Adaptive Observer-Based Sliding Mode Control for a Two-Wheeled Self-Balancing Robot under Terrain Inclination and Disturbances

Ines Jmel,Faouzi M’Sahli,Salim Hadj-Said,Habib Dimassi,Raúl Villafuerte-Segura

doi:10.1155/2021/8853441

Ines Jmel, Faouzi M’Sahli + Show 3 more

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https://doi.org/10.1155/2021/8853441

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Abstract

This paper investigates an output feedback sliding mode control scheme for a two-wheeled self-balancing robot under terrain inclination and disturbances. First of all, an adaptive high-gain observer is designed for the robot to estimate, simultaneously, the unmeasured states and the unknown terrain inclination angle which appears nonlinearly in the dynamics of the wheeled robot, using the only measured linear and angular positions. Then, the estimated states and the reconstructed unknown inclination angle are used by an appropriate continuously implemented sliding mode controller whose the design is based on the boundary layer approximation approach to reduce the chattering phenomenon. The objective of the proposed robust controller is to ensure the tracking control of the two-wheeled robot despite the unknown terrain inclination and the presence of friction disturbances. The stability of the adaptive observer-based output feedback system is established through a Lyapunov analysis, and it is inspired from sliding modes theory. Numerical simulations results highlight the effectiveness of the proposed tracking control scheme applied on two-wheeled self-balancing robot subject to terrain inclination even in the presence of unavailable disturbances.

Highlights

Specific attention has been booked to the design of adaptive observers in order to ensure, under specific condition, a joint estimation of unmeasured states and system parameters with exponential convergence
Motivated by the incontestable advantages of the latter robust control method, we propose, in this paper, a continuously implemented sliding mode controller for the two-wheeled self-balancing robot where the boundary layer approximation method is adopted in the designed controller to reduce the well-known chattering phenomenon often linked to the use of discontinuous controllers
Others were interested in nonlinear systems with linear parameterization as in [38, 39] and nonlinear parameterization as in [40], where the authors had developed an adaptive observer for the nonlinearly parameterized class of nonlinear systems. e exponential convergence is achieved under certain persistent condition by the adjustment of the gain observer

Summary

Context and Problem Statement

En, the estimated states x􏽢(t) and the reconstructed unknown parameter 􏽢ρ(t) generated by the adaptive observer are to be injected into the sliding mode control law in order to perform the following trajectory tracking aims: lim 􏼌􏼌􏼌􏼌x(t) −. We present first the adaptive observer design method for the wheeled robot, and we combine it with the sliding mode controller whose objective is to ensure tracking control despite the presence of unknown terrain inclination and disturbances. Since the unknown terrain inclination angle appears nonlinearly in the dynamic of the two-wheeled self-balancing robot and given the triangular structure of our system, we adopt the adaptive observer treated in [40] and we recall, the main features of this estimation approach. Once the unmeasured states and the unknown parameter are reconstructed by the adaptive observer (6), the estimated signals are employed, by the sliding mode control law in order to build an adaptive sliding mode controller

Adaptive Observer-Based Sliding Mode Control for the

Numerical Simulations

Conclusions