A Comparative Study of a High Gain Observer and a Nonlinear Observer based on the Circle Criterion for Sensorless Induction Motor Control

Jestr

Journal of Engineering Science and Technology Review 17 (5) (2024) 117-125

Research Article

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Engineering Science and Technology Review

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A Comparative Study of a High Gain Observer and a Nonlinear Observer based on the Circle Criterion for Sensorless Induction Motor Control

Abdelhak Benheniche¹, Farid Berrezzek² and Hacene Mellah^3,*

¹Electromechanical Department, M.B. Ibrahimi University, Bordj Bou Arreridj 34000, Algeria

²Fac. Sci & Tec., LEER Lab.Univ. Med Cherif Messaadia University, Souk Ahras 41000, Algeria

³Electrical Engineering Department, Faculty of sciences and applied sciences, University of Bouira, 10000 Bouira, Algeria.

Received 10 January 2024; Accepted 13 September 2024

Abstract

This paper compares between a High-Gain Observer (HGO) with a nonlinear observer based on the Circle Criteria Observer (CCO) for sensorless control of induction motor (IM) drives. The circle criterion method is better for making nonlinear observers because it doesn't require as strict conditions as other methods that try to get rid of system nonlinearities using a transformation nonlinear state. However, the high gain observer makes an effort to dominate the nonlinearities in the system with a high-gain output adjustment term. The suggested study uses the backstepping control method and looks at three performance criteria: tracking the trajectory, rejecting disturbances, and maintaining steady-state stability. It was found that the circle-based nonlinear estimator works better than the interconnected observer, based on the results and the comparison criteria already mentioned.

Keywords: Nonlinear observer, High-gain observer, Backstepping control, Induction motor, Lyapunov stability.

1. Introduction

Over the past decades, the field of sensorless control has become one of the most attractive areas of research in the control of electric actuators. This is due to the increased reliability and reduced cost of the system [1-2]. The essential elements of this domain are the electrical machine, the control strategy and the state observer. Due to their efficiency, effectiveness, simplicity, high reliability, resilience, and power density, asynchronous motors are the most commonly used machines in industries [3]. However, because of the rotor state-space variables and parameters of this motor are not measurable and it is nonlinear, highly linked, time fluctuating multivariate system, controlling, diagnosing, and monitoring is made more difficult [4]. To overcome the above problems and ensure the high performance of this machine, many types of nonlinear control approaches have been proposed and tested in practice. Among these strategies, we can cite the input-output linearization technique [5-6], sliding mode approach [7-8], Backstepping and Integral Backstepping method [9-11], flatness strategy [12-13] and adaptive algorithms [14-15] to solve the problem of time varying parameters. As mentioned above, Backstepping control is a nonlinear strategy widely used in a wide range of nonlinear systems that provides overall stabilization. On the other hand, it performs well even in the presence of variability. This technique is mainly based on the utilization of the Lyapunov function [15]. However, as with all nonlinear control techniques, it is necessary to have reliable and precise information on the various state variables of the system. In this situation, recourse to state-observers becomes an unavoidable solution. It should be noted that a state observer is a system that changes. Which can estimate the non- measurable state variables from the available measurements of the inputs and outputs of the considered system. This

*E-mail address: h.mellah@univ-bouira.dz

ISSN: 1791-2377 © 2024 School of Science, DUTH. All rights reserved. doi:10.25103/jestr.175.16

software sensor is crucial not only for control, but also for system monitoring, diagnostics, and fault tolerant control strategies.

Recently, a number of estimation techniques have been used to estimate IM rotor variables [16]. These approaches include the extended Kalman filter, which is a stochastic recursive estimation strategy for nonlinear systems [17]. Researchers often opt for this approach due to its ease of implementation and popularity in estimation [18]. The nonlinear Luenberger observer is distinguished by its inherent simplicity in comparison to the other approaches, without reducing estimate precision [19]. The Model Reference Adaptive System (MRAS) observer has become very popular in sensorless IM control because of its ease of implementation, good stability, low computational effort, and its good performance [20]. The Sliding Mode (SM) observer has the advantage of being unaffected by rotor time constant fluctuations [21]. Yet, they have the following limitations: the triangle block structures, the sensitivity against measurement noises, and the peaking phenomenon's disturbing influence.

The nonlinear observer constructed on the circle criterion introduced by Arckak and Kokotovich [22] allows for manipulation of the non-linearities directly and with less severe restrictions than the approaches of linearization and large gains [23-24]. Among the observers who have found a place in the sensorless control of electrical machines, we cite the High-Gain Observer (HGO) [25]. The use of these observers is motivated by their capacity to estimate in a robust way the unmeasured states while attenuating in an asymptotic way the disturbances [26-28]. However, the disadvantages of this observer are in their implementation, their calibration, and their very high gain which sometimes limit their use [29- 30]. Motivated by the characteristics of the observers cited above, in this paper, we compare the HGO and the observer using the circle criterion and backstepping strategy control for a sensorless IM control scheme. The present paper is

structured as follows: In Section 2, the IM's modelling is provided. Section three is intended for the description of the nonlinear Circle Criterion Observer (CCO). In Section 4, we present the theory of the HGO. In Section 5, we briefly recall the backstepping control technique. Finally, we end with a comparative simulation and interpretation of the obtained results, which allows us to draw conclusions from this work.

2. Mathematical Modelling of a Three-Phase IM

In the reference frame of the stator fixed (