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Laboratory in Automatic Control

Lab 8Frequency Response Method

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Frequency Response Methods (1/9)

Matlab code

num=5*[0.1 1];f1=[1 0]; f2=[0.5 1];f3=[1/2500 0.6/50 1];den=conv(f1,conv(f2,f3));sys=tf(num,den);bode(sys)

Result

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Result

In LTI Viewer

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Matlab code

2. . 100exp

1P O

K=2;num=[K]; den=[1 3 2 K];sys=tf(num,den);w=logspace(-1,1,400);[mag,phase,w]=bode(sys,w);[mp,l]=max(mag); wr=w(l);

zeta=sqrt(0.5*(1-sqrt(1-1/m p^2)))wn=wr/sqrt(1-2*zeta^2)

ts=4/zeta/wnpo=100*exp(-zeta*pi/sqrt(1-zeta^2))

400 points

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Result

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A unity feedback system has the open-looptransfer function

Generate a plot of the bandwidth versus

the parameter p as 0

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Bode plot

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Matlab code method1

p=[0:0.001:1];w=logspace(-2,1,1000);

n=length(p);for i=1:n

num=[1]; den=[1 20*p(i) 0];sys=tf(num,den);sys_cl=feedback(sys,[1]);[mag,phase]=bode(sys_cl,w);a(1,i)=bandwidth(sys_cl);

endplot(p,a)

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Matlab code method2

p=[0:0.001:1];w=logspace(-2,1,1000);

n=length(p);for i=1:n

num=[1]; den=[1 20*p(i) 0];sys=tf(num,den);sys_cl=feedback(sys,[1]);[mag,phase]=bode(sys_cl,w);a=find(mag

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Result

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1.Consider the feedback system. Obtain the Bode plots of the

(a) open-loop and (b) closed-loop transfer functions using MATLAB.

1

1s 210

3 1s s ( )R s ( )Y s

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12

K1

( 7)s s( )R s( )Y s

2. Consider the feedback system. The specification for the closed-loop system

requires that the overshoot to a step input be less than 10%

(a) find and

(b) Determine the corresponding specifi

n

cation M in the frequency

domain for the closed- loop TF.

(c) Determine the resonant frequency .

(d) Determine the bandwidth of the closed-loop system.

(e) Obtain the Bode plots of the open-loo

pw

r

p system.