Dynamical Adaptive First and Second-Order Sliding Backstepping Control of Nonlinear Nontriangular Uncertain Systems

Abstract

In this paper combined algorithms for the control of nontriangular nonlinear systems with unmatched uncertainties will be presented. The controllers consist of a combination of Dynamical Adaptive Backstepping (DAB) and Sliding Mode Control (SMC) of first and second order. In order to solve a tracking problem, the DAB algorithm (a generalization of the backstepping technique) makes use of virtual functions as well as tuning functions to construct a transformed system for which a regulation problem has to be solved. The new state is extended by an n−ρth order subsystem in canonical form where n is the order of the original system and ρ is the relative degree. The role of the sliding mode control is to replace the last step of the design of the control law to obtain more robustness toward disturbances and unmodeled dynamics. The main advantages of the second-order sliding mode algorithm are the prevention of chattering, higher accuracy, and a significant simplification of the control law. A comparative study of these first and second order sliding controllers will be presented. [S002-0434(00)02604]

Exact compensation of unmatched perturbation via quasi-continuous HOSM

“…The procedure proposed in [4], [5] the original backstepping technique, coupling them with with an auxiliary second order subsystem to which a second order sliding mode control is applied. In [6] the combination of dynamical adaptive backstepping and first and second order sliding mode control is applied to both triangular and nontriangular uncertain observable minimum phase nonlinear systems.…”

Dynamic adaptive backstepping and saturated proportional integral sliding mode control for uncertain nonlinear systems

“…Another approach is to improve the quality of the DAB-SMC algorithm using second-order sliding mode control. 25 However, the output signal has a higher overshoot.…”

Integral terminal sliding mode control for nonlinear systems

“…Besides, to solve the mismatched systems, the backstepping method is used with SMC. Dynamic adaptive backstepping and first and second order SMC are used for the collaboration of triangular and nontriangular uncertain observable minimum phase nonlinear systems [17]. Another approach regarding the problem of mismatched uncertainty compensation is based on the nonlinear block controllable form [18].…”