hw4 solution - university of california, san...
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![Page 1: Hw4 solution - University of California, San Diegocontrol.ucsd.edu/mauricio/courses/mae143b-S2012/hw4… · · 2012-05-04Matlab Code: KD=0.4; KP=21.5; T=tf([200*KD 200*KP],[1 12+200*KD](https://reader033.vdocuments.site/reader033/viewer/2022051800/5acdad6b7f8b9a73128e4bb5/html5/thumbnails/1.jpg)
Hw4 solution
4.22
![Page 2: Hw4 solution - University of California, San Diegocontrol.ucsd.edu/mauricio/courses/mae143b-S2012/hw4… · · 2012-05-04Matlab Code: KD=0.4; KP=21.5; T=tf([200*KD 200*KP],[1 12+200*KD](https://reader033.vdocuments.site/reader033/viewer/2022051800/5acdad6b7f8b9a73128e4bb5/html5/thumbnails/2.jpg)
(C)
Matlab Code:
KD=65;KP=14400;a1=65; num=[KD KP]; den=[1 a1+KD KP]; T1=tf(num,den); s=stepinfo(T1,'SettlingTimeThreshold',0.05);
Set Kp=14400 KD=55 => Settling time=0.04s Overshoot=18.5% Because the overshoot is a little higher than required, let’s increase the damping to lower it: Set Kp=14400 KD=65 => Settling time= 0.04s Overshoot = 16% This is a workable design.
![Page 3: Hw4 solution - University of California, San Diegocontrol.ucsd.edu/mauricio/courses/mae143b-S2012/hw4… · · 2012-05-04Matlab Code: KD=0.4; KP=21.5; T=tf([200*KD 200*KP],[1 12+200*KD](https://reader033.vdocuments.site/reader033/viewer/2022051800/5acdad6b7f8b9a73128e4bb5/html5/thumbnails/3.jpg)
![Page 4: Hw4 solution - University of California, San Diegocontrol.ucsd.edu/mauricio/courses/mae143b-S2012/hw4… · · 2012-05-04Matlab Code: KD=0.4; KP=21.5; T=tf([200*KD 200*KP],[1 12+200*KD](https://reader033.vdocuments.site/reader033/viewer/2022051800/5acdad6b7f8b9a73128e4bb5/html5/thumbnails/4.jpg)
4.26
(b)
![Page 5: Hw4 solution - University of California, San Diegocontrol.ucsd.edu/mauricio/courses/mae143b-S2012/hw4… · · 2012-05-04Matlab Code: KD=0.4; KP=21.5; T=tf([200*KD 200*KP],[1 12+200*KD](https://reader033.vdocuments.site/reader033/viewer/2022051800/5acdad6b7f8b9a73128e4bb5/html5/thumbnails/5.jpg)
![Page 6: Hw4 solution - University of California, San Diegocontrol.ucsd.edu/mauricio/courses/mae143b-S2012/hw4… · · 2012-05-04Matlab Code: KD=0.4; KP=21.5; T=tf([200*KD 200*KP],[1 12+200*KD](https://reader033.vdocuments.site/reader033/viewer/2022051800/5acdad6b7f8b9a73128e4bb5/html5/thumbnails/6.jpg)
Matlab Code:
KD=0.4; KP=21.5; T=tf([200*KD 200*KP],[1 12+200*KD 20+200*KP]); s=stepinfo(T,'SettlingTimeThreshold',0.01);
Set KP=21.5 KD=0.4 => Settling time=0.08s Overshoot=16.1%
Settling time satisfies the requirement but overshoot is too high.
Set KP=21.5 KD=1.0 => Settling time=0.085s Overshoot=3.2%
This set of KD and KP satisfy the specifications.
![Page 7: Hw4 solution - University of California, San Diegocontrol.ucsd.edu/mauricio/courses/mae143b-S2012/hw4… · · 2012-05-04Matlab Code: KD=0.4; KP=21.5; T=tf([200*KD 200*KP],[1 12+200*KD](https://reader033.vdocuments.site/reader033/viewer/2022051800/5acdad6b7f8b9a73128e4bb5/html5/thumbnails/7.jpg)
![Page 8: Hw4 solution - University of California, San Diegocontrol.ucsd.edu/mauricio/courses/mae143b-S2012/hw4… · · 2012-05-04Matlab Code: KD=0.4; KP=21.5; T=tf([200*KD 200*KP],[1 12+200*KD](https://reader033.vdocuments.site/reader033/viewer/2022051800/5acdad6b7f8b9a73128e4bb5/html5/thumbnails/8.jpg)
4.30
(e)
Matlab Code:
KP=-0.1;KI=-12; G=tf(1,[1 60]); D=tf(600*[-KP -KI],[1 0]); Ta=feedback(series(G,D),1); Tb=series(Ta,tf(1,[1 0])); Tc=feedback(G,D)*1500; Td=series(Tc,tf(1,[1 0]));
t=0:0.01:1;
y=step(Ta,t); ref=ones(1,101); plot(t,ref,t,y); plot(t,1-y);
Steady state error goes to 0 as predicted.
t=0:0.01:1; y=step(Tb,t); plot(t,t,t,y); plot(t,t’-y);
![Page 9: Hw4 solution - University of California, San Diegocontrol.ucsd.edu/mauricio/courses/mae143b-S2012/hw4… · · 2012-05-04Matlab Code: KD=0.4; KP=21.5; T=tf([200*KD 200*KP],[1 12+200*KD](https://reader033.vdocuments.site/reader033/viewer/2022051800/5acdad6b7f8b9a73128e4bb5/html5/thumbnails/9.jpg)
KI=-12, steady state error goes to -1/(10*KI)=0.083
t=0:0.01:1; y=step(Tc,t); plot(t,y);
Steady state error goes to 0 as predicted.
t=0:0.01:1; y=step(Td,t); plot(t,y);
![Page 10: Hw4 solution - University of California, San Diegocontrol.ucsd.edu/mauricio/courses/mae143b-S2012/hw4… · · 2012-05-04Matlab Code: KD=0.4; KP=21.5; T=tf([200*KD 200*KP],[1 12+200*KD](https://reader033.vdocuments.site/reader033/viewer/2022051800/5acdad6b7f8b9a73128e4bb5/html5/thumbnails/10.jpg)
KI=-12, steady state error goes to -5/(2*KI)=0.2083