Proper system linearization for tracking problems

I am familiar with the Model linearization tool provided by Matlab, which allows to linearize systems around a specific operating point.

However, in case of tracking control problems (i.e. when the desired refernce point changes in time) we want the system to evolve through many different equilibrium points. In addition, if the reference point moves quickly enough, neither of these equilibrium points may be actually reached by the system.

Suppose I want to design a PID feedback control in such a situation. Which would be the correct approach to follow? Should I linearize the system around a series of different operating points (hopefully known in advance) and then switch between them during the tracking execution? Or maybe Matlab provides a better and more efficient solution?

Answer 1

[Sam Chak]

Hi @Federico Toso

Perhaps you should consider offline-designing a family of PID controllers that give consistent satisfactory closed-loop responses for different equilibrium points.

You can find the example here:

https://www.mathworks.com/help/control/ug/designing-a-family-of-pid-controllers-for-multiple-operating-points.html