Linear Synchronous Motor Servo Research Articles

Adaptive super-twisting-based nonsingular fast terminal sliding mode control of permanent magnet linear synchronous motor

In this study, to reduce the impact that permanent magnet linear synchronous motor (PMLSM) servo system on the sensitivity of external and internal interferences, an adaptive super-twisting-based nonsingular fast terminal sliding mode control (AST-NFTSMC) scheme is put forward. First of all, the mathematical model of PMLSM contains uncertainties is set up, and the control law is established to make position signal converge to given state asymptotically. Second, by introducing the super-twisting algorithm, the chattering caused by nonlinear switching function in traditional method is weakened. However, in actual industrial situations, it is difficult to determine the boundary of lumped disturbance, which makes the switching gains in super-twisting algorithm cannot be accurately selected. Therefore, an adaptive law is introduced to adjust the switching gains online, so that the gains can be dynamically adjusted within a limited range during operation, so as to further weaken chattering. Finally, the practicability of AST-NFTSMC is proved in theory and verified by system experiments. The experimental results prove that AST-NFTSMC can significantly weaken chattering, and result in robust control performance.

Adaptive Jerk Control and Modified Parameter Estimation for PMLSM Servo System With Disturbance Attenuation Ability

The direct-drive industrial technology has put forward much higher requirements for the application of high-performance permanent magnet linear synchronous motor (PMLSM) servo system. To improve the control accuracy and transient performance, a novel disturbance attenuation approach is proposed based on adaptive jerk control (AJC) and modified parameter estimation for PMLSM servo system in this article. Within the control details, AJC is proposed to realize asymptotic stability without requiring <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> knowledge of disturbances, which can release the strong restriction and eliminate the design conservation. Furthermore, a novel adaptive law is designed for feedback gain to further enhance the robustness when the system meets the challenge of high-gain feedback and measurement noise. Meanwhile, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ϵ</i> -modification parameter estimation is employed to approximate and compensate for the parameter variation, which can not only achieve fast convergence rate but also guarantee small overshoot. The asymptotic stability of the proposed control method is analyzed and proved by the Lyapunov theorem. Finally, the experimental results are presented to validate the efficiency with better disturbance attenuation ability.

High-Order Fast Nonsingular Terminal Sliding Mode Control of Permanent Magnet Linear Motor Based on Double Disturbance Observer

In order to realize the high-speed and high-precision movement of the direct drive system, it is important to study the strong robust control strategy of permanent magnet linear synchronous motor (PMLSM) servo system. This article proposes a high-order fast nonsingular terminal sliding mode control strategy for PMLSM based on double disturbance observer. The double disturbance observer is used to observe the mismatched/matched disturbances to reduce the conservativeness of the system to multiple disturbances. In addition, a high-order fast nonsingular terminal sliding mode controller is designed to enhance the robustness of the system. By adding feedback current into the controller, the overall control of current, speed, and position is realized. In addition, the steady-state performance and dynamic performance of position tracking system are improved. The stability and convergence of the closed loop system are proved by the Lyapunov stability theory. Experimental results show that the proposed strategy can effectively improve position tracking accuracy of the system and robustness to uncertain disturbances.

A Novel Robust Super-Twisting Nonsingular Terminal Sliding Mode Controller for Permanent Magnet Linear Synchronous Motors

For accurate position tracking and robust control of permanent magnet linear synchronous motor (PMLSM) servo systems against various uncertainties, such as parameter change, load disturbance, friction force, and so on, this article proposes a novel super-twisting nonsingular terminal sliding mode control method based on a high-order sliding mode observer. First, a dynamic model of PMLSM with uncertainties is established. A novel nonsingular terminal sliding mode function combined with the super-twisting algorithm is then proposed to design a robust super-twisting nonsingular terminal sliding mode controller, which ensures the system convergence to the equilibrium state within a finite time, effectively eliminating the chattering phenomenon and improving the system robustness. To further improve the system tracking performance and anti-interference ability, a high-order sliding mode observer is used to estimate the system uncertainties. The effective tracking performance and robustness of the proposed control method are validated by the experimental results.

High-precision motion control method for permanent magnet linear synchronous motor

In this paper, aiming at the known or unknown uncertainties in permanent magnet linear synchronous motor (PMLSM) servo system, an intelligent backstepping terminal sliding mode control (IBTSMC) method is proposed for accurate position tracking of the servo system. The designed controller makes use of the advantage of backstepping terminal sliding mode control theory to ensure fast convergence and robustness. Finally, the stability analysis is carried out by using Lyapunov stability theory, and the effectiveness of the designed control scheme is proved by experiments.

