Simulink Bode plot of a nonlinear differential system

I prepared the duffing equation model y''(t) + c1*y'(t) + k1*y(t) + k2*y(t)^3 = u(t) in Simulink and I need the bode diagram of this output signal in Simulink. Since it is a nonlinear integro-differential equation model, I am having trouble finding the Bode diagram. Any help would be greatly appreciated.

[Mathieu NOE]

Bode plot of linear system computed from nonlinear Simulink model - Simulink - MathWorks France

Answer 1

[nick]

Hi Ömer Uzuner,

I understand from your query that you want to obtain the Bode plot of your nonlinear differential equation in Simulink.

To achieve this, you may utilize the dedicated "Bode Plot" block available within Simulink. The "Bode Plot" block computes a linear system from a nonlinear Simulink model and plots the linear system on a Bode plot during simulation. This block will allow you to conveniently generate the frequency response of your system. For a step-by-step guide on how to incorporate and use this block in your Simulink model, please refer to the following MathWorks documentation link:

https://www.mathworks.com/help/slcontrol/ug/visualize-bode-response-of-simulink-model-during-simulation.html

Additionally, you can use the "Linearization Manager" found under the "Apps" tab in Simulink. Upon selecting the "Linearization" tab that appears, navigate to the "Model Linearizer". The "Model Linearizer" allows you to perform linear analysis of nonlinear Simulink models. You can mark the signals by right-clicking on the signal and selecting "Linear Analysis Points" to identify open-loop input and open-loop output. For more information about visualizing the Bode response of a Simulink model, you may refer to the following link:

https://www.mathworks.com/help/slcontrol/gs/bode-response-of-simulink-model.html

The following is the bode plot received for the differential equation y''(t) + c1*y'(t) + k1*y(t) + k2*y(t)^3 = u(t) :

Hope this helps,

Regards,

Neelanshu