Open-Loop Response of a Simulink MIMO System

Hey,

i want to obtain the open-loop response of a MIMO feedback loop in order to evaluate the stability margins. However, I am strugging with the Model Linearizer to perfectly linearize the open-loop.

For analyzing the Linearization process, I have modelled a simple MIMO Feedback Loop System with 2 Inputs and 2 PID Controllers. To receive the open-loop feedback, I placed a 'looptransfer' point at the controller output, as shown below.

I now wanted to verify the linearization process. So I added a state-space block that contains my linearized open-loop, added a step input and compared the open-loop outputs. Instead of having identical open-loop responses, the linearized pant differes from my actual open-loop.

It would be awesome if someone can identify, what I am doing wrong and hep me on how to receive the correct open-loop response of my MIMO system.

Thanks a lot.

Cheers,

Flo

Answer 1

[Sam Chak]

I am unsure whether your modeling is correct; however, one obvious observation from the Scope is that you are comparing the output of the linearized system (state-space) to the control signal of the first PID controller.

[Paul]

Furthermore, the system closes a feedback loop for gamma of Plant1 through an error signal and PID control, but the state space model does not.

[Florian]

Tanks for the feedback. How should I adjust the comparison. I thought the output of the linearized open loop is equal to the control input of the plant, where I open the loop for linearization. If i linearize the feedback loop of a MIMO system, the other feedback loop stays closed, isn’t it?

[Paul]

If the goal is to compare the response of the linearized model to the non-linear plant for a small perturbation around the operating point, my suggestion would be to close the loop around the linearized model using copies of the PID blocks so you have two, decoupled closed-loop systems in parallel. Stimulate both closed loop systems with the same step inputs, with the steps small enough to keep the nonlinear system close to the operating point. Make sure that all of the states in the closed loop system with non-linear plant are initialized at the operating point. Then compare the outputs of the two closed-loop systems, keeping in mind that the output of the linearized system, which should have been initalized to zero, approximates the peturbation of the output from of the non-linear system from the operating point.

Or, do the same thing but don't use any feedback at all. Just stimulate the non-linear plant and the linearized model with the same, small, input. This might not work too well if the plant is not stable.