Modified complementary sliding mode control with disturbance compensation for permanent magnet linear synchronous motor servo system

In this study, a modified complementary sliding mode control (MCSMC) method based on a disturbance force observer with mass identification (DFOB-MI) applicable to the permanent magnet linear synchronous motor is proposed to achieve high-performance servo control fields. MCSMC is an improvement on the complementary sliding mode control (CSMC) method, which incorporates an approach angle into the saturation function. MCSMC allows for asymptotic convergence of the position tracking errors and guarantees the global robustness of the system. In addition, compared to hybrid control strategies combining neural networks with CSMC, the MCSMC method has a simpler structure and faster response. However, in practical applications, the mass variation of the mover has a significant impact on system performance. To achieve better dynamic and static characteristics, a disturbance force observer capable of identifying the mass variation based on model reference adaptive identification theory is proposed. DFOB-MI can identify the mass of the mover and provide information on the disturbance caused by the change of the load. Thus, the compensation current is calculated to reduce the disturbance and realise compensation. The more accurate tracking performance and stronger robustness of the proposed control scheme compared to conventional approaches have been confirmed through comparative experimental studies.

Intelligent second‐order sliding mode control for permanent magnet linear synchronous motor servo systems with robust compensator

In this study, an intelligent second-order sliding mode control (SMC) method combining second-order SMC (SOSMC) and recurrent radial basis function neural network (RRBFNN) applicable to the permanent magnet linear synchronous motor (PMLSM) is proposed to achieve high-performance servo control fields. On the basis of a dynamic model of PMLSM and the SMC theory, the chattering problem in SMC is weakened and the tracking accuracy is improved by the design of SOSMC. As for the boundary of the uncertainty factors is difficult to obtain, the optimal performance of SOSMC is hard to achieve, the RRBFNN uncertainty observer is introduced for estimating the value of the uncertainty factors. Owing to the strong learning ability, the network parameters can be trained online. Besides, a robust compensator is developed to suppress the uncertainties such as approximation error, optimal parameter vector and higher Taylor series for further improving the robustness. Moreover, the adaptive learning algorithms are obtained by using the Lyapunov theorem to guarantee the asymptotical stability of the system. The experiments demonstrate that the proposed scheme provides high performance dynamic characteristics and strong robustness to uncertainties.

Nonlinear Robust Optimal Control via Adaptive Dynamic Programming of Permanent-Magnet Linear Synchronous Motor Drive for Uncertain Two-Axis Motion Control System

In this article, a nonlinear robust optimal control (NROC) scheme for uncertain two-axis motion control system via adaptive dynamic programming (ADP) and neural networks (NNs) is proposed. The two-axis motion control system is an X-Y table actuated by permanent-magnet linear synchronous motor servo drives. First, the motions of the tracking contour in X-axis and Y-axis of the X-Y table are stabilized through feedback linearization control (FLC) laws. However, the control performance may be destroyed due to parameter uncertainties and compounded disturbances. Therefore, to improve the robustness of the control system, an NROC is designed to achieve this purpose. The tracking control problem of the X-Y table with uncertainties is transformed to a regulation problem. Then, it is solved by an infinite horizon optimal control using a critic NN. Consequently, the NN is developed via ADP learning algorithm to facilitate the online solution of the Hamilton-Jacobi-Bellman equation corresponding to the nominal system for approximating the optimal control law. The uniform ultimate boundedness of the closed-loop system is proved utilizing the Lyapunov approach and the tracking error asymptotically converges to a residual set. The validation of the proposed control schemes are carried out through experimental analysis. The control algorithms have been implemented using a DSP control board. A comparison of control performances using FLC, adaptive FLC, and FLC-based NROC is investigated. From the experimental results, the dynamic behaviors of the two-axis control system using the proposed FLC-based NROC can achieve robust optimal control performance against parameter uncertainties and compounded disturbances.

