Controller design for an approximated nonlinear system using Wavelet Transform

Abstract

This work presents the method of representing any nonlinear function with Wavelet Transform (WT) coefficients to facilitate the controller design of any nonlinear system. A priori selection of optimal Mother Wavelet (MW) used for the representation purpose involves the statistical method called the Minimum Description Length (MDL) criterion. The dynamics of a benchmark nonlinear system have been taken to validate the above technique, and it has been proven to be superior to the standard linearization technique. Finally, an Adaptive Sliding Mode Controller (ASMC) for the WT-based approximated model (WTAM) of the plant has been designed. The design of the controller uses the Harmony Search Algorithm (HSA) for tuning purposes. The gain of the switching control law is decided by the gain adaptation technique. The Lyapunov Stability criterion is exploited to judge the stability. To validate the controller's performance in real-time, the WTAM of a Cart Inverted Pendulum is taken. The results validate the efficiency of the controller in terms of its ability to handle unbounded disturbances, parametric uncertainties, and chattering.