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An adaptive fuzzy control method is developed to control chaos in the permanent magnet synchronous motor drive system via backstepping. Fuzzy logic systems are used to approximate unknown nonlinearities, and an adaptive backstepping technique is employed to construct controllers. The proposed controller can suppress the chaos of PMSM and track the reference signal successfully. The simulation results illustrate its effectiveness.

Permanent magnet synchronous motors (PMSMs) are intensively used in industrial applications due to their high speed, high efficiency, high power density, and large torque to inertia ratio. Then, it is still a challenging problem to control the PMSM to get the perfect dynamic performance, because the dynamic model of PMSM is nonlinear, multivariable and even experiencing Hopf bifurcation, limit cycles, and chaotic attractors with systemic parameters falling into a certain area [

Backstepping is a newly developed technique to control the nonlinear systems with parameter uncertainty, particularly those systems in which the uncertainty does not satisfy matching conditions. Though the conventional backstepping is successfully applied to the control of PMSM drivers recently, it usually makes the designed controllers' structure to be very complex.

In recent years, fuzzy logic control (FLC) [

In this paper, an adaptive fuzzy control method is developed to control chaos in the permanent magnet synchronous motor drive systems via backstepping technology. During the controller design process, fuzzy logic systems are employed to approximate the nonlinearities of the chaotic PMSM drive system; the adaptive fuzzy controllers are constructed via backstepping. Compared with the conventional backstepping, the designed fuzzy controller has a simple structure, which can suppress the chaos of PMSM and track the reference signal generated by a reference model quite well.

The dimensionless mathematical model of PMSM with the smooth air gap can be described as follows [

In system (

The modern nonlinear theory such as bifurcation and chaos has been widely used to study the stability of PMSM driver system. The study found that the PMSM is experiencing chaotic behavior when the operating parameters

Typical chaotic attractor in PMSM with system parameters

The control objective is to design an adaptive fuzzy controller such that the state variable

Let

In this section, we will develop an adaptive fuzzy control approach to control chaos in PMSM drive system via the backstepping. The backstepping design procedure contains

For the reference signal

Choose Lyapunov function candidate as

Differentiating

Now, choose the Lyapunov function candidate as

Differentiating

Notice that

According to Lemma

Introduce variables

To address the stability analysis of the resulting closed-loop system, substitute (

In order to illustrate the effectiveness of the proposed results, the simulation will be conducted to control chaos in PMSM drive system with two sets. First we tested the chaotic PMSM drive system with

The

The

The

The

The

The

The curve of the controller

And the fuzzy membership functions are:

Based on backstepping technique, an adaptive fuzzy control scheme is proposed to control chaos in the permanent magnet synchronous motor drive systems. The proposed controllers guarantee that the tracking error converges to a small neighborhood of the origin, and all the closed-loop signals are bounded. The simulation results are provided to demonstrate the effectiveness and feasibility of the proposed method.

This paper is partially supported by the Natural Science Foundation of China (60674055, 60774027, 60774047), the Natural Science Foundation of Shandong Province (ZR2009GM034), the State Key Laboratory of Rail Traffic Control and Safety (Beijing Jiaotong University) (RCS2008ZZ004), the cultivating plan of excellent degree thesis (Qingdao University), and Shandong Province Domestic Visitor Foundation.