Elsevier

Neurocomputing

Volume 337, 14 April 2019, Pages 110-119
Neurocomputing

Adaptive fuzzy finite-time command filtered tracking control for permanent magnet synchronous motors

https://doi.org/10.1016/j.neucom.2019.01.057Get rights and content

Abstract

This paper studies the position tracking control problem for permanent magnet synchronous motors (PMSMs) with parameter uncertainties. Firstly, the command filtered method is employed to overcome the “explosion of complexity” in traditional backstepping method. Then, in order to reduce the errors produced by command filters, error compensation mechanism is adopted. In addition, the finite-time control method makes the tracking error converge to the smaller neighborhood in the finite time. The adaptive fuzzy control is used to approximate the nonlinear functions. Finally, the simulation results proved the designed control method can overcome the influence of parameter uncertainties and achieve the satisfactory position tracking control.

Introduction

In recent years, with the rapid development of power electronics, micro computer technology and control theory, permanent magnet synchronous motors (PMSMs) have been widely used in practical applications. And because the permanent magnet synchronous motors have the advantages of simple structure, small volume, high efficiency and reliable operation and et al., permanent magnet synchronous motors are gradually replacing DC motor and stepping motor. Nevertheless, the dynamic mathematical models of permanent magnet synchronous motors (PMSMs) are highly nonlinear and multivariable. Besides, the PMSMs systems are affected by the parameters of the motor. Therefore, in order to achieve high performance control for PMSMs systems, advanced control strategies and control methods are applied to the systems, which make the systems have strong adaptability and anti-interference ability. In order to meet the higher requirement of permanent magnet synchronous motor in practical application, researchers proposed the backstepping control [1], [2], [3], adaptive control [4], [5], [6], sliding mode variable structure control [7], [8], [9], dynamic surface control [10], command filter control [11], [12], [13], [14], [15], and so on [16], [17], [18], [19], [20], [21], [22].

In the above control methods, the backstepping method has shown its advantages in designing robust or adaptive controllers for uncertain systems (especially when disturbances or uncertainties do not satisfy the matching conditions), therefore many papers have studied the application of this method in PMSMs. However, since the backstepping method directly analyzes the derivatives of the virtual control, the computational processes are complicated and easily result in “explosion of complexity” problem. In order to solve the above problems, when designing the controller, the derivatives of the virtual control are approximated by each step passing through the command filter, thus avoiding the complex higher order derivatives and solving the problem of “explosion of complexity”. At the same time, the compensation error signals are adopted to reduce the errors generated by the use of command filters. In another research front, the adaptive control methods via approximation theories have been introduced to cope with the nonlinear systems with parametric uncertainty based on fuzzy logic system (FLS) or neural networks (NNs) approximation [23], [24], [25], [26]. Besides, PMSMs systems have uncertain nonlinear functions problems [27], [28], and the adaptive control method based on fuzzy logic systems (FLS) [29], [30], [31] are introduced to solve these problems.

In another research front line, a finite-time control [32], [33], [34], [35], [36], [37], [38], [39] method is proposed to improve the convergence speed of the PMSMs systems. From the perspective of control system time optimization, the finite-time control method is a time optimal control method. Besides, the research shows that compared with infinite time control techniques, finite-time stable systems have faster convergence near the origin and better robustness and anti-interference. Therefore, combining the finite-time with the command filtered method, the tracking error can be carried out at a faster rate of convergence and higher speed.

According to the above researches, this article presents an adaptive fuzzy command filter finite-time control method for permanent magnet synchronous motors. The designed algorithm has the following advantages:

  • (1)

    The problem of “explosion of complexity” is overcome by introducing command filtered technology. Furthermore, error compensation mechanisms are adopted to lessen the errors generated by the command filters.

  • (2)

    By introducing adaptive fuzzy control method to approximate the nonlinear terms in motor systems, the problem of parameter uncertainty in PMSMs systems are solved.

