Adaptive Wavelets Sliding Mode Control for a Class of Second Order Underactuated Mechanical Systems

Abstract

The control of underactuated mechanical systems (UMS) remains an attracting field where researchers can develop their control algorithms. To this date, various linear and nonlinear control techniques using classical and intelligent methods have been published in literature. In this work, an adaptive controller using sliding mode control (SMC) and wavelets network (WN) is proposed for a class of second-order UMS with two degrees of freedom (DOF).This adaptive control strategy takes advantage of both sliding mode control and wavelet properties. In the main result, we consider the case of un-modeled dynamics of the above-mentioned UMS, and we introduce a wavelets network to design an adaptive controller based on the SMC. The update algorithms are directly extracted by using the gradient descent method and conditions are then settled to achieve the required convergence performance.The efficacy of the proposed adaptive approach is demonstrated through an application to the pendubot.

Adaptive second-order backstepping control for a class of 2DoF underactuated systems with input saturation and uncertain disturbances

“…The properties of the system described by Eq. ( 2 ) can be found in detail 2 , 6 , 12 , and some properties are beneficial for the design and analysis of the closed-loop control system 6 .…”

“…It is assumed that the position and velocity can be obtained with an encoder and tachometer for each DoF 6 .…”

“…Some scholars focus on intelligent control algorithms, and some scholars focus on nonlinear control algorithms. For the intelligent control algorithms, the fuzzy or fuzzy-based control algorithms are proposed 4 , 5 , and neural network (NN) or NN-based controllers are proposed 6 – 8 . For the nonlinear control algorithms, the partial feedback linearization 1 , the adaptive control methods 7 , 9 , the energy- or passivity-based control methods 10 , 11 , the robust control methods 12 , 13 , and the sliding mode-based methods 14 , 15 are proposed.…”