Adaptive sliding mode control of a chaotic nonsmooth-air-gap permanent magnet synchronous motor with uncertainties

Using the sliding mode control approach, a simple adaptive controller design method is proposed for a chaotic nonsmooth-air-gap permanent magnet synchronous motor (PMSM). The proposed method does not require the restrictive assumption that accurate information on the PMSM parameter and load torque values is available, thus it has robustness to model uncertainties. This paper analyzes the stability and convergence of the closed-loop control system, and this paper gives a discretized control algorithm for DSP implementation. Finally, this paper presents some simulation results to illuminate that the proposed method can effectively handle the controller design problem for a chaotic nonsmooth-air-gap PMSM under inaccurate information on the PMSM parameter and load torque values.     

Fuzzy-approximation-based adaptive control of the chaotic permanent magnet synchronous motor

This paper focus on the problem of position tracking control for the chaotic permanent magnet synchronous motor drive system with parameter uncertainties. Fuzzy logic systems are used to approximate the nonlinearities and the adaptive backstepping technique is employed to construct controllers. The proposed adaptive fuzzy controllers guarantee that the tracking error converges to a small neighborhood of the origin. Compared with the conventional backstepping, the designed fuzzy controllers?? structure is very simple. Simulation results show that the proposed control scheme can suppress chaos of PMSM and guarantee the perfect tracking performance even under the unknown parameters.     

Adaptive finite-time control of chaos in permanent magnet synchronous motor with uncertain parameters

Permanent magnet synchronous motor (PMSM) exhibits chaotic behavior when its parameters are within a certain range which seriously affect the stable work of PMSM. In order to eliminate the chaos, many approaches have been proposed. Most of them considered asymptotic stability of the system, while finite-time stability makes more sense in practice. In addition, parameters of PMSM may be uncertain because of some external factors, then adaptive control is a good method to be considered. In this paper, adaptive finite-time stabilization problem is considered to eliminate the chaos in PMSM system with uncertain parameters. To show the effectiveness of the proposed method, some simulation results are provided.     

基于单向滑模的永磁同步电机摩擦自适应控制

针对摩擦条件下永磁同步电机伺服系统的高精度位置控制问题进行了研究。利用单向滑模控制算法和广义麦克斯威尔滑动(GMS)摩擦模型,设计了具备摩擦前馈补偿功能的力矩控制器,对GMS模型的参数进行了自适应调节以补偿摩擦力变化。通过设计适当的趋近率,使得该控制器在保证系统稳定的同时,产生连续的期望电流信号,消除了普通滑模带来的抖振问题,同时采用反步法反推控制电压获得了保证系统总体稳定的控制信号。最后的仿真实验结果表明,提出的方法有利于提高摩擦条件下永磁同步电机控制的控制精度。     

Fuzzy speed control with an acceleration observer for a permanent magnet synchronous motor

Based on the Takagi–Sugeno fuzzy approach we design a fuzzy speed regulator as well as a fuzzy acceleration observer for a permanent magnet synchronous motor (PMSM). The proposed observer-based fuzzy speed regulator is independent of the load torque value. We derive the sufficient conditions for the existence of the regulator and the observer in terms of linear matrix inequalities (LMIs), and also give LMI parameterizations of the gain matrices. Simulation and experimental results are given to verify that the proposed control method can be used to accurately control the speed of a PMSM under model parameter and load torque variations.     

Direct adaptive neural control of chaos in the permanent magnet synchronous motor

In this paper, a direct adaptive neural speed tracking control is addressed for the chaotic permanent magnet synchronous motor (PMSM) drive systems via backstepping. Neural networks are directly used to approximate unknown and desired control signals and a novel direct adaptive tracking controller is constructed via backstepping. The proposed adaptive neural controllers guarantee that the tracking error converges to a small neighborhood of the origin. Compared with the conventional backstepping method, the designed neural controller??s structure is very simple. Simulation results show that the proposed control scheme can suppress the chaos of PMSM and guarantees the perfect tracking performance even with the existence of unknown parameters.     

Adaptive fuzzy tracking control design for permanent magnet synchronous motors with output constraint

Nonlinear Dynamics - In this paper, an adaptive fuzzy output feedback position tracking constraint control method is proposed for permanent magnet synchronous motors (PMSM) system. Fuzzy logic...     

Dynamic control for permanent magnet synchronous generator system using novel modified recurrent wavelet neural network

Because permanent magnet synchronous generator (PMSG) system driven by permanent magnet synchronous motor (PMSM) based on wind turbine emulator (WTE) is a nonlinear and time-varying system with high complication, an accurate dynamic model of the PMSG system directly driven by WTE is difficult to establish for the linear controller design. In order to conquer this difficulty and improve the robustness of dynamic system, the PMSG system controlled by the online-tuned parameters of the novel modified recurrent wavelet neural network (NN)-controlled system is proposed to control output voltages and powers of controllable rectifier and inverter in this study. First, a closed-loop PMSM-driven system based on WTE is designed for driving the PMSG system to generate output power. Second, the rotor speeds of the PMSG, the voltages, and currents of the two power converters are detected simultaneously to yield maximum power output. In addition, two sets of the online-tuned parameters of the modified recurrent wavelet NN controllers in the controllable rectifier and inverter are developed for the voltage-regulating controllers in order to improve output performance. Finally, some experimental results are verified to show the effectiveness of the proposed novel modified recurrent wavelet NN controller for the power output of the PMSG system driven by WTE.     