A novel high-precision motion control for permanent magnet linear synchronous motor servo system

In this paper, a novel high-precision motion control is proposed for a permanent magnet linear synchronous motor (PMLSM) servo system, which is vulnerable to the influence of uncertainties. First, the dynamics of the PMLSM with uncertainties are derived. To cater for the parametric uncertainties, the model-based feedforward control is constructed so that the transient response of the system is improved. Moreover, the adaptive jerk control (AJC) scheme based on a robust integral of the sign of the error (RISE) feedback is adapted to restrain the uncertainties such as external disturbance and nonlinear friction in the system. To alleviate the chattering phenomenon, a novel exponential adaptive law is designed to bound the feedback gain of the jerk, under the condition of the initial term of control efforts considered. Then, the jerk signal is integrated to form the feedback control law, which generates continuous control input and ensures the stability of the system. Compared with sliding mode control (SMC), the experimental results indicate that both the robustness and tracking performance of the system are significantly improved without adding more control efforts. The position tracking error is reduced and high-frequency oscillation is effectively attenuated.

Intelligent Adaptive Jerk Control With Dynamic Compensation Gain for Permanent Magnet Linear Synchronous Motor Servo System

In this paper, an intelligent adaptive jerk control (IAJC) with dynamic compensation gain for the permanent magnet linear synchronous motor (PMLSM) servo system was proposed to improve robustness and tracking performance against nonlinear and time-varying uncertainties. First, the dynamic model of the PMLSM servo system was investigated. Subsequently, the model-based feedforward control was designed for parametric uncertainties. Then, an adaptive jerk control (AJC) was adopted to restrain external load disturbance, nonlinear friction and unmodeled dynamics of the servo system. The adaptive feedback gain of jerk was updated by an exponential function. However, the uncertainties of the PMLSM servo system were unavailable in advance, it was difficult to design the adaptive feedback gain in practice. Thus, in the following part, the IAJC was further developed in which a dynamic compensation gain was designed using a double-loop recurrent feature selection fuzzy neural network (RFSFNN) to compensate for approximation deviation and suppress the chattering phenomenon. The learning algorithms of the double-loop RFSFNN were derived and the stability of the closed-loop system was proved by the Lyapunov approach. Finally, the experimental results demonstrate that the proposed IAC scheme can achieve robust precise tracking performance.

Extended Kalman filter-based disturbance feed-forward compensation considering varying mass in high-speed permanent magnet linear synchronous motor

A disturbance feed-forward compensation method based on 7th-order extended Kalman filter (EKF) is proposed for permanent magnet linear synchronous motor (PMLSM) servo system which is vulnerable to the influence of external disturbances, such as friction force, force ripple and so on. Firstly, a disturbance model which consists of position-dependent functions was developed and utilized as a disturbance feed-forward compensator. Then, the initial position and the varying mass information of plant were estimated by the 7th-order EKF and reflected to the disturbance feed-forward compensator. In addition, the coefficients of the disturbance model were adjusted adaptively to create synchronization between the model and real disturbance and achieve the purpose of varying mass estimation and disturbance compensation. Finally, the system simulation and experiment results confirm that the proposed method is effective and feasible. The PMLSM servo system based on 7th-order EKF has superior performance in disturbance compensation, and it is not affected by the varying mass of PMLSM.

Force ripple compensation in a PMLSM position servo system using periodic adaptive learning control

Force ripple deteriorates the performance of permanent magnet linear synchronous motor (PMLSM) servo systems. Using a model reference adaptive control and periodic adaptive learning control (MRAC–PALC) algorithm, this paper presents a novel compensation method to eliminate the influence of force ripple on the system performance of a position servo system under repetitive motion tasks. The key idea of the proposed method is to utilize the periodic characteristics of both force ripple and system motion. The controller consists of four components: a PD component, a feedforward component, a velocity feedback component and an MRAC–PALC compensator. The first three components are designed in a conventional way. The compensator is divided into two parts: in the 0th-iteration, an MRAC algorithm is employed to obtain the initial information, and in the ith-iteration (i≥ 1), a PALC algorithm is used to learn from the information obtained in the previous period and update the controller parameters for estimating force ripple. Moreover, a theoretical stability analysis is given via Lyapunov stability theorem, and some comparative results are provided through simulations and experiments.

