Elsevier

Information Sciences

Volume 567, August 2021, Pages 298-311
Information Sciences

Full state constraints and command filtering-based adaptive fuzzy control for permanent magnet synchronous motor stochastic systems

https://doi.org/10.1016/j.ins.2021.02.050Get rights and content

Highlights

  • The stochastic disturbance in motor operation is considered.

  • The problem of “explosion of complexity” is solved by using the command filtering technique.

  • The error compensation mechanism is introduced to reduce filtering errors.

  • The barrier Lyapunov function is introduced to ensure that the full state constraints are not violated.

Abstract

In this article, an adaptive fuzzy control scheme based on command filtering is proposed for the position tracking control of permanent magnet synchronous motor (PMSM) stochastic system with full state constraints. Firstly, fuzzy logic systems are employed to approximate unknown stochastic nonlinear functions in PMSM stochastic system. Then, the barrier Lyapunov functions are constructed to ensure that all states of the system do not violate its constrained boundary. In addition, the problem of “explosion of complexity” in traditional backstepping design is solved by using the command filtering technique and the error compensation mechanism is introduced to reduce filtering errors. At last, the effectiveness of the scheme is illustrated by simulation results.

Introduction

Latterly, permanent magnet synchronous motor (PMSM) has been widely valued for its wide range of industrial applications. However, PMSM is a highly nonlinear, multivariable and strong coupling complex control target, and it is easy to be affected by load disturbance, which is difficult to be controlled by traditional control method. A large number of advanced control methods for nonlinear systems have been raised and applied to the control of PMSM to obtain higher performance, such as sliding mode control [3], [18], [32], backstepping [1], [30], [36], and other control methods [5], [17], [27]. Adaptive backstepping technology combined with approximation theory is an effective methed in solving nonlinear system problems. Unknown nonlinear terms are approximated by fuzzy logic system [8], [16], [24], [26] or neural network [2], [13], and the problem of load disturbance is also well solved by combining adaptive backstepping technology. Aiming at the problem of “explosion of complexity” existing in conventional backstepping design process, the dynamic surface control (DSC) [9] technology is adopted by using the first-order filter. But DSC technology does not consider the filtering errors, which will affect the control performance. As an alternative, the command filtered control (CFC) [12], [37] technology is another effective technology to deal with the “explosion of complexity” problem, the error compensation mechanism is introduced to reduce errors caused by the filter. However, the above control methods does not consider the stochastic disturbances of PMSM in actual operation.

During the operation of PMSM, there will be voltage stochastic surge and stochastic noise [7], [19]. In addition, damping torque, torsional elastic torque and saturation of magnetic circuit will change the parameters of motor torque, self-inductance, mutual inductance and winding resistance [11], [31]. These stochastic disturbances may be the source of oscillation or instability of PMSM system, and the existence of these disturbances will seriously affect the control accuracy of PMSM. Therefore, it is highly recommended to consider the stochastic disturbance in PMSM system. With the help of adaptive backstepping control technique, many control methods are studied for stochastic nonlinear systems. For example, in [4], an adaptive fuzzy neural network backstepping tracking control method for a class of pure-feedback stochastic nonlinear systems was present, and the stability of stochastic nonlinear systems was analyzed by using a quartic Lyapunov function. In [39], the position tracking control problem for induction motors stochastic nonlinear systems was studied, and the proposed adaptive fuzzy controller based on CFC technology can make the tracking error arbitrarily small and overcome the influence of stochastic disturbance by selecting appropriate design parameters. In [6], an adaptive neural network tracking control method for switched stochastic nonlinear systems with unknown backlash-like hysteresis was present.

From the above analysis, all states of the stochastic system are unconstrained, which will lead to the lack of practicability. Note that in many practical engineering systems, outputs or states need to be limited to bounded intervals. If outputs or states exceed bounded intervals, the security and dependability of the system can not be assured. In addition, violating output or state constraints can result in performance degradation and crash of system in practical applications. For example, during the operation of PMSM, the motor windings will seriously heat up because of the excessive current, which will lead to accelerated insulation aging and shorten the life of the motor. Therefore, considering the state constraints in the control of PMSM system is very essential. In the past few years, barrier Lyapunov functions (BLFs) [15], [23], [25], [34] are good candidate functions to cope with the output or state constraints. Based on BLFs, many advanced control methods are proposed for nonlinear systems. For example, in [28], the tracking control for SISO nonlinear systems of strict feedback form with an output constraint was studied. In [20], full state constraints are considered by constructing symmetric and asymmetric BLFs. In [21], an adaptive neural network learning control method for nonlinear systems with full state constraints is investigated. However, as far as we know, the position tracking control problem of PMSM stochastic nonlinear system based on command filtered control technique and full state constraints has not been fully considered.

