Problem 2: Write a script called \"yourLastNamehw5p2.m\". Consider the following

Question

Problem 2: Write a script called "yourLastNamehw5p2.m". Consider the following plant transfer function Y(s) U(s) s2-3s +4 (a) Open-loop control. 1. Open a figure, plot the poles of the plant transfer functiin the complex plane, and give the figure the title "Problem 2, part a: poles". 2. State whether the transfer function is stable or not. Use a command like display('Problem 2 part a: The plant transfer function is stable. ') todisplay your answer in the com- mand window 3. Open a second figure and plot the plant's response to a unit step input, and give the figure the title “Problem 2, part a: step response" (b) Proportional feedback control. Set Kp-1 and Kd -Ki0 and define the transfer function for the contler and for the closed-loop system. 1. Open a new figure and plot the closed-loop poles in the complex plane. Give the plot the 2. Open a new figure and plot the response of the system to a unit step input. Give the plof 3. Add one to the proportional gain Kp again and again until the system is stable redefining the 4. What is the first Kp for which the system is stable? Use a command like display 'Problem 2 title “Problem 2, part b: poles". the title “Problem 2, part b: step respchse". system each time and plotting the poles and step response each time. part b: The system is stable for Kp20. ) to display your answer in the command win (c) Proportional-Derivative feedback control. Set KP-10. Kd = 0.1, and Ki-0 and define the transfer function for the closed-loop system. 1. Open a new figure and plot the closed-loop poles in the complex plane. Give the plot the 2. Open a new figure and plot the response of the system to a unit step input. Give the plot 3. Add 0.1 to the derivative gain Kd again and again until the response is stable, plotting the title "Problem 2, part c: poles" the title "Problem 2, part c: step response" poles and step response each time. What is the first Kd for which the response is stable? Use a command like display('Problem 2, part c: The system is stable for Kd -20.') to display your answer in the command window (d) Comments. In the comments box on Blackboard write a few sentences about why the plant in Problem 1 is different from the plant in Problem 2. Why were the effects of feedback different? 4

Explanation / Answer

a. 1.2.3 matlab cod ein bold

s=tf('s');
g=1/(s^2-3*s+4);
pzmap(g)
title(' Problem 2 part a : poles')
display(' Problem 2 part a : The plant transfer function is unstable');
figure
step(feedback(g,1))
title(' Problem I part a : Step response')

b. 1.2.3.4. matlab code in bold;

s=tf('s');
g=1/(s^2-3*s+4);
gc=feedback(g,1)
pzmap(gc)
title(' Problem 2 part b : poles')
figure
step(gc)
title(' Problem 2 part b : step response')
display(' Problem 2 part b : The system is unstable for all values of Kp')

c . 1. 2. 3. matlab code in bold:

s=tf('s');
g=1/(s^2-3*s+4);
gc=(10+0.1*s);
gclosed=feedback(g*gc,1);
pzmap(gclosed);
title(' Problem 2 part c: poles')
figure
step(gclosed)
title(' Problem 2 part c: Step response')
gcnew=(10+4.5*s)
gclosednew=feedback(g*gcnew,1);

figure

step(gclosednew)

display('problem 2,part c : The system is stable for Kd=4.5')

commets: In problem one the open loop and close dloop poles are on the right hand s-plane so for any value of gain the system is unstable. but in case c the system is stable after adding an compensator

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