Adaptive Neural Network Nonsingular Fast Terminal Sliding Mode Control for Permanent Magnet Linear Synchronous Motor

For the problem that the position tracking accuracy of permanent magnet linear synchronous motor (PMLSM) servo system is easily affected by uncertain factors such as parameters change, load disturbance and friction and so on, an adaptive neural network nonsingular fast terminal sliding mode control (ANNNFTSMC) method is proposed. Firstly, the PMLSM dynamic mathematical model with uncertainty is established. Then, the nonsingular fast terminal sliding mode control (NFTSMC) can avoid the singularity problem and make the state of the system converge to the equilibrium point quickly, so as to improve the response speed of the system. Secondly, in order to minimize the influence of disturbance and dynamic uncertainty, the dynamic model of PMLSM servo system is estimated by RBF neural network, and the uncertain upper bound of PMLSM servo system is estimated in real time combined with adaptive control, which weakens the chattering phenomenon and enhances the robustness of the system. It is proved theoretically that the control scheme can make the system achieve fast convergence and good tracking. Finally, the system experiments show that the proposed control scheme has the advantages of high tracking accuracy, good robustness, fast response speed and small position error.

Research on Multi-Loop Nonlinear Control Structure and Optimization Method of PMLSM

Recently, the permanent magnet linear synchronous motor (PMLSM) servo control technology has become a research hotspot. However, the control performance under the traditional PID control is not ideal, which usually has the problems of slow response speed, large overshoot and poor anti-interference performance. In addition, adding nonlinear links with certain characteristics purposefully can greatly improve the performance of the system and achieve the expected effect that the traditional linear controllers cannot achieve. Based on this, this paper introduces the nonlinear PID control strategy into the field of servo control, and proposes a nonlinear control strategy of the three-loop of the servo system to improve the above problems. Firstly, the proposed structure is explained and the rule of nonlinear parameters selection is discussed. Secondly, the conditions for the structural stability of the proposed nonlinear control strategy are analyzed. Finally, experiments on the servo system platform are carried out and the results verify the fast dynamic response, precise positioning and good anti-disturbance performance.

Approach Angle-Based Saturation Function of Modified Complementary Sliding Mode Control for PMLSM

In this paper, an approach angle-based saturation function of modified complementary sliding mode control (MCMSC) method was proposed to overcome the influence of uncertainties such as parameter variations and external disturbances on permanent magnet linear synchronous motor (PMLSM) servo system. On the foundation of the mathematical model considering uncertainties of PMLSM and the theory of sliding mode control (SMC), complementary sliding mode control (CSMC) method was designed by combining the integral sliding surface with the complementary sliding surface. By using the continuous saturation function, CSMC can efficiently eliminate the system chattering phenomenon caused by the discontinuous function in SMC and further improve the position tracking accuracy. However, the saturation function makes the boundary layer in CSMC constant, so the asymptotic stability of the system cannot be guaranteed. Hence, an approach angle-based saturation function of MCSMC was designed to realize the dynamic change of the boundary layer, which can diminish the boundary layer with the change of state trajectory until it converges to the sliding surface, thereby further improving the robustness of the system. Additionally, the hybrid SMC methods, such as fuzzy-SMC and neural network-SMC (NN-SMC), are avoided. A precise test platform based on digital signal processor (DSP) was implemented, and experimental results are shown to demonstrate the effectiveness and correctness of the proposed method.

Adaptive Nonlinear Disturbance Observer Using a Double-Loop Self-Organizing Recurrent Wavelet Neural Network for a Two-Axis Motion Control System

This paper proposes an adaptive nonlinear disturbance observer (ANDO) for identification and control of a two-axis motion control system driven by two permanent-magnet linear synchronous motors servo drives. The proposed control scheme incorporates a feedback linearization controller (FLC), a new double-loop self-organizing recurrent wavelet neural network (DLSORWNN) controller, a robust controller, and an 1-1 controller. First, an FLC is designed to stabilize the XY table system. Then, a nonlinear disturbance observer (NDO) is designed to estimate the nonlinear lumped parameter uncertainties that include the external disturbances, cross-coupled interference, and frictional force. However, the XY table performance is degraded by the NDO error due to parameter uncertainties. To improve the robustness, the ANDO is designed to attain this purpose. In addition, the robust controller is designed to recover the approximation error of the DLSORWNN, while the 1-1 controller is specified such that the quadratic cost function is minimized and the worst-case effect of the NDO error must be attenuated below a desired attenuation level. The online adaptive control laws are derived using the Lyapunov stability analysis and 1-1 control theory, so that the stability of the ANDO can be guaranteed. The experimental results show the improvements in disturbance suppression and parameter uncertainties, which illustrate the superiority of the ANDO control scheme.

