Non-Parametric Tuning of PID Controllers via Modified Second-Order Sliding Mode Algorithms

An application of the modified second-order sliding mode (SOSM) algorithms to a PID controller tuning is presented. The proposed method utilizes the opportunity of exciting test oscillations in the controller-process loop at the frequency corresponding to a desired phase lag of the process. This allows for this frequency to become the phase crossover frequency in the closed-loop system with a PID controller if the tuning rules are formulated as non-parametric rules in terms of the “ultimate frequency” and “ultimate gain”. The use of those properties results in designing a simple tuning method that provides the desired stability of the system. A simple test that involves measurements of the amplitude and of the frequency of the self-excited oscillations and non-parametric tuning rules that provide desired gain margins exactly are presented.