Title: Feedback control of bilinear distributed parameter system by input-output linearisation

Authors: Nouara Habrache; Ahmed Maidi; Jean-Pierre Corriou

Addresses: Laboratoire de Conception et Conduite des Systèmes de Production, Université Mouloud Mammeri, 15 000 Tizi-Ouzou, Algérie, Algeria ' Laboratoire de Conception et Conduite des Systèmes de Production, Université Mouloud Mammeri, 15 000 Tizi-Ouzou, Algérie, Algeria ' Reaction and Process Engineering Laboratory, UMR 7274-CNRS, Lorraine University, ENSIC 1, rue Grandville, BP 20451, 54001 Nancy Cedex, France

Abstract: In this paper, a control law that enforces the tracking of a boundary controlled output for a bilinear distributed parameter system is developed in the framework of geometric control. The dynamic behaviour of the system is described by two weakly coupled linear hyperbolic partial differential equations. The stability of the resulting closed-loop system is investigated based on eigenvalues of the spatial operator of a weakly coupled system of balance equations. It is shown that, under some reasonable assumptions, the stability condition is related to the choice of the tuning parameter of the control law. The performance of the developed control law is demonstrated, through numerical simulation, in the case of a co-current heat exchanger. The control objective is to control the outlet cold fluid temperature by manipulating its velocity. Both tracking and disturbance rejection problems are considered.

Keywords: partial differential equation; bilinear distributed parameter system; geometric control; characteristic index; exponential stability; co-current heat exchanger; input-output linearisation.

DOI: 10.1504/IJMIC.2019.099812

International Journal of Modelling, Identification and Control, 2019 Vol.31 No.4, pp.323 - 330

Received: 10 Mar 2017
Accepted: 14 Jul 2017
Published online: 23 May 2019 *

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