Intelligent tracking control of a PMLSM using self‐evolving probabilistic fuzzy neural network

This study presents a self-evolving probabilistic fuzzy (PF) neural network with asymmetric membership function (SPFNN-AMF) controller for the position servo control of a permanent magnet linear synchronous motor (PMLSM) servo drive system. In the beginning, the dynamic model for the PMLSM is analysed on the basis of field-oriented control. Subsequently, an SPFNN-AMF control system, which integrates the advantages of self-evolving NN, PF logic system, and AMF, is proposed to handle vagueness, randomness, and time-varying uncertainties of the PMLSM servo drive system during the control process. For the SPFNN-AMF, the proposed learning algorithm consists of the structure learning and parameter learning in which the former is used to grow and prune the fuzzy rules automatically, whereas the latter is utilised to train the network parameters dynamically. Finally, detailed experimental results of two position commands tracking at different operation conditions demonstrate the validity and robustness of the proposed SPFNN-AMF for controlling the PMLSM servo drive system.

Self-Organizing Recurrent Fuzzy Wavelet Neural Network-Based Mixed $\rm{H}_{2}\rm{/ H}_{\rm{\infty }}$ Adaptive Tracking Control for Uncertain Two-Axis Motion Control System

In this paper, an intelligent adaptive tracking control system (IATCS) based on the mixed $H_{2}/ H_{\rm{\infty }}$ approach for achieving high precision performance of a two-axis motion control system is proposed. The two-axis motion control system is an X-Y table driven by two permanent-magnet linear synchronous motors (PMLSMs) servo drives. The proposed control scheme incorporates a mixed $H_{2}/ H_{\rm{\infty }}$ controller, a self-organizing recurrent fuzzy-wavelet-neural-network controller (SORFWNNC), and a robust controller. The SORFWNNC is used as the main tracking controller to adaptively estimate an unknown nonlinear dynamic function (UNDF) that includes the lumped parameter uncertainties, external disturbances, cross-coupled interference, and frictional force. Furthermore, a robust controller is designed to deal with the approximation error, optimal parameter vectors, and higher order terms in Taylor series. Besides, the mixed $H_{2}/ H_{\rm{\infty }}$ controller is designed such that the quadratic cost function is minimized and the worst case effect of the UNDF on the tracking error must be attenuated below a desired attenuation level. The online adaptive control laws are derived based on Lyapunov theorem and the mixed $H_{2}/ H_{\rm{\infty }}$ tracking performance so that the stability of the IATCS can be guaranteed. The experimental results confirm that the proposed IATCS grants robust performance and precise dynamic response to the reference contours regardless of external disturbances and parameter uncertainties.

Fractional Order Modeling And Nonlinear Fractional Order Pi‐Type Control For PMLSM System

AbstractIn this paper, firstly a fractional order (FO) model is proposed for the speed control of a permanent magnet linear synchronous motor (PMLSM) servo system. To identify the parameters of the FO model, a practical modeling algorithm is presented. The algorithm is based on a pattern search method and its effectiveness is verified by real experimental results. Second, a new fractional order proportional integral type controller, that is, (PIμ)λ or FO[FOPI], is introduced. Then a tuning methodology is presented for the FO[FOPI] controller. In this tuning method, the controller is designed to satisfy four design specifications: stability requirement, specified gain crossover frequency, specified phase margin, flat phase constraint, and minimum integral absolute error. Both set point tracking and load disturbance rejection cases are considered. The advantages of the tuning method are that it fully considers the stability requirement and avoids solving a complex nonlinear optimization problem. Simulations are conducted to verify the effectiveness of the proposed FO[FOPI] controller over classical FOPI and FO[PI] controllers.

An Adaptive FNN Control Design of PMLSM in Stationary Reference Frame

A robust control approach for permanent magnet linear synchronous motor servo drive is presented in this work. First, the nonlinear motor dynamics is described in the stationary reference frame instead of the d–q axis synchronous rotating reference frame. Then, a backstepping control technique is employed to the systematic analysis and design of the drive system. To ensure satisfactory performance of the position control, an adaptive fuzzy neural network is introduced to deal with the uncertain dynamics. The online adaptation law is deduced by using the Lyapunov functional method so that the asymptotic stability of the closed-loop system is guaranteed. In contrast to the conventional current vector control strategy, this work develops a voltage control scheme via a complete theoretic derivation, which considers both the mechanical and electrical dynamics of motor’s behavior. Moreover, the proposed control algorithm performs without using the Park and inverse Park coordinate transformations, and the computation efficiency can be improved as a result. Finally, the practical experiment and a comparison study with the conventional current control approach are carried out to illustrate the effectiveness of the proposed control scheme.