I am new to control theory and have difficulties about this question control system scheme

R is the input, Td is the disturbance, C is the output Given that G1=K/(s^2+A*s), where K is the gain and A is a parameter greater than zero. The question is, for what value of the step disturbance the system can become unstable? How do I solve this?


1 Answer 1


The stability is a property of the linear systems themselves, hence there is no meaning in considering stability as regarded with the input disturbance $T_d$.

To verify if the closed-loop system $C/T_d$ is stable/unstable, you ought to compute the roots of the characteristic polynomial.

Given that $$ \frac{C}{T_d} = - \frac{s^2+As}{s^2+As+K}, $$ the roots of $s^2+As+K$ − poles of the closed-loop system − are: $$ s_{1,2} = \frac{-A \pm \sqrt{A^2-4K}}{2}. $$ For $C/T_d$ to be unstable, at least one pole needs to have a positive real part, thus $K<0$.


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