Problem with derivative block simulink

I want to simulate these two equations in simulink to get the results. It's about adaptive control.

The outputs are dy1 and ddy2 How to simulate without using derivative block that makes the simulation infinite numbers? e.g integrator instead.

The inputs are y1ref and y2ref and y1 and y2ref and the equations are separate.

All The k11 k21 and k22 are constant numbers.

Any help is appreciated.

[Purvaja]

Hello,

I feel that this model needs some initial conditions/limits for integration, due to which it is difficult to model the equation as is. Do share if anything is missing or correct me if I am wrong.

[Mathieu NOE]

hello

first I would probably choose to use fixed step solver , because I would use discrete high pass filters instead of "true" derivatives - if your inputs (y1ref and y2ref)are like step inputs , or anything with very sharp transients (maybe not).

high pass filters can be viewed as a band limited derivative. set the corner frequency high enough - compared to your input signal frequency content

otherwise , you will of course some integrators , I assume you knew it already

[Sam Chak]

Hi @Purvaja

What is the issue of running these two so-called adaptive control equations in Simulink? I'm unfamiliar, but the OP mentioned that the measurable outputs are dy1 and ddy2, which I presume to be and , respectively. The state in the 1st equation can be obtained by integrating . Both and in the 2nd equation can be obtained by peforming and , respectively.

If both reference signals and are constants, then . If both and can be described by at least 2-times differentiable continuous-time mathematical models, then , , and can be manually computed beforehand. The real issue is when and are time series data.

However, do take note that the dynamics will be unstable if .

[Purvaja]

Hello @Sam Chak

I am just a beginner in Simulink. I had some hands on on integrator block. This question intrigued me because here equations need to use 2 integrators in same equation, and I was not sure how to simulate it in Simulink, can you please explain me with respect to blocks in Simulink or best how to handle such equations with derivatives of 2 different variables used in same equation using integrator block?

Answer 1

[Sam Chak]

Hi @Purvaja

Based on the information provided by the OP, I will likely construct the model as illustrated. However, if the reference is time series data, I believe that @Mathieu NOE's suggestion to use a high-pass filter to approximate the derivative signals is better.

[Purvaja]

Thankyou @Sam Chak.