Chaotic Permanent Magnet Synchronous Motor Research Articles

Disturbance Observer‐Based Neural Adaptive Command Filtered BacksStepping Funnel‐Like Control for the Chaotic PMSM With Asymmetric Prescribed Performance Constraints

ABSTRACTThis paper suggests a neural adaptive command filtered backstepping tracking control strategy for the chaotic permanent magnet synchronous motors with asymmetric prescribed performance constraints. Therefore, enable chaotic permanent magnet synchronous motors (PMSM) to obtain good robustness and better universality in practical industrial environments, and realizes more accurate control effect. The main challenge lies in devising a valid funnel‐like solution within the backstepping frame to handle the asymmetric performance constraints that traditional solutions cannot solve. To achieve this, a novel funnel‐like function is introduced, integrating a performance boundary function independent of initial output error, thereby transforming the system into an unbounded one. Additionally, the “explosion of complexity” with conventional backstepping is mitigated by introducing command filtering and constructing an error compensating system to reduce errors. By combining the theory of Lyapunov function and backstepping technique, the virtual controller and the real controller with adaptive law ensure the stability of the system. The disturbance observer and neural network solve the external disturbance and the uncertain nonlinear problem, respectively. Simulation comparisons confirm the robustness of the proposed control scheme and demonstrate its superiority over existing solutions.

Finite-time stability control with hardware-in-the-loop testing of a chaotic permanent magnet synchronous motor

Stability of Permanent Magnet Synchronous Motor (PMSM) is of prime importance for the successful operation of the drive system, which is found to be dependent on initial operating conditions showing chaotic characteristic. Therefore, the paper presents the stabilization of a chaotic PMSM system through the finite-time stability approach. From this aspect, three controllers have been developed which are effective for the suppression of machine chaotic behaviour. Proposed controllers are simpler and numerically stable in comparison with previous works. Furthermore, performance comparisons of the proposed controllers are also presented in term of their settling time and peak overshoot. Selection among the proposed controllers depends on the consideration of a particular operating index (settling time or peak overshoot) wherein, performance also varies on system parameter λ. Performance evaluation of proposed controllers has been presented in MATLAB environment. In order to validate the obtained MATLAB results, a real-time analysis has been carried out using Typhoon Hardware-in-the-loop (HIL) emulator. The comparison shows that both results follow the same trend and are closely coordinated with each other, which validates the proposed controllers.

Dynamic Modeling and Chaos Suppression of the Permanent Magnet Synchronous Motor Drive with Sliding Mode Control

The permanent magnet synchronous motor (PMSM) is mathematically modeled and simulated in this study using MATLAB. PMSM is a nonlinear, multi-variable and time-varying system and due to nonlinearities and its strong coupling between its variables, the dynamical behaviour of the PMSM is complex. Therefore, under specified parameters and conditions, chaotic undesirable phenomenon arise in the PMSM. For a chaotic PMSM drive system, this paper proposes a sliding mode control (SMC) approach based on the Lyapunov stability theory to control and suppress the chaotic motion emergence. Firstly, the dynamic characteristics of the state equations of the PMSM drive system is analysed and demonstrated that it will appear chaos phenomenon at some certain parameters. Finally, the SMC strategy and Lyapunov stability theory are combined to introduce a sliding surface and produce a control rule. Simulation results are presented to verify that the proposed strategy can be successfully employed to control a chaotic PMSM and make the system asymptotically stable to the equilibrium point.

Predefined-time smooth stability analysis of nonlinear chaotic systems with applications in the PMSM system and Hindmarsh-Rose neuron model

This article investigates the predefined-time stabilization of nonlinear chaotic systems with applications in the permanent magnet synchronous motor (PMSM) system and Hindmarsh-Rose neuron model. Distinguished from the traditional predefined-time control methods, this investigation develops the smooth control protocols, in which the discontinuous absolute value and signum functions are not used anymore, so that the unfavorable chattering phenomenon can be avoided effectively. By the Lyapunov stability analysis, the sufficient condition is derived to achieve the predefined-time stable for nonlinear chaotic systems, in which the upper-bound time estimation (TE) of arriving at the stable state is explicit in contrast to the traditional finite-/fixed-time convergence. Specifically, the analytical results are successfully applied into stabilizing the PMSM system and Hindmarsh-Rose neuron model within the predefined-time. Finally, the numerical simulations for stabilizing the chaotic PMSM system and Hindmarsh-Rose neuron model verify the effectiveness and advantages of theoretical analysis.

