Authors: Abdelkader Maddi; Abderrezak Guessoum; Daoud Berkani
Addresses: Electronics Department, Faculty of Technology, Saad Dahlab University of Blida, Algeria ' Electronics Department, Faculty of Technology, Saad Dahlab University of Blida, Algeria ' Department of Electrical Engineering, National Polytechnic School of Algiers, Algeria
Abstract: In this paper, a new design of an adaptive model following control (AMFC) system is proposed and analysed for a class of multi-input multi-output (MIMO) linear time-varying plants with unknown bounded parameters, and sufficiently slowly varying with time. We then show that the new approach based on combined Lyapunov method and hyper-stability criteria tries to overcome the problems of stability and zero tracking error. The main difficulty of Lyapunov methods is in finding an appropriate Lyapunov control function for the closed-loop system, therefore different choices of Lyapunov functions may result in different control structures and control performance. We show that the design of AMFC for the class of linear time-varying systems could be composed of a stable linear block in the feed forward path which turns out to be easily solvable by Lyapunov equation and a nonlinear time-varying block in the feedback path can be handled with using adaptive control techniques, such that the closed-loop dynamics of the system approaches the reference model. This structure results in greater flexibility in the choice of the adaptive laws. Finally, a typical numerical example to an aircraft control problem is analysed.
Keywords: adaptive control; model following; Lyapunov function; hyperstability criteria; aircraft model.
International Journal of Systems, Control and Communications, 2020 Vol.11 No.4, pp.364 - 380
Accepted: 09 Feb 2020
Published online: 10 Sep 2020 *