2 DOF System is unstable? "Warning: The closed-loop system is unstable"

Question

Bob 2016-4-5

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/277230-2-dof-system-is-unstable-warning-the-closed-loop-system-is-unstable

编辑： Bob 2016-4-29

I want to find the gain margin so I can calculate the parameters (kp,ki,kd) of ZN method. But I got this error.

%%Parameters
m1 = 2500;   % (kg)
m2 = 320;    % (kg)
k1 = 80000;  % (N/m)
k2 = 500000; % (N/m)
b1 = 350;    % (N*s/m)
b2 = 15020;  % (N*s/m)
% G(s) = (X1(s)-X2(s))/W(s)
num = [(0) (-m1*b2) (-m1*k2) (0) (0)]; 
den = [(m1*m2) (m1*b1+m1*b2+m2*b1) (m1*k1+m1*k2+m2*k1+b1*b2) (b1*k2+k1*b2) (k1*k2)];
G = tf(num,den);

Warning

Warning: The closed-loop system is unstable. 
> In ctrlMsgUtils.warning (line 25)
  In DynamicSystem/margin (line 65)**

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Answer 1

Sebastian Castro 2016-4-5

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https://ww2.mathworks.cn/matlabcentral/answers/277230-2-dof-system-is-unstable-warning-the-closed-loop-system-is-unstable#answer_216504

Negative gain and phase margins means that the open-loop system is unstable.

You're right that a mass-spring-damper system shouldn't be unstable. Maybe there was some error in converting the system equations to that transfer function representation. Double-check the equations -- especially any minus signs that should have been positive, or vice-versa.

- Sebastian