Adaptive neural control for chaotic permanent magnet synchronous motor with asymmetric input saturation

This paper develops an adaptive neural control scheme for chaotic permanent magnet synchronous motor with asymmetric input saturation and full-state constraints. To solve the state constrain problem, a barrier Lyapunov function is introduced. Then, a sliding-mode differentiator is designed to avoid the “explosion of complexity” issue. A simulation example is given to verify the validity of the proposed scheme.

Command filtering-based adaptive control for chaotic permanent magnet synchronous motors considering practical considerations

In this paper, an efficient adaptive control is designed for chaotic Permanent Magnet Synchronous Motors (PMSMs) with full-state asymmetric time-varying constraints in the input saturation presence. The strategy that is suggested in this work is equipped with the command filtering for addressing the problem of the “explosion of complexity” available in the common backstepping method. In addition, the filtering errors are incorporated into the control design procedure for improving the control system performance. During the control design, the asymmetric barrier Lyapunov functions (BLFs) are employed so that the restriction of state variables in the given intervals is guaranteed. In the suggested control method, for approximating unknown nonlinear functions, the Bessel series is utilized as a simple but effective function approximation approach as a universal approximator. The presented design provides this advantage that by considering practical considerations, a reduced-order observer is also designed so that there is no need to mount the physical sensors to measure the position and the velocity of the chaotic PMSM. The Lyapunov stability theory is used to establish the boundedness of all the closed-loop signals. According to the comparative results obtained with neural networks, the presented control design is able to suppress the chaotic behavior of the PMSM drive system while ensuring an excellent tracking performance.

Adaptive Neural Dynamic Surface Control for the Chaotic PMSM System with External Disturbances and Constrained Output

Background:This article studies the issue of adaptive neural dynamic surface control for the chaotic permanent magnet synchronous motor system with constrained output, external disturbances and parameter perturbations.Methods:Firstly, a virtual controller and two practical controllers are created based on the backstepping framework. In the process of creating controllers, adaptive technique and radial basis function neural networks are used to handle unknown parameters and nonlinearities, respectively. The nonlinear damping items are applied to overcome external disturbances. The barrier Lyapunov function is used to prevent the violation of system output constraint. Meanwhile, the first-order filter to eliminate the “explosion of complexity” of traditional back stepping has been introduced. Then, it is proved that all the closed-loop signals are uniform ultimate asymptotic stability and the tracking error converges to a small set of origin.Results:The effectiveness and robustness of the developed approach are illustrated by numerical simulations.Conclusion:The raised control scheme is a useful tool for enhancing the performance of the chaotic PMSM system with external disturbances, constrained output and parameter perturbations.

Barrier Lyapunov function–based adaptive neural network control for incommensurate fractional-order chaotic permanent magnet synchronous motors with full-state constraints via command filtering

This article considers the problem of adaptive neural network control via command filtering for incommensurate fractional-order chaotic permanent magnet synchronous motors with full-state constraints and parameter uncertainties. First, a neural network state observer based on a K-filter is established to reconstruct unmeasured feedback information. Then, the command filtered technology is used to overcome the inherent “explosion of complexity” problem under fractional-order framework. Furthermore, to eliminate the errors generated by filters, an error compensation system is used. Meanwhile, the nonlinear unknown functions are approximated by using neural networks. In addition, the barrier Lyapunov functions are designed to avoid the violation of the state constraints. Finally, the availability of the proposed control algorithm is revealed by numerical simulations.

Novel prescribed performance-tangent barrier Lyapunov function for neural adaptive control of the chaotic PMSM system by backstepping

This paper investigates a neural adaptive output tracking prescribed performance control of the chaotic permanent magnet synchronous motor system with output-constrained, time-delays, parameter perturbations and external disturbances. Firstly, a novel prescribed performance-tangent barrier Lyapunov function is created to tackle the prespecified constraints of tracking error and output. Subsequently, backstepping controllers have been suggested. In specific steps, Chebyshev neural networks and the Nussbaum-type function are exploited to solve unknown nonlinearities and the unknown gain sign. Time-delays are tackled by constructing Lyapunov–Krasovskii functions (LKFs). Meanwhile, the “explosion of complexity” caused by the differentiation of virtual input is removed by plugging tracking differentiator into the controller. Furthermore, it is demonstrated that all the closed-loop signals are ultimate boundedness and predefined constraints are not violated. Finally, simulation studies were performed to confirm the validities and robustness of the raised scheme.

