I have an unstable system that doesn't have a useable output when open-loop excitation is applied.

Subsequently I've used a controller to control its output. I want to use the system identification tool on MATLAB, but don't know how to calculate the open-loop input to the plant for a closed-loop system.

All the reading material is advanced and theoretical and has largely gone over my head. Can anyone explain how this open-loop plant input can be derived from known parameters of the controller and the plant output?

  • \$\begingroup\$ What's this stuff that you call "open-loop input" ? \$\endgroup\$ – Dirceu Rodrigues Jr May 1 '19 at 14:12
  • \$\begingroup\$ @DirceuRodriguesJr 'u' \$\endgroup\$ – el16a2t May 1 '19 at 15:42

Closed loop: $$H(s) =\dfrac{F(s)}{1+F(s)}$$ where F(s) is function of the open loop system. Now if you have a controller C(s) in series with the system this becomes: $$H(s) =\dfrac{F(s)\cdot C(s)}{1+F(s)\cdot C(s)}$$

You have to solve F(s) from known C(s) and H(s).

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