to the hippies. Alan Ginsberg, a popular beat poet was a favorite of many hippies. Rock and folk music were also big contributors to this new movement. (2) In my opinion, the one thing that gave the most inspiration to the counterculture movement, beyond everything else, is the nationwide recreational use of LSD. LSD opened up the minds of the American youth, prompting them to explore life beyond the norms of society. It made people think critically about the information that is fed to us by the establishment. LSD was the tool to see through all the propaganda of the American capitalist's, and see the truths. The truth is what sparked many young people of this time period to stand up for their beliefs. Drugs like LSD seemed to be a good way to cure ones self from the brainwashing of American media and corporate bureaucracies.

Choose the Right Path in Life Essay

Damion Booker is a 6’5 point guard from Rialto, California that is supposedly the best point guard since Magic Johnson. Magic Johnson was an incredible athlete he was versatile, had basketball IQ, he averaged a double double, and most of all a leader on the court. Damion Booker followed those same exact aspects. Damion Booker was the first round draft pick and was drafted to Los Angles Hokies and previously went to Rialto State University (RSU). Damion Booker majored in Business and had a GPA of 3.9. Not only did he have great athleticism and skill, he was intelligent. He made honor roll every year and challenged himself more and more. Every teacher loved him and was very popular around campus. He was also involved in many activities such as karate, played piano, and volunteered at a senior citizen home a couple of hours every summer break. While being involved in many activities he met a guy named Elijah Hearth. Elijah Hearth was a good friend, but also a troublemaker. In addition, while Damion Booker was hanging out with his friend Elijah Hearth he met a new agent and felt he was fit for the job. His first agent was unreliable and not trustworthy. A few days later Damion Booker got a call saying there was an NBA Lockout while at home. His agent said he didn’t have an idea when the new season was going to begin. He was very shocked and heartbroken, He couldn’t believe it. Damion Booker had to find some way to make money so he decided to own a business that he’s been attempting since he was a senior in college. Damion Booker was bored so he became more involved. A few weeks later his resteraunt opened it was named Damion Booker Palace. He made big bucks and had a lot of money. As a result, he became very cocky in everything he did. It took a lot of his time to owning that restaurant. He took time away from basketball to put in work to own the Palace. He had earned money twice as fast as regular people who started their business. For most people it takes years to own a business, but for Damion Booker it took him a month. The background behind that was that he made this special sauce that attracted people all over the world. Damion Booker made a tasty, scrumptious sauce that was called the Damion Cold Killer Pasta Sauce. It was supposedly the best sauce nationwide and it’s the bestseller at Damion Palace. It attracted wild, bizarre eaters like Andrew Zimmern. The pasta sauce was so good Andrew Zimmern said it was the best pasta he ever tasted. As a result, to the Cold Killer Pasta Sauce it did have a secret ingredient. The secret ingredient was this famous pepper that came from Peruvia. It was called the Peruvian Puff Pepper. The Puff Pepper had this special flavor that made ingredients spicier and more flavorful. The sauce also had extra amounts of salt and other excessive ingredient but the extra salt and the puff peppers are the ones that made the sauce taste better and more addicting. The sauce became so addicting that it made skinny people fat and the fat people become fatter. The sauce is sort of in comparison to a big mac from McDonald’s. Lots of people bought it and it was very addicting. The Puff Pepper had a special element that made you beg for more and more. Damions Palace put many businesses on bankrupt because of how good their specialty was. The only business that remained standing were McDonald’s, Jack in the Box, Carls Jr, Taco Bell, Applebee’s, Panda Express, and Denny’s but th ey were losing the average customers because Damion Palace was taking over because of their special pasta sauce. They were also losing money to in which that was a bad thing and tried putting more advertisements onto TV commercials, radios, billboards, and blimps. People didn’t care to much about the advertisement of TV commercials, blimps, billboards, and radios all the people cared about was Damions Palace and their special pasta sauce. Damion Booker came up with the idea on one boring weekend and decided to cook. All of a sudden, he came up with making pasta sauce because that was his mother’s favorite thing to eat while she was young and she would make it on special occasions. He went into his cabinet and pulled things such seasonings such as salt and pepper, and all kinds of sauces that his mom had stored. Then, Damion pulled out a bowl and started mixing a concoction. He tasted a