Control System Lab

Object : To design 2nd

order electrical network and study its transient

response 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 voltage

and V2(s) is output voltage across capacitor C. Then transfer function of

network is given as

G(s) = V2(s)/V1(s)

���� � � 1� /�� � ��� � � �

1��

Characteristic equation =� � ���� � � �����

Here, Wn^2=[���]

Z= � � �

���

��

V2(s)C

R L

V1(s)

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)

%

n3=inv(L*C3);

d3=[1 R3*[inv(L)] inv(L*C3)];

sys3=tf(n3,d3)

[y3,x3]=step(sys3,t)

%

clf

subplot(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 + 1

Transfer function2:

1

-----------

s^2 + s + 1

Transfer function3: 0.25/[s^2 + 2 s + 0.25]