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I would need help to model a motorized system controlled in a closed loop. It is a personal project.

At first, I am looking to obtain the transfer function and simulate the system on computer. In a second step (not the aim of this thread), I would like to use this simulation to search for good PID coefficients for my corrector. I know there are practical ways to find them, but I would like to learn how to model mechanical systems. It will help me later for other personal project. It is an area that interests me. So I would need a boost, a direction to follow, to model this system.

Here is the project situation:

I am currently making a motorized stop for a metal saw in my workshop. The system is functional.

A DC motor is controlled in PWM via a driver.

The displacement is measured by a relative rotary encoder sufficiently precise for this application (OMRON E6B2-CWZ6C 600P/R).

The engine moves a belt, itself fixed on a cart (stop) which slides on a linear rail.

The operation is simple: I enter a position (in mm) to be reached, the program calculates the gap with the current position, the number of driving turns to be carried out, and moves the cart to the desired position.

The PID corrector (error = difference between measured position and set position) allows me to have a slightly softer and precise reaction.

My situation

I am 33 years old. I did my studies in electronics, my last mechanics courses dates back to the high school in the science of the engineer.

I did research on the subject, and what I understand / suppose / deduced (correct me if I have false):

-If my system is order 1 or 2, I can get its transfer function. Otherwise, I have to decompose it in the subsystem of order 2.

- The current / couple relationship is a first order. The tension / speed relationship is a second order. The enslavement in a position is a third order. So I have to decompose my system in subsystems.

- On my position measurement, the traced curve looks like an order 2, which contradicts the previous point.

- On certain website, I see that it is recommended to make a loop for each order, to simulate each loop, and to define PID coefficients for each loop. It seems a little disproportionate to me.

It's a bit vague for me and I don't really see what end start.

Could you give me a track? A beginning of explanation? A website on which to find the solution?

Thanks in advance,

Have a good day.