Loop tuning with specification on gain and phase margins via modified second-order sliding mode control algorithm

The modified second-order sliding mode algorithm is used for controller tuning. Namely, the modified suboptimal algorithm-based test (modified SOT) and non-parametric tuning rules for proportional-integral-derivative (PID) controllers are presented in this article. In the developed method of test and tuning, the idea of coordinated selection of the test parameters and the controller tuning parameters is introduced. The proposed approach allows for the formulation of simple non-parametric tuning rules for PID controllers that provide desired amplitude or phase margins exactly. In the modified SOT, the frequency of the self-excited oscillations can be generated equal to either the phase crossover frequency or the magnitude crossover frequency of the open-loop system frequency response (including a future PID controller) - depending on the tuning method choice. The first option will provide tuning with specification on gain margin, and the second option will ensure tuning with specification on phase margin. Tuning rules for a PID controller and simulation examples are provided.