Optimal Adaptive Sliding Mode Controller Design for a Wavelet-based Approximated Nonlinear System

Abstract

Abstract This work presents an optimization-based robust Adaptive Gain Sliding Mode (AGSM) controller for a nonlinear system where wavelet-based approximation technique is employed in contrary to the linearization technique. To find out the mother wavelet corresponding to the best approximation of nonlinear model, Minimum Description Length (MDL) criterion is utilized. Three different wavelet series are considered to find the best mother wavelet function. The constant of the sliding surface follows dynamical adaptive nature using Harmony Search Algorithm (HSA) based optimization technique to mitigate the extent of chattering. On the other hand, the gain adaptation method is used to calculate the gain of the switching control law of Sliding Mode Control. To ensure the stability of the closed-loop system with adapted gain as well as optimal sliding constants, Lyapunov Stability Criterion is exploited. To validate the performance of the proposed controller (Optimal AGSM Controller) in real time, an Inverted Pendulum System is taken with its wavelet approximated model. The results obtained from simulation as well as hardware validate the efficacy of the proposed design with the assurance of handling unbounded disturbances, parametric uncertainties, and chattering.