Stability and stabilization for the coupling permanent magnet synchronous motors system with input delay

Nonlinear Dynamics - This paper studied the problem of stability and stabilization for a coupling permanent magnet synchronous motors (CPMSMs) system with input delay. Input delays caused by...     

Adaptive robust fuzzy control for a class of uncertain chaotic systems

In this paper, the output feedback control of uncertain chaotic systems is addressed via an adaptive robust fuzzy approach. Fuzzy logic systems are employed to approximate uncertain nonlinear functions in the chaotic systems. Because only partial information of the system’s states is needed to be known, an observer is given to estimate the unmeasured states. Compared with the existing results in the observer design, the prior knowledge on dynamic uncertainties is relaxed and a class of more general chaotic systems is considered as well as robustness to the approximation error is improved. It can be proven that the closed-loop system is stable in the sense that all the variables are bounded. Simulation example for the unified chaotic systems is given to verify the effectiveness of the proposed method. This work was supported in part by the National Natural Science Foundation of China (60874056) and the Foundation of Educational Department of Liaoning Province (2008312).     

Nonlinear vibration of permanent magnet synchronous motors in electric vehicles influenced by static angle eccentricity

Nonlinear Dynamics - An additional transverse electromagnetic moment caused by the inclination of the rotor of the permanent magnet synchronous motors in electric vehicles is modeled based on...     

Adaptive backstepping optimal control of a fractional-order chaotic magnetic-field electromechanical transducer

Nonlinear Dynamics - This paper develops an adaptive backstepping optimal control scheme for a fractional-order chaotic magnetic-field electromechanical transducer with the saturated control...     

The magnetic field of a permanent hollow cylindrical magnet

Based on the rational version of MAXWELL’s equations according to TRUESDELL and TOUPIN or KOVETZ, cf. (Kovetz in Electromagnetic theory, Oxford University Press, Oxford, 2000; Truesdell and Toupin in Handbuch der Physik, Bd. III/1, Springer, Berlin, pp 226–793; appendix, pp 794–858, 2000), we present, for stationary processes, a closed-form solution for the magnetic flux density of a hollow cylindrical magnet. Its magnetization is constant in axial direction. We consider MAXWELL’s equations in regular and singular points that are obtained by rational electrodynamics, adapted to stationary processes. The magnetic flux density is calculated analytically by means of a vector potential. We obtain a solution in terms of complete elliptic integrals. Therefore, numerical evaluation can be performed in a computationally efficient manner. The solution is written in dimensionless form and can easily be applied to cylinders of arbitrary shape. The relation between the magnetic flux density and the magnetic field is linear, and an explicit relation for the field is presented. With a slight modification the result can be used to obtain the field of a solid cylindrical magnet. The mathematical structure of the solution and, in particular, singularities are discussed.     

Adaptive sliding mode control of uncertain chaotic systems with input nonlinearity

This paper is concerned with the stabilization problem of uncertain chaotic systems with input nonlinearity. The slope parameters of this nonlinearity are unmeasured. A new sliding function is designed, then an adaptive sliding mode controller is established such that the trajectory of the system converges to the sliding surface in a finite time and finite-time reachability is theoretically proved. Using a virtual state feedback control technique, sufficient condition for the asymptotic stability of sliding mode dynamics is derived via linear matrix inequality (LMI). Then the results can be extended to uncertain chaotic systems with disturbances and adaptive sliding mode H _∞ controllers are designed. Finally, a simulation example is presented to show the validity and advantage of the proposed method.     

Adaptive terminal sliding mode control for anti-synchronization of uncertain chaotic systems

This paper presents an adaptive terminal sliding mode control method for anti-synchronization of uncertain chaotic systems. By fusion of the terminal sliding mode control and the adaptive control techniques, a robust controller is designed so that the states tracking error can reach the terminal sliding mode surface and converge to zero in a finite time. Finally, some simulation results are included to demonstrate the effectiveness and the feasibility of the proposed anti-synchronization scheme.     

Adaptive output feedback control of uncertain nonlinear chaotic systems based on dynamic surface control technique

In this paper, an adaptive output feedback control algorithm based on the dynamic surface control (DSC) is proposed for a class of uncertain chaotic systems. Because the system states are assumed to be unavailable, an observer is designed to estimate those unavailable states. The main advantage of this algorithm can overcome the problem of “explosion of complexity” inherent in the backstepping design. Thus, the proposed control approach is simpler than the traditional backstepping control for the uncertain chaotic systems. The stability analysis shows that the system is stable in the sense that all signals in the closed-loop system are uniformly ultimately bounded (UUB) and the system output can track the reference signal to a bounded compact set. Finally, an example is provided to illustrate the effectiveness of the proposed control system.     

Interaction of a magnetic liquid with a conductor containing current and a permanent magnet

The present study investigates the force exerted by a magnetic liquid on a conductor with a current or a permanent magnet located near its infinite free surface. It is shown that this force is equal to the weight of the liquid raised by the magnetic field above the original horizontal level. The force is found for the cases when the liquid is weakly magnetic and when the shape of its surface differs little from plane. Consideration is given to the equilibrium of a magnet suspended on a small spring near the surface of the magnetic liquid. The critical height is found at which the magnet ceases to be held by the spring and is torn off into the liquid. The experimentally obtained values of the magnitude of of the force acting on the magnet and the height of collapse of the magnet into the liquid are in good agreement with the theoretical results.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 176–181, March–April, 1988.The authors are grateful to V. V. Gogosov for valuable discussion of the study.