Is there any numerical method to judge control system stability?
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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.
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Rick Rosson
am 22 Jun. 2011
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
Rick Rosson
am 22 Jun. 2011
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
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