ITAE optimal variable structure control of second order systems with input signal and velocity constraints

Abstract

Purpose

The purpose of this paper is to design a new sliding mode control algorithm for the second order dynamic system subject to input signal and velocity constraints.

Design/methodology/approach

The proposed algorithm employs a time‐varying switching line. At the initial time t=t₀, the line passes through the representative point of the system in the error state space. Afterwards, the line moves with a constant velocity and a constant angle of inclination to the origin of the space and having reached the origin it stops moving. Parameters of the line are selected in such a way that the integral of the time multiplied by the absolute error is minimized with the input signal and the system velocity constraints. First, each of the constraints is taken into account separately, and then both of them are considered at the same time.

Findings

The algorithm introduced in this paper ensures insensitivity of the controlled system with respect to external disturbance and model uncertainty since the very beginning of its motion. Furthermore, the algorithm guarantees fast tracking error convergence to zero without overshoots or oscillations.

Originality/value

In this paper, new systematic methods of the switching line design for the second order system are presented. Input signal and velocity constraints are explicitly taken into account in the design process.

Citation

Nowacka‐Leverton, A. and Bartoszewicz, A. (2009), "ITAE optimal variable structure control of second order systems with input signal and velocity constraints", Kybernetes, Vol. 38 No. 7/8, pp. 1093-1105. https://doi.org/10.1108/03684920910976844