Oscillation shaping in uncertain linear plants with nonlinear PI control: Analysis and experimental results

Linear systems controlled by a nonlinear version of the PI algorithm are under study. The modified PI controller in question is known in the literature as the Super–Twisting (STW) algorithm (see Levant (1993)), and it belongs to the family of second order sliding mode controllers. The considered closed–loop system exhibits self–sustained stable oscillations (chattering) when the relative degree of the linear plant is higher than one (see Boiko and Fridman (2005)) and it is the task of the present paper to present a systematic yet simple procedure for tuning the STW algorithm parameters in order to obtain pre–specified frequency and magnitude of the resulting chattering oscillation. The proposed methodology is based on the Describing Function (DF) approach. The approach is theoretically illustrated and verified by means of, both, simulation analysis and experiments carried out by making references to a DC motor.