couple of mixes and didn’t like them to well. After a couple of more mixes he tasted a delightful sauce that he believed tasted quite amusing. They didn’t have much because they Damion’s mom didn’t make much money. They weren’t poor but they weren’t fortunate. After tasting the sauce he knew he was going to become successful in the future. While doing this he realized he needed a backup plan for when the NBA comes out of its lockout. His backup was to have his brother take over Damion Palace when the NBA lockout ends. By the time Damion got settled to being a business owner the lockout had ended and it was time for Damion to start basketball again. The first couple of weeks the Palace ran very smoothly. At one point they had more customers than ever recorded. Damion was getting settled with basketball and his brother was taking over the best restaurant in the nation. Life couldn’t get any better for the Booker family! As life ran smoothly they became extremely arrogant until a fire burned down the Palace. Damion was gloomy and felt like a complete failure, but still confident. Although the palace burned down, Damion didn’t know the place was burned down until the all-star break he checked in and called his brother to ask how the restaurant was running. Damion brother told him the place got burned down. Damion was furious! Damion’s Brother didn’t want to interfere with Damion’s basketball career. Their relationship was corrupted and didn’t talk to one another for a long time. They constantly would argue and have many quarrelsome disagreements. When The Bookers lost their restaurant, they became unfortunate again and were very depressed. Their family began to go on corners and beg for money for a living but not for very long. They were going through some tough times but they always overcome the tough situations. By the time the Bookers started making more money Damion had started preseason basketball with the Los Angles Hokies. He was a star on his team like the whole world already suspected. To modern times Damion Booker came to the NBA similar to Kyrie Irving. Kyrie Irving was a first round draft pick and immediately became a star in the NBA. Life became good for Damion Booker again he was getting fame and publicity. He was getting so much fame and publicity that he acted as if he forgot that his own restaurant got burned down and started treating his family very well. He started to be in magazines, commercials, and on the internet. Damion Booker became the face of basketball and more importantly the face of Rookies. Overtime Damion Booker became cocky bad things begin to happened to him again. Damion booker was going for a slam dunk on a fast break and hurt his ankle. He was on the ground for 10 minutes and couldn’t get up. He felt paralyzed and the medical staff had to pick Damion up & put him on a stretcher. The next day he went to the doctor and they told him he had a ruptured Achilles tendon and that he will never be able to play basketball again. Damion Booker was upset because basketball was his life and if you took basketball away from him it was like taking his life away. Basketball was his Life! He played it almost every day and whenever he had the time. On the offseason of when Damion was in college he would always go to the park and have pickup games. He would dominate and win almost every single game. Damion didn’t want to listen to the doctors. He refused to listen to anything they said. Damion was going to come back and play in the NBA regardless if they said he could or couldn’t. The network technician believed that he was going to be out for his career and so did the whole world. Unbelievably Two months later, Damion stepped on the court and the nation was shocked. It was a remarkable return and on his debut from returning he had twenty- two points, six assists, and five rebounds. People knew this kid was special because nobody had ever recovered from a ruptured Achilles tendon and also because of how fast he recovered from his injury. Later, he got rookie of the year and averaged 18 points a game and became cocky again. In Addition, to Damion getting cocky after he won rookie of the year he began to get caught and this time he was messed up for life. He started getting influenced by his friends and thinking he was better than everyone in the world. That same night he won rookie of the year Damion went out partying with his friend. There was drugs and alcohol that he got into that just completely messed up his mindset. He started missing several practices, get to the team room late, disrespect the coaches, and many other things that got him into some trouble. Also, his numbers dropped, and appeared always tired. Instead of Damion averaging 18 points a game coming from the injury he averaged about 8 points a game. As he kept doing these actions they noticed a drastic change and ordered Damion to take a drug test. A couple days later the team got the results and he failed the drug test. After they got the results the Hokies released him to free agency and no other team wanted him. He realized he made a mistake and started to feel depressed. As a result, he got kicked out of the NBA and felt so lost he committed suicide.

