Title: Robust guaranteed-cost sliding control for brushless DC motors by LMI

Authors: Hisham M. Soliman; Ehab H.E. Bayoumi; Mostafa Soliman

Addresses: Electrical Engineering Department, Faculty of Engineering, Cairo University, Giza 12613, Egypt. ' Power Electronics and Energy Conversion Department, Electronics Research Institute (ERI), Cairo 12622, Egypt. ' Electrical Engineering Department, Faculty of Engineering, Cairo University, Giza 12613, Egypt; Department of Electrical and Computer Engineering, University of Calgary, Alberta, Canada T2N 1N4, Canada

Abstract: Two state feedback sliding mode control schemes are developed for position control for brushless DC motor drives. The first controller design achieves the desired swiftness of response. In addition to swiftness, the second controller drastically reduces system's chattering by adding the guaranteed cost constraint. The proposed controller consists of two parts, linear and non-linear. Linear matrix inequalities (LMIs) optimisation is used to design the linear part that achieves the desired dynamic performance: it is robust against system uncertainties, and is based on a new sufficient condition for the existence problem; the non-linear part is created to guarantee that the sliding surface is attained. System uncertainty due to changes in drive's load inertia is represented with norm- bounded structure. The main advantages of this technique are that: the LMI algorithm includes an optimal part to preclude high control efforts, and the control burden is heavily placed on the linear part to improve the chattering problem of the conventional sliding mode control.

Keywords: DC machines; electric drives; nonlinear systems; sliding mode control; SMC; state feedback; guaranteed cost control; linear matrix inequalities; LMIs; robust control; brushless DC motors; feedback control; controller design; chattering; vibration.

DOI: 10.1504/IJMIC.2012.049691

International Journal of Modelling, Identification and Control, 2012 Vol.17 No.3, pp.251 - 260

Published online: 17 Dec 2014 *

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