Ziegler Nichols PID Method
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Hi,
I have a problem ,this is my G(s)=59000/(s^2+59000)
I want to apply the tangent method of Ziegler-Nichols, but my step is a sinusoid undumped. How I can approximate my G(s) to apply this method? Thanks very much.
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Answers (1)
Sam Chak
on 18 May 2024
I revisit your problem. I'm unsure if you are looking for something like this:
%% original system (marginally stable)
a = 59000;
G = tf(a, [1, 0, a])
%% stabilizer
Kd = 2*sqrt(a)/a;
Gc = pid(0, 0, Kd);
%% closed-loop system (exponentially-stabilized dynamic process)
Gcl = feedback(G, Gc)
tfin= 0.04;
step(Gcl, tfin), grid on
hold on
t = 0:1e-5:tfin;
sol = @(t) exp(-10*sqrt(590)*t).*(exp(10*sqrt(590)*t) - 10*sqrt(590)*t - 1);
m = 89.3576; % max slope
tm = 0.00411693; % time where max slope is
c = - (m*tm - sol(tm)); % offset
y = m*t + c; % line equation
td = 0.00116027; % time delay
plot(t, y)
xline(td, '-.', sprintf('Dead Time: %.5f sec', td), 'color', '#7F7F7F')
ylim([-0.2, 1.2])
hold off
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