consider a unity negative feedback system Consider a unity negative feedback sys
ID: 2082341 • Letter: C
Question
consider a unity negative feedback system Consider a unity negative feedback system with the plant P(s) = 80(s + 10)/s(s + 3)(s + 20). Use the root locus design method to find a lag compensator so that the closed-loop system has an overshoot no more than 20% for a unit step input; has a steady-state error no more than 0.05 for a unit ramp input. If the maximum overshoot exceeds the requirement, make a fine tuning and reduce it to approximately the specified value or less. Make sure to show the detailed calculation and list all the MATLAB commands used.Explanation / Answer
MATLAB Command Used for given P(s):
num=[80 10] % Numerator
den=[1 23 60 0] % Denominator
'P(s)' % Display title P(s)
P=tf(n,d) % Transfer Function
rlocus(P) % Plot the root locus of uncompensated system
M=input('Enter percentage overshoot')
zeta=sqrt(log(M)^2 /(pi^2 + log(M)^2)) % Calculate the damping ratio
sgrid(zeta,0) % Draw line from the origin with angle of cos^(-1)zeta
[K p]=rlocfind(P) % Find the gain K at the point of Sd
Kvu=input('Enter Uncompensated Vel VConst')
ess=input('Enter steady state error')
Kvd=1/ess;
A=Kvd/Kvu;
Beta=1.2*A;
root=roots(d); % Finding the roots of denominator
T=1/(-0.1*root(2)) % Using the second root
Zc=1/T
Pc=1/(Beta*T)
Gc=tf([1 Zc],[1,Pc])
sys=Gc*P*K
rlocus(sys) % Root locus plot for the compensated system
pause
sys=feedback(sys,1,-1)
step(sys)
hold on
P=feedback(P,1,-1)
step(P)
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