Matlab Code:
clc;clear;
Kp = 0.01:0.01:10;
tr = 0.43;
err1 = zeros(1000,1);
err2 = zeros(1000,1);
err3 = zeros(1000,1);
G = tf(60,[1 3.57 3]);
for i = 1:1000
Gc = Kp(i);
C = feedback(G*Gc,1);
S1 = stepinfo(C,'RiseTimeThreshold',[0 0.90]);
Tr1 = S1.RiseTime;
err1(i) = Tr1-tr;
S2 = stepinfo(C,'RiseTimeThreshold',[0.0 1.0]);
Tr2 = S2.RiseTime;
err2(i) = Tr2-tr;
S3 = stepinfo(C,'RiseTimeThreshold',[0.10 0.90]);
Tr3 = S3.RiseTime;
err3(i) = Tr3-tr;
end
%Rise time for 90% criterion
[p, a] = min(abs(err1));
kp1 = Kp(a)
%Rise time for 100% criterion
[p, a] = min(abs(err2));
kp2 = Kp(a)
%Rise time for 10% to 90% criterion
[p, a] = min(abs(err3));
kp3 = Kp(a)
There are 3 ways to determine rise time use the value you use commonly in your class.
Rise time for 90% criterion: 0.29
Rise time for 100% criterion: 0.34
Rise time for 10% to 90% criterion : 0.18
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For the closed-loop system shown, and given:
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