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This paper investigates the finite-time chaos control of a permanent magnet synchronous motor system with complex variables. Based on the finite-time stability theory, two control strategies are proposed to realize stabilization of the complex permanent magnet synchronous motor system in a finite time. Two numerical simulations have been conducted to demonstrate the validity and feasibility of the theoretical analysis.

Permanent magnet synchronous motors (PMSMs) are widely used in various industrial fields because of their simple structure, high efficiency, high power density, low manufacturing cost, and large torque to inertia ratio [

The existing methods stabilize chaotic systems asymptotically; that is, the trajectories of chaotic systems converge to zero with infinite settling time. However, from the practical engineering point of view, it is more crucial to stabilize chaotic systems in a finite time. Therefore, it is important to consider the problem of finite-time stabilization of chaotic systems. Finite-time control is a very useful technique to achieve faster convergence speed in control systems. In addition, the finite-time control technique has demonstrated better robustness and disturbance rejection properties [

Since Fowler et al. [

Motivated by the above discussion, in the present paper, we construct controllers to stabilize a complex PMSM system. Based on the finite-time stability theorem, two control strategies are proposed to realize chaos control in a finite time. Numerical simulation results show that the proposed controllers are very effective.

A PMSM system in a field-oriented rotor can be described by the following equation [

Finite-time stability means that the states of the dynamic system converge to a desired target in a finite time.

Consider the nonlinear dynamical system modeled by

Assume that a continuous, positive-definite function

For any real number

In order to control chaotic oscillation in the complex PMSM system (

By separating the real and imaginary parts, we have the following real system:

Next, we apply the finite-time stability theory to design controllers to globally stabilize the unstable equilibrium

If the controllers are designed as

Construct the following Lyapunov function:

Substituting the controllers (

If the controllers are designed as

The design procedure is divided into two steps.

When

Choose the following Lyapunov function for system (

Then from Lemma

Strategy 1 is easier to implement than Strategy 2, but the controllers (

In this section, two numerical examples are presented to illustrate the theoretical analysis. In the following numerical simulations, the fourth-order Runge-Kutta method is employed with time step size 0.001. The system parameters are selected as

Consider Strategy 1 with the controllers (

The states of the controlled system (

Consider Strategy 2 with the controllers (

The states of the controlled system (

Nowadays, the complex modeling of phenomena in nature and society has been the object of several investigations based on the methods originally developed in a physical context. In this paper, a complex PMSM system has been considered and the fast stabilization problem of this system has been investigated. Based on the finite-time stability theory, two kinds of simple and effective controllers for the complex PMSM system have been proposed to guarantee the global exponential stability of the controlled systems. During the past decades, the

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was supported by the Natural Science Foundation of China under Grant nos. 11161055 and 61263042.