Journal of Sensors

Volume 2016 (2016), Article ID 8567429, 10 pages

http://dx.doi.org/10.1155/2016/8567429

## Sliding Mode Control for Bearingless Induction Motor Based on a Novel Load Torque Observer

^{1}School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212013, China^{2}Automotive Engineering Research Institute, Jiangsu University, Zhenjiang 212013, China

Received 11 June 2016; Revised 26 August 2016; Accepted 6 September 2016

Academic Editor: Rafael Morales

Copyright © 2016 Zebin Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

For the problem of low control performance of Bearingless Induction Motor (BIM) control system in the presence of large load disturbance, a novel load torque sliding mode observer is proposed on the basis of establishing sliding mode speed control system. The load observer chooses the speed and load torque of the BIM control system as the observed objects, uses the speed error to design the integral sliding mode surface, and adds the low-pass filter to reduce the torque observation error. Meanwhile, the output of the load torque is used as the feedforward compensation for the control system, which can provide the required current for load changes and reduce the adverse influence of disturbance on system performance. Besides, considering that the load changes lead to the varying rotational inertia, the integral identification method is adopted to identify the rotational inertia of BIM, and the rotational inertia can be updated to the load observer in real time. The simulation and experiment results all show that the proposed method can track load torque accurately, improve the ability to resist disturbances, and ameliorate the operation quality of BIM control system. The chattering of sliding mode also is suppressed effectively.

#### 1. Introduction

Based on the similarity principles of magnetic bearing and alternating current (AC) motor stator structure, BIM is formed. Two sets of windings are embedded in the stator slot of BIM, which can separately produce electromagnetic torque and radial levitation force. BIM achieves the integration of rapid rotation and stable suspension of rotor by changing the currents in the windings and avoids the mechanical bearing friction, wear and tear, and lubrication. It breaks the bottleneck of traditional asynchronous motor developing towards the higher precision and higher speed direction [1–5]. BIM has many better advantages than the traditional asynchronous motor, such as simple structure, uniform air gap, high mechanical strength, high speed, and ultrahigh speed running in the corrosion or other special environments. Therefore, it shows broad development prospect in medical equipment, transportation, national defense, and so forth [6–9]. However, BIM has the characteristics of nonlinearity, multivariability, and strong coupling. The traditional PI controller cannot acquire high-performance control for BIM when the control system is disturbed by load torque [10].

Sliding mode variable structure control, as a kind of special nonlinear control, can operate in accordance with the trajectory designed by people and purposefully adjust operation according to the system status, which can gain excellent control performance. Due to the fact that the sliding mode control not only can be set by people, but also does not need high precision mathematical model and has strong robustness to disturbances, it is becoming a hot research topic [11–15], and it is gradually applied in the AC servo system. In [16], a new reaching law was designed to improve the operation quality of sliding mode. At the same time, it was applied in the speed control, which effectively enhanced the robustness of permanent magnet synchronous motor (PMSM) system. In [17], the sliding mode control combining with model reference adaptive was used to obtain the speed. The results showed that it increased the estimation precision of rotor velocity for PMSM and decreased the chattering. In [18], the sliding mode control was used in a generator based on the exercise equipment with nonlinear - characteristic curves. The amount of generator input current harmonic is greatly reduced. In [19], the conventional sliding mode control was united with the adaptive fuzzy backstepping scheme. The simulation proved that this method improved the performance of mismatched uncertain system. In [20], the sliding mode control dealt with the difficult problem of obtaining the counterelectromotive force, and it finally implemented the direct torque control of brushless direct current motor. In [21], the sliding mode control was used to detect the speed and position for PMSM. The experimental results proved the validity of the proposed sliding mode observer. In [22], based on the nonsingular terminal sliding mode algorithm and backstepping method, the sliding mode observer and position controller were put forward, which can estimate the torque accurately and track the position quickly. In [23], the adaptive sliding mode control for uncertain singularly perturbed nonlinear system was designed. It not only reduced the effects of uncertainty, but also guaranteed the control performance. In [24, 25], the load sliding mode observers were proposed. They diminished the adverse effects of load changes on PMSM and improved the antidisturbance ability of controlled system at some level. However, they all ignored the problem that the load changes result in the different rotational inertia and the controlled system had large chattering. Hence, the system cannot achieve the best dynamic performance.

A novel sliding mode observer of load torque, of which the state variables are the speed and load torque, is proposed to suppress the impacts of the load torque changes on BIM control system. A low-pass filter used in the observer reduces the observation error of torque. Moreover, the observer as feedforward compensation for the given current alleviates the output pressure of sliding mode controller (SMC). In addition, adopting the integral identification method validly identifies the rotational inertia and improves the precision of BIM. The simulation and experimental results show that the proposed method overcomes the disadvantageous effects on the speed regulation system generated by load disturbances and strengthens the antidisturbance ability of the system.

#### 2. The Dynamics Model of BIM

According to the electromagnetic field theory, the radial levitation force of BIM in the coordinates can be established as [6] where , , and ; and are the components of the radial levitation force in and directions; the subscript “” represents the torque windings, the subscript “” represents the radial levitation force windings, “” represents the stator, and “” represents the rotor; and separately represent the pole pairs of torque windings and suspension windings; and are the current components of the stator in levitation force windings under the axis; is mutual inductance of the levitation force windings; is the effective length of the rotor; is the stator inner diameter; is the permeability of vacuum; and , respectively, show the effective number of turns of the torque windings and the levitation force windings; and and are the components of flux linkage for the torque winding in the coordinates, respectively.

With the torque windings and the levitation force windings, BIM is a nonlinear, strongly coupled, and complex system. In order to simplify the analysis of BIM, a hypothesis is given that the levitation force windings only create a rotating magnetic field. The rotor voltage equation can be described aswhere and are the rotor voltages of torque windings in coordinates; is the rotor resistance; and are separately the air gap field speed and rotor speed; and is the differential operator.

The flux linkage can be expressed aswhere and are the stator leakage inductance and rotor leakage inductance of torque windings, respectively.

The electromagnetic torque equation is set up as

The equation of motion is written aswhere is the load torque and is the rotational inertia.

After coordinate transforming, the rotor flux in axis can be expressed asMaking the axis of the rotating coordinates coincide with the rotor flux linkage of torque windings, it is written as . Formula (6) can be simplified as

Putting Formula (7) into Formula (2), the excitation current and slip speed can be obtained as follows:where and is the time constant of rotor.

The electromagnetic torque equation turns intowhere is the rotor self-induction. Figure 1 is the block diagram of rotor field-oriented decoupling control.