Transfer Functions

ECM2105 – Control Engineering Dr Mustafa M Aziz (2010) ________________________________________________________________________________ TRANSFER FUNCTIONS AND BLOCK DIAGRAMS 1. Introduction 2. Transfer Function of Linear Time-Invariant (LTI) Systems 3. Block Diagrams 4. Multiple Inputs 5. Transfer Functions with MATLAB 6. Time Response Analysis with MATLAB 1. Introduction An important step in the analysis and design of control systems is the mathematical modelling of the controlled process. There are a number of mathematical representations to describe a controlled process:Differential equations: You have learned this before. Transfer function: It is defined as the ratio of the Laplace transform of the output variable to the Laplace transform of the input variable, with all zero initial conditions. Block diagram: It is used to represent all types of systems. It can be used, together with transfer functions, to describe the cause and effect relationships throughout the system. State-space-representation: You will study this in an advanced Control Systems Design course. 1. 1. Linear Time-Variant and Linear Time-Invariant SystemsDefinition 1: A time-variable differential equation is a differential equation with one or more of its coefficients are functions of time, t. For example, the differential equation: d 2 y( t ) t2 + y( t ) = u ( t ) dt 2 (where u and y are dependent variables) is time-variable since the term t2d2y/dt2 depends explicitly on t through the coefficient t2. An example of a time-varying system is a spacecraft system which the mass of spacecraft changes during flight due to fuel consumption. Definition 2: A time-invariant differential equation is a differential equation in which none of its coefficients depend on the independent time variable, t.For example, the differential equation: d 2 y( t ) dy( t ) m +b + y( t ) = u ( t ) 2 dt dt where the coefficients m and b are constants, is time-invariant since the equation depends only implicitly on t through the dependent variables y and u and their derivatives. 1 ECM2105 – Control Engineering Dr Mustafa M Aziz (2010) ________________________________________________________________________________ Dynamic systems that are described by linear, constant-coefficient, differential equations are called linear time-invariant (LTI) systems. 2. Transfer Function of Linear Time-Invariant (LTI) SystemsThe transfer function of a linear, time-invariant system is defined as the ratio of the Laplace (driving function) U(s) = transform of the output (response function), Y(s) = {y(t)}, to the Laplace transform of the input {u(t)}, under the assumption that all initial conditions are zero. u(t) System differential equation y(t) Taking the Laplace transform with zero initial conditions, U(s) Transfer function: System transfer function G (s) = Y(s) Y(s) U(s) A dynamic system can be described by the following time-invariant differential equation: an d n y( t ) d n ? 1 y( t ) dy( t ) + a n ? 1 + L + a1 + a 0 y( t ) n ? 1 dt dt dt d m u(t) d m ? 1 u ( t ) du ( t ) = bm + b m ? 1 + L + b1 + b 0 u(t) m m ? 1 dt dt dt Taking the Laplace transform and considering zero initial conditions we have: (a n ) ( ) s n + a n ? 1s n ? 1 + L + a 1s + a 0 Y(s) = b m s m + b m ? 1s m ? 1 + L + b1s + b 0 U(s) The transfer function between u(t) and y(t) is given by: Y(s) b m s m + b m ? 1s m ? 1 + L + b1s + b 0 M (s) = = G (s) = U(s) N(s) a n s n + a n ? 1s n ? 1 + L + a 1s + a 0 where G(s) = M(s)/N(s) is the transfer function of the system; the roots of N(s) are called poles of the system and the roots of M(s) are called zeros of the system.By setting the denominator function to zero, we obtain what is referred to as the characteristic equation: ansn + an-1sn-1 + + a1s + a0 = 0 We shall see later that the stability of linear, SISO systems is completely governed by the roots of the characteristic equation. 