Title: Proof of stability and boundedness of a real-time motor resistance estimation and compensation scheme

Authors: Ravindra Patankar, Liangtao Zhu

Addresses: Department of Mechanical Engineering – Engineering Mechanics, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931, USA. ' Department of Mechanical Engineering – Engineering Mechanics, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931, USA

Abstract: This paper presents and proves the stability and boundedness of a scheme for estimation of one parameter in a complex nonlinear system. The proof presented in this paper does not assume discretised plant equations. This scheme is applied to estimate resistance of a brushless DC motor and compensate for the resistance change in real-time via feedback control. A non-dynamic motor inverse model, which neglects the electrical dynamics of the motor, is used to achieve torque control of the motor. Variations of the motor parameters, due to environmental factors, such as temperature, build variations, ageing, etc., directly impart inaccuracies in the motor control, and thus affect the performance of the system. Comparison of simulations for closed-loop voltage control of automotive electric power steering system actuator confirms a lower bound of error of the estimated parameter and faster adaptation with the proposed scheme compared to previously employed methods.

Keywords: brushless DC motors; adaptive parameter estimation; voltage control; stability; boundedness; motor resistance estimation; compensation; nonlinear systems; feedback control; torque control; automotive steering; electric power steering.

DOI: 10.1504/IJAAC.2009.025246

International Journal of Automation and Control, 2009 Vol.3 No.2/3, pp.264 - 279

Available online: 17 May 2009 *

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