# Linearization of Unstable Nonlinear Plant Dynamics

Hi,
I have an unstable nonlinear plant in Simulink which I am linearizing around an operating point using Matlab's linmod function.
My question is in the validation of the linear model:
Since the system is open-loop unstable, I am finding it difficult to validate the linear model I produce by just running the simulation open-loop (I am guessing the difficulty arises from the fact that the simulation departs very quickly from the region where the linear model is valid). Is there anything fundamentally wrong with closing the loop on the nonlinear system to stabilize it and using the same loop on the linear system to compare the closed-loop performance and see if they are close... that way, if the closed loop performance is similar and they both have the same loop wrapped around them, then the dynamics must be similar?
Any other suggestions on how I can validate a linear model in this situation?
Thanks!
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Simualtion is just simulation. The nonlinear unstable plant is just a 'simulated' mathematical model. You may need to simulate the nonlinear plant model with controller designed based on the linear model. Compare may go to controller designed based on linear plant and controller designed based on linear plant.
Thomas
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abahei wrote:

I don't see anything wrong with closing the loop on the thing then comparing to your linear model.
You could also do this open-loop by setting the initial conditions of both models to equivalent values and seeing how they take off.
I'd probably do it in closed loop and argue that since you're going to use the linearization in closed loop then that's probably how you want to test it.
--

Tim Wescott
Wescott Design Services
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Thats what I guessed too, thanks.
I'm finding that linmod has difficulties linearizing the unstable system. It has worked great for me in the past for stable systems. Anybody else have trouble with linmod?
Thanks!