Control System LabObject : To design 2nd order electrical network and study its transientresponse for step input and follo...
Program:L=1;R1=1;C1=1;R2=2;C2=1;R3=2;C3=4;t=0:0.1:25;%n1=inv(L*C1);d1=[1 R1*[inv(L)] inv(L*C1)];sys1=tf(n1,d1)[y1,x1]=step...
n3=inv(L*C3);d3=[1 R3*[inv(L)] inv(L*C3)];sys3=tf(n3,d3)[y3,x3]=step(sys3,t)%clfsubplot(311);plot(y1,t);title(z=0.5)subplo...
2nd order electrical network
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2nd order electrical network

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2nd order electrical network

  1. 1. Control System LabObject : To design 2nd order electrical network and study its transientresponse for step input and following cases- (a) underdamped system(b) overdamped system (c) critically damped system.Theory: Consider a simple series RLC network. V1(s) is input voltageand V2(s) is output voltage across capacitor C. Then transfer function ofnetwork is given as G(s) = V2(s)/V1(s) R LV1(s) C V2(s) 1 ܴ 1 ‫ ܩ‬ሺ‫ݏ‬ሻ ൌ ൜ ൠ /ሾ‫ ݏ‬ଶ ൅ ൜ ൠ ‫ ݏ‬൅ ൜ ൠሿ ‫ܥܮ‬ ‫ܮ‬ ‫ܥܮ‬ ோ ଵ Characteristic equation =‫ ݏ‬ଶ ൅ ቄ ቅ ‫ ݏ‬൅ ቄ ቅ ௅ ௅஼ ଵ Here, Wn^2=[ ] ௅஼ భ ோ ஼ మ Z= ‫כ‬ ቂ ቃ ଶ ௅
  2. 2. Program:L=1;R1=1;C1=1;R2=2;C2=1;R3=2;C3=4;t=0:0.1:25;%n1=inv(L*C1);d1=[1 R1*[inv(L)] inv(L*C1)];sys1=tf(n1,d1)[y1,x1]=step(sys1,t)%n2=inv(L*C2);d2=[1 R2*[inv(L)] inv(L*C2)];sys2=tf(n2,d2)[y2,x2]=step(sys2,t)%
  3. 3. n3=inv(L*C3);d3=[1 R3*[inv(L)] inv(L*C3)];sys3=tf(n3,d3)[y3,x3]=step(sys3,t)%clfsubplot(311);plot(y1,t);title(z=0.5)subplot(312);plot(y2,t);title(z=1)subplot(313);plot(y3,t);title(z=2)Output:Transfer function 1: 1-------------s^2 + 2 s + 1Transfer function2: 1-----------s^2 + s + 1Transfer function3: 0.25/[s^2 + 2 s + 0.25]

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