Since the stochastic disturbance and state constraints always exist in the operation of PMSM, it is of great significance for us to conduct this research. Meanwhile, compared with the existing results, controller design for PMSM stochastic systems with full state constraints is more complex, this is a very challenging task for us.

Motivated by the above analysis, based on command filtered control technique and barrier Lyapunov functions, an adaptive fuzzy control method is studied for PMSM stochastic system with full state constraints. Compared with the existing control methods, the main advantages of the control method proposed in this paper are listed as follows:

  • 1)

    Compared with the [38], the stochastic disturbance in motor operation is considered, the design of the controller is more in line with the engineering practice.

  • 2)

    Distinct from [22], command filtering technology combined with error compensation mechanism not only solves the “explosion of complexity” in traditional backstepping method, but also reduces the filtering error. This will ensure the accuracy and performance of the control.

  • 3)

    The barrier Lyapunov function is introduced for the PMSM stochastic systems to ensure that the full state constraints are not violated, which will ensure the practicability of the proposed control method.

Section snippets

Mathematical model and preliminaries

Under the synchronous rotating coordinate (d-q), the model of PMSM can be expressed as follows [29]:dΘdt=ωJdwdt=32np[(Ld-Lq)idiq+Φiq]-Bω-TLLqdiqdt=-Rsiq-npωLdid-npωΦ+uqLddiddt=-Rsid+npωLqiq+udwhere ω and Θ stand for the rotor angular velocity and the rotor angular position, id and iq are the d-q axis currents, ud and uq denote the d-q axis voltages for the control inputs of the system, np,B,J,TL,Rs and Φ represent the pole pair, viscous friction velocity, rotor moment of inertia, load torque,

Command filtering-based adaptive fuzzy controllers design

Based on command filtered control technique and barrier Lyapunov functions, an adaptive fuzzy position tracking controller for PMSM stochastic system will be constructed in this section.

The error variables are defined as follows:z1=x1-xd,z2=x2-x1,c,z3=x3-x2,c,z4=x4v1=z1-ξ1,v2=z2-ξ2,v3=z3-ξ3,v4=z4-ξ4where xd denote the desired reference signal, αi and xi,c(i=1,2) are the input and output signals of the filter, respectively. The filtering errors xi,c-αi are dealt with by error compensation

Stability analysis

In [25], it was proven that logkbi4/(kbi4-vi4)<vi4/(kbi4-vi4) in the set vi<kbi. By using Young’s inequality, it’s easy for us to get -θ̃θ̂-θ̃22+θ22, From the above inequality and (44), it can be known thatLV-i=14kilogkbi4kbi4-vi4-m2rθ̃2+i=2414Ii2+12hi2+14εi4+14d4+m2rθ2-aV+bin which a=min4k1,4k2J,4k3,4k4,m,b=i=2414Ii2+12hi2+14εi4+14d4+m2rθ2.

Next, the boundedness of the compensation signals will be proved. Choose the Lyapunov function as followsV=12ξ12+J2ξ22+12ξ32+12ξ42.Then, we haveV̇=ξ1

Simulation results

In this section, simulation and comparison experiments are given in the MATLAB environment to prove the effectiveness and reliability of the proposed methed. The parameters of PMSM [35] are selected in Table 1:

Choosing the reference signal as xd=sin(t), the initial condition is [0.2, 0, 0, 0], load torque TL=1, and the fuzzy membership functions μFij=exp-(x+n)22where j=1,2,3,,11. i=2,3,4 and n = −5, −4, −3, …, 5.

  • (a). First, full state constraints and command filtering-based adaptive fuzzy

Conclusion

Based on command filtered control technique and barrier Lyapunov functions, an adaptive fuzzy position tracking controller for PMSM stochastic nonlinear systems has been constructed in this paper. The barrier Lyapunov functions are constructed to ensure that all states of the system do not violate its constrained boundary and stochastic disturbances are taken into account in this paper. The fuzzy logic systems are utilized to cope with unknown stochastic nonlinear functions and command filtered

CRediT authorship contribution statement

Qi Jiang: Methodology, Software, Validation, Writing - original draft. Jiapeng Liu: Conceptualization, Writing - review & editing. Jinpeng Yu: Conceptualization, Methodology, Writing - review & editing, Supervision, Funding acquisition. Chong Lin: Validation, Methodology.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

This work was supported by National Key Research and Development Plan (2017YFB1303503), the National Natural Science Foundation of China (61973179), Taishan Scholar Special Project Fund (TSQN20161026), and Qingdao key research and development special project (21-1-2-6-nsh).

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