More accurate alternative to rlocfind to analyze root locus in control systems engineering

27 vues (au cours des 30 derniers jours)
To find the gain at the point where the root locus intersects a line of constant damping ratio, the rlocfind function can be used, but the user has to manually select a point and Matlab finds the closest point on the root locus to the selection. Is there a way to find the exact point of intersection without having to make the selection manually?
h = tf([2 5 1],[1 2 3]);
rlocus(h) % Root locus
z = 0.707; sgrid(z,0)
k = rlocfind(h)

Réponses (2)

Arkadiy Turevskiy
Arkadiy Turevskiy le 1 Mai 2023
Modifié(e) : Arkadiy Turevskiy le 1 Mai 2023
Here is a way to do it (not the most efficient, but it works).
% Define the transfer function
h = tf([2 5 1], [1 2 3]);
% Define the desired damping ratio
zeta = 0.707;
% Get the poles and zeros of the transfer function
[num, den] = tfdata(h);
% Loop through different values of k to find the desired damping ratio
for k = 0:0.001:100
% Get the poles of the transfer function at gain k
p_k = roots(cell2mat(den) + k * cell2mat(num));
% Use the damp function to calculate the damping ratio of the poles
[wn, zeta_k] = damp(p_k);
% If the damping ratio is close to the desired value, print the gain and break out of the loop
if abs(zeta_k - zeta) < 0.001
fprintf('The gain k for a damping ratio of %f is %f\n', zeta, k);
The gain k for a damping ratio of 0.707000 is 0.196000

Paul le 1 Mai 2023

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