2 ECM2105 – Control Engineering Dr Mustafa M Aziz (2010) ______________ __________________________________________________________________ A transfer function has the following properties: †¢ The transfer function is defined only for a linear time-invariant system. It is not defined for nonlinear systems. The transfer function between a pair of input and output variables is the ratio of the Laplace transform of the output to the Laplace transform of the input. †¢ All initial conditions of the system are set to zero. †¢ The transfer function is independent of the input of the system. To derive the transfer function of a system, we use the following procedures: 1. Develop the differential equation for the system by using the physical laws, e. g. Newton’s laws and Kirchhoff’s laws. 2. Take the Laplace transform of the differential equation under the zero initial conditions. 3.Take the ratio of the output Y(s) to the input U(s). This ratio is the transfer function. Example: Consider the following RC circuit. 1) Find the transfer function of the network, Vo(s)/Vi(s). 2) Find the response vo(t) for a unit-step input, i. e. ?0 t < 0 v i (t) = ? ?1 t ? 0 Solution: 3 R vi(t) C vo(t) ECM2105 – Control Engineering Dr Mustafa M Aziz (2010) ________________________________________________________________________________ Exercise: Consider the LCR electrical network shown in the figure below. Find the transfer function G(s) = Vo(s)/Vi(s). L R i(t) vi(t) vo(t) CExercise: Find the time response of vo(t) of the above system for R = 2. 5? , C = 0. 5F, L=0. 5H and ? 0 t < 0 . v i (t) = ? ?2 t ? 0 4 ECM2105 – Control Engineering Dr Mustafa M Aziz (2010) ________________________________________________________________________________ Exercise: In the mechanical system shown in the figure, m is the mass, k is the spring constant, b is the friction constant, u(t) is an external applied force and y(t) is the resulting displacement. y(t) k m u(t) b 1) Find the differential equation of the system 2) Find the trans fer function between the input U(s) and the output Y(s). 5ECM2105 – Control Engineering Dr Mustafa M Aziz (2010) ________________________________________________________________________________ 3. Block Diagrams A block diagram of a system is a pictorial representation of the functions performed by each component and of the flow of signals. The block diagram gives an overview of the system. Block diagram items: Summing point Takeoff point Block Transfer function +_ The above figure shows the way the various items in block diagrams are represented. Arrows are used to represent the directions of signal flow. A summing point is where signals are algebraically added together.The takeoff point is similar to the electrical circuit takeoff point. The block is usually drawn with its transfer funciton written inside it. We will use the following terminology for block diagrams throughout this course: R(s) = reference input (command) Y(s) = output (controlled variable) U(s) = input (act uating signal) E(s) = error signal F(s) = feedback signal G(s) = forward path transfer function H(s) = feedback transfer fucntion R(s) Y(s) E(s) G(s) +_ F(s) H(s) Single block: U(s) Y(s) Y(s) = G(s)U(s) G(s) U(s) is the input to the block, Y(s) is the output of the block and G(s) is the transfer function of the block.Series connection: U(s) X(s) G1(s) Y(s) G2(s) 6 Y(s) = G1(s)G2(s)U(s) ECM2105 – Control Engineering Dr Mustafa M Aziz (2010) ________________________________________________________________________________ Parallel connection (feed forward): G1(s) + U(s) Y(s) Y(s) = [G1(s) + G2(s)]U(s) + G2(s) Negative feedback system (closed-loop system): R(s) E(s) +_ The closed loop transfer function: Y(s) G(s) Y(s) G(s) = R(s) 1 + G(s) Exercise: Find the closed-loop transfer function for the following block diagram: R(s) Y(s) E(s) G(s) +_ F(s) H(s) 7 ECM2105 – Control Engineering Dr Mustafa M Aziz (2010) __________________________________________________________________ _____________ Exercise: A control system has a forward path of two elements with transfer functions K and 1/(s+1) as shown. If the feedback path has a transfer function s, what is the transfer function of the closed loop system. R(s) +_ Y(s) 1 s +1 