Lab-4 (Solution by Adnan)
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Control Systems Lab 4. LTI Models & their Operations 1 Lab No. 04 LTI Models & their Operations TASK No. 4.1 Find the Step response and Transfer function by using M-file and also implement it on simulink (A). Series Configuration: S+1 / S+3 1 / 100S 2 Matlab Code & Result >> clear all >> close all >> numa=[1 1]; dena=[1 3]; numb=1; denb=[100 0 0]; A=tf(numa,dena); B=tf(numb,denb); s=series(A,B); >> step(s) >> Tf=tf(s) Transfer function: s + 1 ----------------- 100 s^3 + 300 s^2
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Transcript of Lab-4 (Solution by Adnan)
Control Systems
Lab 4. LTI Models & their Operations 1
Lab No. 04 LTI Models & their Operations
TASK No. 4.1
Find the Step response and Transfer function by using M-file and also implement it on simulink
(A). Series Configuration:
S+1 / S+3 1 / 100S2
Matlab Code & Result >> clear all >> close all >> numa=[1 1]; dena=[1 3]; numb=1; denb=[100 0 0]; A=tf(numa,dena); B=tf(numb,denb); s=series(A,B); >> step(s) >> Tf=tf(s) Transfer function: s + 1 ----------------- 100 s^3 + 300 s^2
Control Systems
Lab 4. LTI Models & their Operations 2
Control Systems
Lab 4. LTI Models & their Operations 3
Simulink Diagram & Step Response Results
Control Systems
Lab 4. LTI Models & their Operations 4
(B). Parallel Configuration:
Matlab Code & Result >> clear all >>close all >> numa=[1]; dena=[1 1]; numb=[2]; denb=[3 0 9]; A=tf(numa,dena); B=tf(numb,denb); p=parallel(A,B) Transfer function: 3 s^2 + 2 s + 11 ----------------------- 3 s^3 + 3 s^2 + 9 s + 9 >> step(p) >>
1 / S+1
2 / 3S2+ 9
Control Systems
Lab 4. LTI Models & their Operations 5
Simulink Diagram & Result
Control Systems
Lab 4. LTI Models & their Operations 6
(C). Feedback System
Matlab Code & Result: >>clear all >>close all >>numc = [ 1 1] ; >> denc = [ 1 2 ] ; >>numg = [ 1 ] ; >> deng = [ 500 0 0] ; >>c = tf(numc, denc); >>g = tf(numg, deng); >>s = series(c, g) >>f=1;; >>r = feedback(s, 1)
S+ 1 / S+2 1 / 500S2 -
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Control Systems
Lab 4. LTI Models & their Operations 7
Transfer function: s + 1 -------------------------- 500 s^3 + 1000 s^2 + s + 1
Simulink Diagram & Result
Control Systems
Lab 4. LTI Models & their Operations 8
… Use an alternate code for this implementation ( Lab Task No. 4.2
Find the step response on simulink of the diagram below
Simplify the Diagram & obtain a Transfer Function
Also plot the step response for the simplified one and compare these results.
6 s / s^2 + s + 4
s / s + 2
3 / s+3
R(s)
C(s)
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Control Systems
Lab 4. LTI Models & their Operations 9
Matlab Code & Results
>> clear all >>close all >> numa=[1 0]; >> dena=[1 2]; >> A=tf(numa,dena); >> numb=6; >> denb=1; >> B=tf(numa,denb); >> numc=3; >> denc=[1 3]; >> C=tf(numc,denc); >> numd=[1 0]; >> dend=[1 1 4]; >> D=tf(numd,dend); >> sys1=B-A; >> f=1; >> sys2=feedback(sys1,f); >> sys3=series(sys2,D) Transfer function: 5 s^2 + 12 s -------------------------- 6 s^3 + 20 s^2 + 38 s + 56 >> sys4=feedback(sys3,C) Transfer function: 5 s^3 + 27 s^2 + 36 s -------------------------------------- 6 s^4 + 38 s^3 + 113 s^2 + 206 s + 168 >> step(sys4) >>
Control Systems
Lab 4. LTI Models & their Operations 10
Simulink Diagram & Result
Control Systems
Lab 4. LTI Models & their Operations 11
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