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For the speed tracking control problem of Permanent Magnet Synchronous Motor (PMSM), a disturbance observer-based (DOB) backstepping speed tracking control method is presented in this paper. First, to reconstruct the load disturbance, a slowly time-varying disturbance observer for PMSM is constructed. Next, by stability theory, the norm of the observation error and disturbance observer design method are obtained. On the basis of these, through the designing of the virtual control input that include the reconstruction disturbances, and using backstepping control strategy, the DOB controller of the closed-loop system is proposed. The obtained controller can achieve high precision speed tracking and disturbance rejection. Finally, some results of evaluative experiments verified the effectiveness of the proposed method for high-performance control and disturbance rejection for the PMSM drive.

Permanent magnet synchronous motor (PMSM) is receiving increasing attention in high-performance industrial servo applications due to its advantages such as high torque to current ratio, super power density, and fast response, as well as low noise [

Over the last decades, various design methods have been developed for PMSM control systems, such as adaptive control [

To further improve the disturbance rejection performance of SMC, extended sliding-mode disturbance observer was proposed in [

Recently, disturbance observer-based (DOB) [

Backstepping is a well-known recursive and systematic design methodology for the feedback control of uncertain nonlinear system with matched uncertainties [

Motivated by the discussions above, in this paper, we mainly investigate backstepping speed control for PMSM based on disturbance observer. A nonlinear disturbance observer is first constructed to estimate the external slowly time-varying disturbance. Then, based on the backstepping control theory, the PMSM rotor speed and current tracking backstepping controllers are designed. Meanwhile, global asymptotic stability is guaranteed by Lyapunov stability analysis.

The rest of this paper is structured as follows. In Section

Assume that magnetic circuit is unsaturated and hysteresis and eddy current loss are ignored. With above standard assumptions, the mathematical model of a conventional surface mounted PMSM with mismatched external disturbances can be given in the

To formulate the design problem, according to system (

For the PMSM control system (

The external disturbance

For all

The main control objective is to design a DOB backstepping controller to keep all the signals in the closed-loop system bounded and ensures global asymptotic convergence of the desired speed and current tracking errors to zero eventually.

Motivated by the disturbance observers in [

To show that the disturbance can be observed asymptotically by observer (

For nonlinear system (

It can be obtained that

Define a monochromatic Lyapunov function as

It follows from Lemma

In the backstepping procedure, a virtual control state is firstly defined and then it is forced to become a stabilizing function. By defining a corresponding error variable and using Lyapunov stability theory, the related control input can be obtained to stabilize the error dynamics [

In the first step of the backstepping control design, a fictitious control input for the rotor speed

In order to realize the complete decoupling and speed tracking of PMSM, the virtual input current can be chosen as

Choose the second Lyapunov function to stabilize

Setting

On the other hand, from (

As to design of command input for

Choose the last Lyapunov function candidate as

If parameters

In this section, the numerical example and experimental results are presented to demonstrate the validity of the proposed method.

The parameters of PMSM.

Parameter | numerical value |
---|---|

Pole Pairs | 3 |

Friction factor | 0.001 |

Stator Inductance | 0.0153 |

Rotor moment of inertia | 0.0021 |

Permanent magnet flux | 0.82 |

Stator Resistance | 0.56 |

Block diagram of the proposed DOB backstepping PMSM control system.

In this simulation, to illustrate the effectiveness of the proposed method, the phase traces by the conventional backstepping (BS) method [

Rotation speed responses.

Three-phase stator current.

Load torque responses.

Figure

Load torque responses.

The results of the experiment are shown in Figures

Rotation speed responses.

Load torque response.

Three-phase stator current.

The load torque and current responses of DOB-BS method is shown in Figures

From these results, it can be observed that the proposed DOB-BS method is effective under different operating conditions and has a better performance at most conditions than that of BS method.

In this paper, a disturbance observer-based (DOB) backstepping speed tracking control method has been presented for the speed tracking control PMSM. Through disturbance estimation, the DOB backstepping control strategy can achieve high precision speed tracking and disturbance rejection performance. Both simulation and experimental results have shown the effectiveness of the proposed method.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this paper. There have no financial and personal relationships with other people or organizations that will influence our work, there is no professional or other personal interest of any nature or kind in any product, service, and/or company that could be construct as influencing the position presented in or the review of the manuscript.

This work was supported in part by the National Natural Science Foundation of China (61573298), Scientific Research Fund of Hunan Provincial Education Department (15B238), and the Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education.