K s Moving a summing point ahead of a block: R(s) Y(s) G(s) + R(s) Y(s) +  ± G(s)  ± F(s) 1/G(s) F(s) Y(s) = G(s)R(s)  ± F(s) Moving a summing point beyond a block: R(s) Y(s) + R(s) G(s) Y(s) G(s)  ± +  ± F(s) G(s) F(s) Y(s) = G(s)[R(s)  ± F(s)] Moving a takeoff point ahead of a block: R(s) Y(s) R(s) Y(s) G(s) G(s) Y(s)Y(s) G(s) Y(s) = G(s)R(s) 8 ECM2105 – Control Engineering Dr Mustafa M Aziz (2010) ________________________________________________________________________________ Moving a takeoff point beyond a block: R(s) Y(s) R(s) Y(s) G(s) G(s) R(s) R(s) 1/G(s) Y(s) = G(s)R(s) Moving a takeoff point ahead of a summing point: R(s) Y(s) + Y(s)  ± F(s) R(s)  ± F(s) +  ± Y(s) + Y(s) Y(s) = R(s)  ± F(s) Moving a t akeoff point beyond a summing point: R(s) R(s) Y(s) + Y(s) +  ±  ± F(s)  ± R(s) F(s) R(s) + Y(s) = R(s)  ± F(s) Exercise: Reduce the following block diagram and determine the transfer function. R(s) + _ + G1(s) G2(s) G3(s) _ Y(s) + + H1(s)G4(s) H2(s) 9 ECM2105 – Control Engineering Dr Mustafa M Aziz (2010) ________________________________________________________________________________ Exercise: Reduce the following block diagram and determine the transfer function. H1 + R(s) +_ + G H2 10 Y(s) ECM2105 – Control Engineering Dr Mustafa M Aziz (2010) ________________________________________________________________________________ 4. Multiple Inputs Control systems often have more than one input. For example, there can be the input signal indicating the required value of the controlled variable and also an input or inputs due to disturbances which affect the system.The procedure to obtain the relationship between the inputs and the output for such systems is: 1. 2. 3. 4. Set all inputs except one equal to zero Determine the output signal due to this one non-zero input Repeat the above steps for each of the remaining inputs in turn The total output of the system is the algebraic sum (superposition) of the outputs due to each of the inputs. Example: Find the output Y(s) of the block diagram in the figure below. D(s) R(s) +_ G1(s) + + H(s) Solution: 11 Y(s) G2(s) ECM2105 – Control Engineering Dr Mustafa M Aziz (2010) _______________________________________________________________________________ Exercise: Determine the output Y(s) of the following system. D1(s) R(s) +_ G1(s) + + Y(s) G2(s) H1(s) + + D2(s) 12 H2(s) ECM2105 – Control Engineering Dr Mustafa M Aziz (2010) ________________________________________________________________________________ 5. Transfer Functions with MATLAB A transfer function of a linear time-invariant (LTI) system can be entered into MATLAB using the command tf(num,den) where num and den are row vectors co ntaining, respectively, the coefficients of the numerator and denominator polynomials of the transfer function.For example, the transfer function: G (s) = 3s + 1 s + 3s + 2 2 can be entered into MATLAB by typing the following on the command line: num = [3 1]; den = [1 3 2]; G = tf(num,den) The output on the MATLAB command window would be: Transfer function: 3s+1 ————s^2 + 3 s + 2 Once the various transfer functions have been entered, you can combine them together using arithmetic operations such as addition and multiplication to evaluate the transfer function of a cascaded system. The following table lists the most common systems connections and the corresponding MATLAB commands to implement them.In the following, SYS refers to the transfer function of a system, i. e. SYS = Y(s)/R(s). System MATLAB command Series connection: R(s) Y(s) G1 G2 SYS = G1*G2 or SYS = series(G1,G2) Parallel connection: G1 + R(s) SYS = G1  ± G2 or SYS = parallel(G1, ±G2) Y(s)  ± G2 Negative feedback connection: R(s) Y(s) +_ G(s) SYS = feedback(G,H) H(s) 13 ECM2105 – Control Engineering Dr Mustafa M Aziz (2010) ________________________________________________________________________________ R(s) Y(s) +_ G1 G2 H Example: Evaluate the transfer function of the feedback system shown in the figure above using MATLAB where G1(s) = 4, G2(s) = 1/(s+2) and H(s) = 5s.Solution: Type the following in the MATLAB command