Integral Sliding Modes with NonlinearH∞-Control for Time-Varying Minimum-Phase Underactuated Systems with Unmatched Disturbances

Roger Miranda-Colorado,Luis T Aguilar,Carlos Chavez

doi:10.1155/2017/4876019

Abstract

This paper presents a methodology for controlling nonlinear time-varying minimum-phase underactuated systems affected by matched and unmatched perturbations. The proposed control structure consists of an integral sliding mode control coupled together with a global nonlinearH∞-control for rejecting vanishing and nonvanishing matched perturbations and for attenuating the unmatched ones, respectively. It is theoretically proven that, using the proposed controller, the origin of the free-disturbance nonlinear system is asymptotically stabilized, while the matched disturbances are rejected whereas theL2-gain of the corresponding nonlinear system with unmatched perturbation is less than a given disturbance attenuation levelγwith respect to a given performance output. The capability of the designed controller is verified through a flexible joint robot manipulator typically affected by both classes of external perturbations. In order to assess the performance of the proposed controller, an existing sliding modes controller based on a nonlinear integral-type sliding surface is also implemented. Both controllers are then compared for trajectory tracking tasks. Numerical simulations show that the proposed approach exhibits better performance.

Highlights

Much research in recent years has focused on the stabilization and control of mechanical systems operating under uncertain conditions such as external disturbances, uncertain parameters of the plant, and parasitic dynamics
Disturbances acting in the nonactuated part of an underactuated mechanical system are a typical example where the unmatched disturbances must be counteracted
The numerical simulations considered two trajectories to follow: (1) A sinusoidal desired link reference signal described by qd (t) = sin (3t) [rad]

Summary

Introduction

Much research in recent years has focused on the stabilization and control of mechanical systems operating under uncertain conditions such as external disturbances, uncertain parameters of the plant, and parasitic dynamics. In spite of the rich and diverse literature on the matter (see, e.g., [1,2,3]), the unmatched disturbances are still a challenging problem, faced by control engineers, that adversely affect the performance of any system to be controlled. This kind of disturbances cannot be trivially neglected since they can be aroused by unavoidable noise in the measurements or perturbing the output as well. The problem becomes more complicated for the motion control of this kind of systems since unmodeled dynamics can emerge (see, e.g., [4])

Objectives

Methods

Results

Conclusion