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The speed tracking control problem of permanent magnet synchronous motors with parameter uncertainties and load torque disturbance is addressed. Fuzzy logic systems are used to approximate nonlinearities, and an adaptive backstepping technique is employed to construct controllers. The proposed controller guarantees the tracking error convergence to a small neighborhood of the origin and achieves the good tracking performance. Simulation results clearly show that the proposed control scheme can track the position reference signal generated by a reference model successfully under parameter uncertainties and load torque disturbance without singularity and overparameterization.

Permanent magnet synchronous motors (PMSMs) are of great interest for industrial applications requiring dynamic performance 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 PMSM to get the perfect dynamic performance because the motor dynamic model of PMSM is nonlinear and multivariable, the model parameters such as the stator resistance and the friction coefficient are also not be exactly known. The control of PMSM drivers has recently received wide attention and become an active research area. Some advanced control techniques, such as sliding mode control [

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 backstepping is successfully applied to the control of PMSM drivers recently, it usually makes the designed controllers' structure to be very complex.

Fuzzy logic control (FLC) has been found one of the most popular and conventional tools in functional approximations. An FLC [

In this paper, an adaptive fuzzy control approach is proposed for speed tracking control of PMSM drive system via the backstepping technique. During the controller design process, fuzzy logic systems are employed to approximate the nonlinearities, the adaptive fuzzy controllers are constructed via backstepping. The designed fuzzy controller can track the reference signal quite well even the existence of the parameter uncertainties and load torque disturbance. Compared with the existing controller design schemes via backstepping, the proposed method is very simple and the proposed controller has a simple structure.

In this section, some preparatory knowledge of a PMSM will be introduced. The following assumptions are made in the derivation of the mathematical model of a PMSM [

Saturation and iron losses are neglected although it can be taken into account by parameter changes.

The back emf is sinusoidal.

The model of a PMSM can be described in the well known (

The denotation of the PMSM parameters.

Parameter | Denotation | Parameter | Denotation |
---|---|---|---|

The rotor angular velocity | The stator resistance | ||

The | The | ||

The | The | ||

The | The | ||

The pole pair | The rotor moment of inertia | ||

The electromagnetism torque | The load torque | ||

The viscous friction coefficient | The magnet flux linkage of inertia |

To simplify the previous method mode, the following notations are introduced:

Let

For the system (

For the reference signal

Choose Lyapunov function candidate as

As the parameters

Differentiating

Now, choose the Lyapunov function candidate as

Apparently, there are two nonlinear terms in (

At this step, we will construct the control law

At the present stage, to estimate the unknown constants

In this section, the stability analysis of the resulting closed-loop system will be addressed. Substituting (

For the term

To illustrate the effectiveness of the proposed results, the simulation will be done for the PMSM motor with the parameters:

The curve of the rotor speed

The curve of the speed tracking error.

The curve of the rotor position

The curve of the speed tracking error.

Based on adaptive fuzzy control approach and backstepping technique, an adaptive fuzzy control scheme is proposed to control a permanent magnet synchronous motor. The proposed controllers guarantee that the tracking error converges to a small neighborhood of the origin and all the closed-loop signals are bounded. Simulation results illustrate the effectiveness of the presented method.

The controller of PMSM based on conventional backstepping technique is briefly reviewed here. The detailed design procedure is in [

This work is partially supported by the Natural Science Foundation of China (60674055, 60774027, 60444047), the National 863 High Technology Plan of China (2007AA11Z247), the State Key Laboratory of Rail Traffic Control and Safety (Beijing Jiaotong University) (RCS2008ZZ004, SKL2007K006), the Shan Dong Province Key Laboratory of Industrial Control Technique, and Shandong Province Domestic Visitor Foundation (2007001).