line: G1 = tf([0 4],[0 1]); G2 = tf([0 1],[1 2]); H = tf([5 0],[0 1]); SYS = feedback(G1*G2,H) This produces the following output on the command window (check this result): Transfer function: 4 ——-21 s + 2 Exercise: Compute the closed-loop transfer function of the following system using MATLAB. R(s) +_ 1 s +1 14 s+2 s+3 Y(s) ECM2105 – Control Engineering Dr Mustafa M Aziz (2010) ________________________________________________________________________________ 6. Time Response Analysis with MATLABAfter entering the transfer function of a LTI system, we can compute and plot the time response of this system due to different input stimuli in MATLAB. In particular, we will consider the step response, the impulse response, the ramp response, and responses to other simple inputs. 6. 1. Step response To plot the unit-step response of the LTI system SYS=tf(num,den) in MATLAB, we use the command step(SYS). We can also enter the row vectors of the numerator and denominator coefficients of the transfer function directly into the step function: step(num,den).Example: Plot the unit-step response of the following system in MATLAB: Y (s) 2s + 10 =2 R (s) s + 5s + 4 Solution: Step Response 2. 5 num = [0 2 10]; den = [1 5 4]; SYS = tf(num,den); step(SYS) Amplitude 2 or directly: step(num,den) 1. 5 1 MATLAB will then produce the following plot on the screen. Confirm this plot yourself. 0. 5 0 0 1 2 3 Time (sec. ) 4 5 For a step input of magnitude other than unity, for example K, simply multiply the transfer function SY S by the constant K by typing step(K*SYS). For example, to plot the response due to a step input of magnitude 5, we type step(5*SYS).Notice in the previous example that that time axis was scaled automatically by MATLAB. You can specify a different time range for evaluating the output response. This is done by first defining the required time range by typing: t = 0:0. 1:10; % Time axis from 0 sec to 10 sec in steps of 0. 1 sec and then introducing this time range in the step function as follows: step(SYS,t) % Plot the step response for the given time range, t This produces the following plot for the same example above. 15 6 ECM2105 – Control Engineering Dr Mustafa M Aziz (2010) _______________________________________________________________________________ Step Response 2. 5 Amplitude 2 1. 5 1 0. 5 0 0 2 4 6 8 10 Time (sec. ) You can also use the step function to plot the step responses of multiple LTI systems SYS1, SYS2, †¦ etc. on a single figure in MATLAB by typing: st ep(SYS1,SYS2,†¦ ) 6. 2. Impulse response The unit-impulse response of a control system SYS=tf(num,den) may be plotted in MATLAB using the function impulse(SYS). Example: Plot the unit-impulse response of the following system in MATLAB: Y(s) 5 = R (s) 2s + 10 Solution: Impulse Response um = [0 5]; den = [2 10]; SYS = tf(num,den); impulse(SYS) 2. 5 2 impulse(num,den) Amplitude or directly 1. 5 1 This will produce the following output on the screen. Is that what you would expect? 0. 5 0 0 0. 2 0. 4 0. 6 Time (sec. ) 16 0. 8 1 1. 2 ECM2105 – Control Engineering Dr Mustafa M Aziz (2010) ________________________________________________________________________________ 6. 3. Ramp response There is no ramp command in MATLAB. To obtain the unit ramp response of the transfer function G(s): multiply G(s) by 1/s, and use the resulting function in the step command.The step command will further multiply the transfer function by 1/s to make the input 1/s2 i. e. Laplace transform of a un it-ramp input. For example, consider the system: Y(s) 1 =2 R (s) s + s + 1 With a unit-ramp input, R(s) = 1/s2, the output can be written in the form: Y(s) = 1 1 1 R (s) = 2 ? s + s +1 (s + s + 1)s s 2 1 ? ?1 =? 3 2 ?s + s + s ? s which is equivalent to multiplying by 1/s and then working out the step response. To plot the unitramp response of this system, we enter the numerator and denominator coefficients of the term in square brackets into MATLAB: num = [0 0 0 1]; en = [1 1 1 0]; and use the step command: step(num,den) The unit ramp response will be plotted by MATLAB as shown below. Step Response 12 10 Amplitude 8 6 4 2 0 0 2 4 6 Time (sec. ) 17 8 10 12 ECM2105 – Control Engineering Dr Mustafa M Aziz (2010) ________________________________________________________________________________ 6. 