  • (3)

    Compared with the fuzzy adaptive command filter control method and finite-time dynamic surface fuzzy adaptive control method, the finite-time fuzzy adaptive command filter control method proposed in this paper not only solved the problem of “explosion of complexity”, but also achieved faster convergence speed and stronger anti-interference ability.

The rest of this paper is organized as follows. Section 2 gives mathematical model of the PMSMs and preliminaries. Section 3 gives the command filtered finite-time fuzzy control design for PMSMs. Section 4 gives simulation results. Section 5 gives the conclusion of this paper.

Section snippets

The mathematical model for PMSMs and preliminaries

The permanent magnet synchronous motors dynamic mathematical model can be expressed as:{dθdt=ωJdωdt=TTLBω=32np[(LdLq)idiq+Φiq]TLBωLddiddt=Rsid+npωLqiq+udLqdiqdt=RsiqnpωLdidnpωΦ+uqwhere θ represents the rotor position, ω represents the rotor angular velocity, T represents the electromagnetism torque, TL represents the load torque, B represents the viscous friction coefficient,  id and iq stand for the d-q axis currents,  ud and  uq stand for the d-q axis voltage, Rs represents the

Command filtered finite-time fuzzy control design for PMSMs

Define the tracking error variables:{z1=x1xdz2=x2x1,cz3=x3x2,cz4=x4where xd is the desired position signal, x1,c and x2,c are the outputs of the command filter. virtual controllers αi(i=1,2) are the input signals of the command filter.

Construct the compensated signals as: vi=ziξi, where ξi(i=1,2,3,4) are the error compensating signals.

Remark 2

It should be mentioned that the command filters will create errors and will add the difficulty of getting satisfactory tracking performance. Therefore, the

Simulation results

To illustrate the advantage and effectiveness of the proposed control method in this paper, the permanent magnet synchronous motor is simulated with the following parameters: np=3, J=0.00379Kgm 2, Rs=0.68Ω, Ld=0.00315H, Lq=0.00285H. The reference signal is selected: xd=0.5sin(t)+0.5sin(0.5t), TL is chosen as TL={0.5,0t3,5,t>3.

  • (a)

    The finite-time command filtered adaptive fuzzy control method (FTCFC) is designed. Selected the following control parameters: k1=100,k2=100,k3=100,k4=100,r1=600,r2=5,l1=

Conclusion

In this article, the adaptive fuzzy finite-time command filtered method has been proposed to solve position tracking of permanent magnet synchronous motor. The adaptive fuzzy control is adopted to approximate the unknown nonlinear functions. The finite-time method is combined with the command filtered method, which solved the problem of “explosion of complexity” in the backstepping method, and improves the accuracy of tracking error, the convergence speed and the ability to resist interference.

Acknowledgments

This work was partially supported by the National Key Research and Development Plan (2017YFB1303503) and Taishan Scholar Special Project Fund (TSQN20161026).

Xueting Yang received the B.Sc. degree in automation of Qingdao University, Qingdao, China, in 2016. She is currently working toward the M.Sc. degree in the control science and engineering, Qingdao University, Qingdao, China. Her research interests include electrical energy conversion and motor control, applied nonlinear control and intelligent systems.

References (41)

  • X. Zhang et al.

    Finite time stabilization by state feedback control for a class of time-varying nonlinear systems

    Automatica

    (2012)
  • X.J. Liu et al.

    Backstepping control with speed estimation of PMSM based on MRAS

    Autom. Control Comput. Sci.

    (2016)
  • Y.C. Wang et al.

    Command filtered adaptive fuzzy backstepping control method of uncertain nonlinear systems

    IET Control Theory Appl.

    (2016)
  • Y.C. Wang et al.

    Command filtered adaptive fuzzy backstepping control method of uncertain non-linear systems

    IET Control Theory Appl.

    (2016)
  • L. Zhao et al.

    Neural network-based distributed adaptive attitude synchronization control of spacecraft formation under modified fast terminal sliding mode

    Neurocomputing

    (2015)
  • M.L. Corradini et al.

    A quasi-sliding mode approach for robust control and speed estimation of PM synchronous motors

    IEEE Trans. Ind. Electron.

