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2 Systems Science

2 2003

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Robust sliding mode control of multivariable time-delay systems

Jafarov E.M.

Systems Science

2003

Vol. 29, nr 3

17-36

In this paper, robust stabilization of multivariable single state-delayed systems with mismatching parameter uncertainties and matching/mismatching external disturbances is considered. To achieve this goal two types of robust sliding mode controller design techniques are advanced. The first one is an integral sliding mode controller design modification to Shyu and Yan type controller design. By using the Lyapunov-Razumikhin-Hale method the mismatching sliding conditions are parametrically obtained and formulated in terms of matrix norm inequalities. In the second contribution, a new combined sliding mode controller design technique for the stabilization of multivariable single state-delayed systems with mismatching parameter perturbations are advanced by using Lyapunov-Krasovskii V-functional method. The sliding, global stability and β-stability conditions are parametrically obtained and formulated in terms of matrix inequalities. Numerical examples with simulation results show the effectiveness of design procedures.

PD-sliding mode controller for robot manipulators: A comparison analysis

Parlakci M.N.A., Jafarov E.M., Istefanopulos Y.

Systems Science

2003

Vol. 29, nr 2

145-155

This paper introduces a new robust position variable structure controller design method for robot position systems with parameter perturbations. In most situations, the exact knowledge of the robot dynamics does not exist. For this reason a robust variable structure PD-control scheme is proposed for the set-point regulation problem of robot systems. The controller compensates for the inexact information about the robot system. It uses only some robot bound parameters and measurable joint variables. The sufficient conditions are derived for the existence of a sliding mode in the robot system. The techniques of matrix norm inequalities are often addressed for robustness analysis of the controller. In addition, the stability conditions are also investigated in a global sense. Effective parameter-independent conditions are developed by using a full quadratic form of Lyapunov function. Comparative simulation results with classical PD-controller have been presented indicating that the sliding mode PD-like controller yields faster and smoother performance.