Finite-time adaptive neural network control for fractional-order chaotic PMSM via command filtered backstepping

A finite-time adaptive neural network position tracking control method is considered for the fractional-order chaotic permanent magnet synchronous motor (PMSM) via command filtered backstepping in this paper. Firstly, a neural network with a fractional-order parametric update law is utilized to cope with the nonlinear and unknown functions. Then the command filtered technique is introduced to address the repeated derivative problem in backstepping. In addition, a novel finite-time control method is proposed by employing the fractional-order terminal sliding manifolds, designing the error compensation mechanism and the new virtual control laws. The finite-time convergence of the tracking error can be guaranteed by the proposed controller. Finally, the designed control method is verified by simulation results.

Permanent magnet synchronous motor: chaos control using single controller, synchronization and circuit implementation

The aim of this paper is to address the problem of the electronic implementation of chaos control using a single controller and synchronization of chaotic permanent magnet synchronous motor (PMSM). Firstly, different dynamical behaviors of the PMSM including steady state, periodic and chaotic behaviors are found using numerical methods such as two-dimensional largest Lyapunov exponents graph associated with two parameters of PMSM. Secondly, two simple and single controllers are designed and added to the chaotic PMSM in order to suppress chaotic behavior. The performance of the two proposed simple and single controllers is illustrated by numerical simulations. Thirdly, controllers are designed to achieve synchronization of unidirectional coupled identical chaotic PMSMs. Numerical simulations are also used to verify the effectiveness of the synchronization. Finally, the existence of chaos in PMSM and the physical feasibility of the proposed two simple and single controllers as well as the chaos synchronization are validated through the circuit implementation on OrCAD-PSpice software. The circuit implementation results comply fairly with those of the numerical simulation results and establish that the existence of chaotic behavior in the PMSM and the achievement of chaos synchronization in unidirectional coupled identical PMSMs designed and the two single controllers designed are effective and successful in suppressing chaotic behavior in PMSM.

Mechanical analysis and ultimate boundary estimation of the chaotic permanent magnet synchronous motor

In this paper, we present the dimensionless form of a chaotic permanent magnet synchronous motor (PMSM). Its Kolmogorov formalism, which can be used to describe dissipative-forced dynamical systems, shows that there exist four types of torques, i.e., inertial torque, internal torque, dissipative torque and external torque. The mechanical analysis of the dimensionless PMSM is given for five different combinations of these torques. Numerical simulations show that the occurrence of chaos depends on these four types of torques. Moreover, the ultimate boundary estimation of the dimensionless chaotic PMSM is also investigated theoretically and numerically.

Chaos synchronisation of two different PMSMs via a fractional-order sliding mode controller

This paper deals with the design problem of a Fractional-Order (FO) sliding mode control to synchronise two different chaotic Permanent Magnet Synchronous Motors (PMSMs). By constructing FO sliding mode surfaces, it is proved that the corresponding synchronisation errors are Mittag-Leffler stable. The simulation results show that the proposed controller is strongly robust against the parametric variations, modelling uncertainties and unknown external disturbances, and can significantly reduce the chattering level.

Observer-Based Command Filtered Adaptive Neural Network Tracking Control for Fractional-Order Chaotic PMSM

In this paper, an observer-based command filtered adaptive neural network tracking control problem is addressed for a fractional-order chaotic permanent magnet synchronous motor (PMSM) with the immeasurable state, parameter uncertainties, and external load disturbance. First, the Chebyshev neural networks are introduced to approximate the nonlinear and unknown functions. Next, a neural network reduced-order state observer is designed to obtain the unmeasured state. Then, the command filtering approach based on the first-order Levant differentiator is developed to solve the “explosion of complexity” issue of backstepping, and a novel fractional-order error compensation mechanism is employed, which can remove the filtering errors in finite time. After that, the continuous frequency distributed model is investigated to design proper Lyapunov function, and it is demonstrated that the proposed control method not only ensures that all signals in the fractional-order PMSM system are bounded but also suppresses chaotic oscillation. Finally, the simulation studies are provided to verify the correctness and effectiveness of the proposed scheme.