    (2012)
  • Z. Qiao et al.

    New sliding-mode observer for position sensorless control of permanent-magnet synchronous motor

    IEEE Trans. Ind. Electron.

    (2013)
  • R. Delpoux et al.

    High-order sliding mode control for sensorless trajectory tracking of a PMSM

    Int. J. Control

    (2014)
  • Z.H. Peng et al.

    Predictor-based neural dynamic surface control for uncertain nonlinear systems in strict-feedback form

    IEEE Trans. Neural Netw. Learn. Syst.

    (2017)
  • J.A. Farrell et al.

    Command filtered adaptive backstepping

    IEEE Trans. Autom. Control

    (2009)
  • Cited by (0)

    Xueting Yang received the B.Sc. degree in automation of Qingdao University, Qingdao, China, in 2016. She is currently working toward the M.Sc. degree in the control science and engineering, Qingdao University, Qingdao, China. Her research interests include electrical energy conversion and motor control, applied nonlinear control and intelligent systems.

    Jinpeng Yu received the B.Sc. degree in automation of Qingdao University, Qingdao, China, in 2002, the M.Sc. degree in system engineering of Shandong University, Jinan, China, in 2006 and the Ph.D. degree from the Institute of Complexity Science, Qingdao University, Qingdao, China, in 2011. He is currently a Distinguished Professor at the School of Automation and Electrical Engineering, Qingdao University. He is a recipient of the Shandong Province Taishan Scholar Special Project Fund and Shandong Province Fund for Outstanding Young Scholars. His research interests include electrical energy conversion and motor control, applied nonlinear control and intelligent systems.

    Qing-Guo Wang received, respectively, B.Eng. in Chemical Engineering in 1982, M. Eng. in 1984 and Ph.D. in 1987 both in Industrial Automation, all from Zhejiang University, PR China. He held Alexander-von-Humboldt Research Fellowship of Germany from 1990 to 1992. From 1992 to 2015, he was with the Department of Electrical and Computer Engineering of the National University of Singapore, where he became a Full Professor in 2004. He is currently a Distinguished Professor with Institute for Intelligent Systems, University of Johannesburg, South Africa. His present research interests are mainly in modeling, estimation, prediction, control, optimization and automation for complex systems, including but not limited to, industrial and environmental processes, new energy devices, defense systems, medical engineering, and financial markets. He has published over 250 international journal papers and 6 books. He received nearly 11000 citations with h-index of 58.

    Lin Zhao received his B.S. degree in Mathematics and Applied Mathematics from Qingdao University, Qingdao, China, in 2008, his M.S. degree in Operational Research and Cybernetics from Ocean University of China, Qingdao, China, in 2011 and the Ph.D. degree in Applied Mathematics from Beihang University (BUAA), Beijing, China, in 2016. Since 2016, he has been working in Qingdao University. His current research interests include spacecraft control and distributed control of multiagent systems.

    Haisheng Yu received the B.S. degree in electrical automation from Harbin University of Civil Engineering and Architecture in 1985, M.S. degrees in computer applications from Tsinghua University in 1988, and Ph.D. degree in control science and engineering from Shandong University in 2006, China. Now he is a professor in School of Automation Engineering, Qingdao University, China. His research interests include electrical energy conversion and motor control, applied nonlinear control, computer control and intelligent systems.

    Chong Lin (SM’06) received the B.Sci and the M.Sci in Applied Mathematics from the Northeastern University, P.R.China, in 1989 and 1992, respectively, and the Ph.D. in Electrical and Electronic Engineering from the Nanyang Technological University, Singapore,in 1999. He was a Research Associate with the Department of Mechanical Engineering, University of Hong Kong, in 1999. From 2000 to 2006, he was a Research Fellow with the Department of Electrical and Computer Engineering, National University of Singapore. Since 2006, he has been a professor with the Institute of Complexity Science, Qingdao University, China. He has published more than 60 research papers and co-authored two monographs. His current research interests are mainly in systems analysis and control, robust control and fuzzy control.

    View full text