designing a PID for a rotating shaft

I have the following equation of motion that I am attempting to design a controller for

where a, b, c and d are constants, ω is the frequency and Q is the control force.

What block functions do I need to use to solve this control problem?

[Sam Chak]

Hi @Samuel Adshead

Do you intend to solve the control problem using Simulink blocks or MATLAB functions?

What are performance requirements?

The differential equation can be rearranged to become

.

If the disturbance can accurately measured, then you can try to cancel it out.

[Samuel Adshead]

i want to measure the amplitude of the system and control it through the variable Q. I intend to use either byt simulink blocks is preferable. The equation of motion is describing a rotaing shaft for a submarine and the requirment of the controller is to minimise oscillations. a, b,c, d represent numeric constants that come from the properties of the system eg mass, lenghth, ect

Answer 1

[Sam Chak]

Hi @Samuel Adshead

Based on your non-specific descriptions or the control problem above, you generally need to get from here

to arrive at this equation

, after applying the signal as a function of time t and the state variables z, .

If you intend to model this system in Simulink, you may interactively tune the Q 'block', by using the Control System Tuner app.

[Samuel Adshead]

Hi @Sam Chak

how would i go about it in matlab? im struggling with the fact that the controller acts by varing the value of Q and not the whole system to reduce the error to zero

[Sam Chak]

Hi @Samuel Adshead

For this specific task, I recommend exploring the features in the Control System Designer app in MATLAB/Simulink since you have a better understanding of the system dynamics than I do. Take your time to read tutorials and examples, as mastering the basic design skills may require 1 to 2 years.