define an objective function of field oriented control (FOC)

What objective function should I use to determine the optimal coefficients for PI controllers in field-oriented control of an induction motor?

Answer 1

[Epsilon]

Hi Milad,

PI controller gains are tuned based on the time domain or the frequency domain specifications mentioned by the user. The goal is to select coefficients such that the mentioned specifications are met.

MATLAB has a 'PID tuner app' to achieve your desired time or frequency domain response. To launch the PID Tuner, double-click the PID Controller block to open its block dialog. In the Main tab, click Tune. PID tuner app will automatically select the best possible coefficient (optimal value) such that the specifications are met.

Therefore, the optimal coefficients (the best fit) are achieved by the PID tuner(implicitly). Objective functions are used in optimal control but not in PI controller.

For further information please refer to the documentation, https://www.mathworks.com/help/slcontrol/ug/automated-tuning-of-simulink-pid-controller-block.html

[Sam Chak]

The OP, Milad, is probably using an optimization algorithm to find the right gains for the PI controller. So, it’s possible to provide a custom objective function for the optimizer to search for those gains.

However, many novice users tend to rely too much on the auto-tune feature without really understanding how it generates the gain values. Some users think it’s smart or intelligent, believing they don’t need to supply the objective function because they seemingly meet their performance requirements.