Motion control of chaotic permanent-magnet synchronous motor servo system with neural network–based disturbance observer

The permanent-magnet synchronous motor system will display a variety of chaotic phenomenon when its parameters or external inputs satisfy certain condition, and thus its performance would be deteriorated. Therefore, chaos should be suppressed or eliminated. In this article, a practical method which combines adaptive robust control with a single-layer neural network–based disturbance observer is proposed for elimination of the chaos and high-performance motion control of permanent-magnet synchronous motor. The proposed controller not only accounts for the load torque disturbance but also takes the parametric uncertainties into account. A single-layer neural network–based disturbance observer is designed to estimate the disturbance while an adaptive control law is designed to estimate the parameters respectively. Then, all the estimated values are used in the feedforward cancelation item in the controller via a backstepping technique. Lyapunov’s method is used to prove the stability of the novel control scheme. Sufficient comparative simulation results are obtained to validate the effectiveness of the proposed control strategy.

Nonlinear mapping‐based feedback technique of dynamic surface control for the chaotic PMSM using neural approximation and parameter identification

This study presents a novel non-linear mapping-based feedback technique for controlling chaotic permanent magnet synchronous motor (PMSM) using dynamic surface control (DSC), neural approximation and parameter identification. Neural networks are utilised to online approximating the unknown system dynamics, adaptive parameter identification is designed to estimate the unknown parameter, and DSC technique circumvents the problem of `explosion of complexity' in the traditional backstepping methodology. The major feature of the non-linear mapping-based feedback technique lies in that the merits of high-gain and low-gain control are synthesised by virtue of a novel non-linear continuous differentiable mapping feedback function, and a novel non-quadratic Lyapunov function is used to analyse the closed-loop system stability caused by the compound function of non-linear feedback. Finally, unprejudiced comparative results are given to demonstrate the effectiveness and advantages of the proposed control scheme.

A robust suboptimal control system design of chaotic PMSMs

Chaotic phenomenon of power electronic systems and electric motor drives were introduced a few decades ago and has been followed with numerous of published work. However, chaos of permanent magnet synchronous motors (PMSMs), in particular, did not receive enough deserved interest. Considering this fact, this paper introduces a robust suboptimal control system for chaotic PMSMs. The proposed control system includes a suboptimal speed controller and a suboptimal load torque observer. The stability analysis and robustness properties of the proposed control system are presented in detail in this paper. Thanks to its robustness properties, the proposed suboptimal control system can not only eliminate the chaos but also provide better performances than conventional methods. Extensive simulations results under various scenarios prove the superiority of the proposed control technique over conventional controllers for chaotic PMSMs even under the condition of parameter uncertainties and variations of load torque disturbance.

Finite-time integral sliding mode control for chaotic permanent magnet synchronous motor systems

AbstractIn this paper, an integral finite-time sliding mode control scheme is presented for controlling a chaotic permanent magnet synchronous motor (PMSM). The controller can stabilize the system output tracking error to zero in a finite time. Using Lyapunov’s stability theory, the stability of the proposed scheme is verified. Numerical simulation results are presented to present the effectiveness of the proposed approach.

Reduced-order observer-based adaptive fuzzy tracking control for chaotic permanent magnet synchronous motors

This paper studies an adaptive fuzzy control method combined with reduced-order observer technology for the position tracking control of chaotic permanent magnet synchronous motor (PMSM) drive system. Fuzzy logic systems (FLSs) are introduced to solve the problem of nonlinear and unknown functions appeared in the PMSM drive system, reduced-order observer is used to calculate its angle speed. Meanwhile, adaptive backstepping mechanism is applied for the design procedure of controllers. The control technique developed in this paper can ensure that the tracking error falls into a small neighborhood of origin. Compared with the existing results, the proposed algorithm can solve the explosion of complexity issue and it does not require measuring the speed signal of motors and the number of adaptive parameters has been reduced to only one. Simulation results show that the chaos of PMSM can be successfully suppressed by the proposed method and the system can track the reference signals very well.

Control Chaos for Permanent Magnet Synchronous Motor Base on Adaptive Backstepping of Error Compensation

Permanent magnet synchronous motor (PMSM) can appear chaos phenomenon when PMSM in turn on or turn off. When control chaotic PMSM to zero, the state variables of the system can appear fluctuate which is not the ideal control result. In order to overcome fluctuate in control chaos. This paper propose adaptive backstepping of error compensation to control chaotic PMSM, an error compensation item is developed in the virtual control design of each backstepping step to compensate the effect of unknown error dynamics on system for obtaining smooth process of chaos control. This scheme can eliminate oscillation in course of control chaos. Numerical simulations further test the effectiveness of the theoretical analysis.