Is there any numerical method to judge control system stability?

Dear all, recently I meet a problem. Given a transfer function of a control system with time-delay, then, is there any numerical method to judge the stability of the system?

Nyquist criterion needs to count the cylinder numbers manually, which is not suitable for me. Also, I do not want to use Pade approximation to approach the delay link.

Thank you for your attention.

Answer 1

[Rick Rosson]

Bounded-Input, Bounded-Output Method

I am not 100 percent sure, but it might make sense to run a numerical simulation where you provided a step-function input to the transfer function, and then evaluated whether the response is bounded or unbounded (using an appropriate numerical test).

Essentially, this approach uses the step-response to evaluate the Bounded Input, Bounded Output, or BIBO, definition of stability.

Does that make sense? Would it work in all situations? I am not sure, but it might be worth a try.

Rick

[Chao]

Thanks for your answer. In my opinion, BIBO stable does not imply internal stable. And if I observe the system, it is not easy for me to set the "bound". Also, some system reacts slowly, so they may go out-of-bounds after a long time. The time threshold is not easy to choose.

Answer 2

[Rick Rosson]

Poles on the Right-Hand Side of the s-plane

Another approach that might work would be to convert the transfer function to pole-zero form, and then determine whether any of the poles are on the right-hand side of the complex s-plane. If so, then the system is unstable.

In other words, determine whether the real-part of each pole is positive or negative. If any of them is positive, then the system is unstable. If all of them are negative, then the system is stable.

HTH.

Rick

[Chao]

A time-delay system has infinite roots.

Thank you all the same.