4. Arbitrary response To obtain the time response of the LTI system SYS=tf(num,den) to an arbitrary input (e. g. exponential function, sinusoidal function .. etc. ), we can use the lsim command (stands for ‘linear simulation') as follows: lsim(SYS,r,t) or lsim(num,den,r,t) here num and den are the row vectors of the numerator and denominator coefficients of the transfer function, r is the input time function, and t is the time range over which r is defined. Example: Use MATLAB to obtain the output time response of the transfer function: Y(s) 2 = R (s) s + 3 when the input r is given by r = e-t. Solution: Start by entering the row vectors of the numerator and denominator coefficients in MATLAB: num = [0 2]; den = [1 3]; Then specify the required time range and define the input function, r, over this time: t = 0:0. 1:6; r = exp(-t); % Time range from 0 to 6 sec in steps of 0. 1 sec Input time function Enter the above information into the lsim function by typing: lsim(num,den,r,t) This would produce the following plot on the screen. Linear Simulation Results 0. 4 0. 35 Amplitude 0. 3 0. 25 0. 2 0. 15 0. 1 0. 05 0 0 1 2 3 Time (sec. ) 18 4 5 6 ECM2105 – C ontrol Engineering Dr Mustafa M Aziz (2010) ________________________________________________________________________________ TUTORIAL PROBLEM SHEET 3 1. Find the transfer function between the input force u(t) and the output displacement y(t) for the system shown below. y(t) b1 u(t) m b2 where b1 and b2 are the frictional coefficients.For b1 = 0. 5 N-s/m, b2 = 1. 5 N-s/m, m = 10 kg and u(t) is a unit-impulse function, what is the response y(t)? Check and plot the response with MATLAB. 2. For the following circuit, find the transfer function between the output voltage across the inductor y(t), and the input voltage u(t). R u(t) L y(t) For R = 1 ? , L = 0. 1 H, and u(t) is a unit-step function, what is the response y(t)? Check and plot the result using MATLAB. 3. Find the transfer function of the electrical circuit shown below. R L u(t) y(t) C For R = 1 ? , L = 0. 5 H, C = 0. 5 F, and a unit step input u(t) with zero initial conditions, compute y(t).Sketch the time function y(t) and pl ot it with MATLAB. 19 ECM2105 – Control Engineering Dr Mustafa M Aziz (2010) ________________________________________________________________________________ 4. In the mechanical system shown in the figure below, m is the mass, k is the spring constant, b is the friction constant, u(t) is the external applied force and y(t) is the corresponding displacement. Find the transfer function of this system. k u(t) m For m = 1 kg, k = 1 kg/s2, b = 0. 5 kg/s, and a step input u(t) = 2 N, compute the response y(t) and plot it with MATLAB. b y(t) 5.Write down the transfer function Y(s)/R(s) of the following block diagram. R(s) Y(s) K +_ G(s) a) For G(s) = 1/(s + 10) and K = 10, determine the closed loop transfer function with MATLAB. b) For K = 1, 5, 10, and 100, plot y(t) on the same window for a unit-step input r(t) with MATLAB, respectively. Comment on the results. c) Repeat (b) with a unit-impulse input r(t). 6. Find the closed loop transfer function for the following diagram. R(s) E(s) Y(s) G(s) +_ F(s) H(s) a) For G(s) = 8/(s2 + 7s + 10) and H(s) = s+2, determine the closed loop transfer function with MATLAB. ) Plot y(t) for a unit-step input r(t) with MATLAB. 7. Determine the transfer function of the following diagram. Check your answer with MATLAB. _ R(s) +_ s s + + 1/s s 20 1/s Y(s) ECM2105 – Control Engineering Dr Mustafa M Aziz (2010) ________________________________________________________________________________ 8. Determine the transfer function of the following diagram. R(s) +_ +_ 50 s +1 Y(s) s 2/s 1/s2 2 +_ a) Check you result with MATLAB. b) Plot y(t) for a unit-impulse input r(t) with MATLAB. 9. Determine the total output Y(s) for the following system. D(s)