Dynamics and Stability of Permanent-Magnet Synchronous Motor

The aim of this article is to explore the dynamic characteristics and stability of the permanent-magnet synchronous motor (PMSM). PMSM equilibrium local stability condition and Hopf  bifurcation condition, pitchfork bifurcation condition, and fold bifurcation condition have been derived by using the Routh-Hurwitz criterion and the bifurcation theory, respectively. Bifurcation curves of the equilibrium with single and double parameters are obtained by continuation method. Numerical simulations not only confirm the theoretical analysis results but also show one kind of codimension-two-bifurcation points of the equilibrium. PMSM, with or without external load, can exhibit rich dynamic behaviors in different parameters regions. It is shown that if unstable equilibrium appears in the parameters regions, the PMSM may not be able to work stably. To ensure the PMSMs work stably, the inherent parameters should be designed in the region which has only one stable equilibrium

The design of quasi-sliding mode control for a permanent magnet synchronous motor with unmatched uncertainties

AbstractIn this study, the concept of a quasi-sliding mode control (QSMC) is introduced for the robust control of a permanent magnet synchronous motor (PMSM) system subjected to unmatched uncertainties, and even with input nonlinearity. On the basis of the new concept of QSMC, continuous control is obtained, to avoid the chattering phenomenon. As expected, the system state can be stabilized and driven into a predictable neighborhood of zero. Also, this approach only uses a single controller to achieve chaos control, which reduces the cost and complexity of implementation. The results of numerical simulations demonstrate the validity of the proposed QSMC design method

Adaptive Sliding Mode Control of Chaos in Permanent Magnet Synchronous Motor via Fuzzy Neural Networks

In this paper, based on fuzzy neural networks, we develop an adaptive sliding mode controller for chaos suppression and tracking control in a chaotic permanent magnet synchronous motor (PMSM) drive system. The proposed controller consists of two parts. The first is an adaptive sliding mode controller which employs a fuzzy neural network to estimate the unknown nonlinear models for constructing the sliding mode controller. The second is a compensational controller which adaptively compensates estimation errors. For stability analysis, the Lyapunov synthesis approach is used to ensure the stability of controlled systems. Finally, simulation results are provided to verify the validity and superiority of the proposed method

Adaptive control of sinusoidal brushless DC motor actuators

Electrical Power Assisted Steering system (EPAS) will likely be used on future automotive power steering systems. The sinusoidal brushless DC (BLDC) motor has been identified as one of the most suitable actuators for the EPAS application. Motor characteristic variations, which can be indicated by variations of the motor parameters such as the coil resistance and the torque constant, directly impart inaccuracies in the control scheme based on the nominal values of parameters and thus the whole system performance suffers. The motor controller must address the time-varying motor characteristics problem and maintain the performance in its long service life. In this dissertation, four adaptive control algorithms for brushless DC (BLDC) motors are explored. The first algorithm engages a simplified inverse dq-coordinate dynamics controller and solves for the parameter errors with the q-axis current (iq) feedback from several past sampling steps. The controller parameter values are updated by slow integration of the parameter errors. Improvement such as dynamic approximation, speed approximation and Gram-Schmidt orthonormalization are discussed for better estimation performance. The second algorithm is proposed to use both the d-axis current (id) and the q-axis current (iq) feedback for parameter estimation since id always accompanies iq. Stochastic conditions for unbiased estimation are shown through Monte Carlo simulations. Study of the first two adaptive algorithms indicates that the parameter estimation performance can be achieved by using more history data. The Extended Kalman Filter (EKF), a representative recursive estimation algorithm, is then investigated for the BLDC motor application. Simulation results validated the superior estimation performance with the EKF. However, the computation complexity and stability may be barriers for practical implementation of the EKF. The fourth algorithm is a model reference adaptive control (MRAC) that utilizes the desired motor characteristics as a reference model. Its stability is guaranteed by Lyapunov’s direct method. Simulation shows superior performance in terms of the convergence speed and current tracking. These algorithms are compared in closed loop simulation with an EPAS model and a motor speed control application. The MRAC is identified as the most promising candidate controller because of its combination of superior performance and low computational complexity. A BLDC motor controller developed with the dq-coordinate model cannot be implemented without several supplemental functions such as the coordinate transformation and a DC-to-AC current encoding scheme. A quasi-physical BLDC motor model is developed to study the practical implementation issues of the dq-coordinate control strategy, such as the initialization and rotor angle transducer resolution. This model can also be beneficial during first stage development in automotive BLDC motor applications

Fast Adaptive Robust Differentiator Based Robust-Adaptive Control of Grid-Tied Inverters with a New L Filter Design Method

In this research, a new nonlinear and adaptive state feedback controller with a fast-adaptive robust differentiator is presented for grid-tied inverters. All parameters and external disturbances are taken as uncertain in the design of the proposed controller without the disadvantages of singularity and over-parameterization. A robust differentiator based on the second order sliding mode is also developed with a fast-adaptive structure to be able to consider the time derivative of the virtual control input. Unlike the conventional backstepping, the proposed differentiator overcomes the problem of explosion of complexity. In the closed-loop control system, the three phase source currents and direct current (DC) bus voltage are assumed to be available for feedback. Using the Lyapunov stability theory, it is proven that the overall control system has the global asymptotic stability. In addition, a new simple L filter design method based on the total harmonic distortion approach is also proposed. Simulations and experimental results show that the proposed controller assurances drive the tracking errors to zero with better performance, and it is robust against all uncertainties. Moreover, the proposed L filter design method matches the total harmonic distortion (THD) aim in the design with the experimental result

Some Permanent Magnet Synchronous Motor (PMSM) Sensorless Control Methods based on Operation Speed Area

This paper compares some sensorless Permanent Magnet Synchronous Motor (PMSM) controls for driving an electric vehicle in terms of operating speed. Sensorless control is a type of control method in which sensors, such as speed and position sensors, are not used to measure controlled variables.  The controlled variable value is estimated from the stator current measurement. Sensorless control performance is not as good as a sensor-based system. This paper aims are to recommend a control method for the PMSM sensorless controls that would be used to drive an electric vehicle. The methods that we will discuss are divided into four categories based on the operation speed area.  They are a startup, low speed, high speed, and low and high-speed areas. The low and high-speed area will be divided into with and without switching.  If PMSM more work at high speed, the most speed area that is used, we prefer to choose the method that works at high speed, that is, the modification or combination of two or more conventional methods

Comparative Study of Sensorless Control Methods of PMSM Drives

Recently, permanent magnet synchronous motors (PMSMs) are increasingly used in high performance variable speed drives of many industrial applications. This is because the PMSM has many features, like high efficiency, compactness, high torque to inertia ratio, rapid dynamic response, simple modeling and control, and maintenance-free operation. In most applications, the presence of such a position sensor presents several disadvantages, such as reduced reliability, susceptibility to noise, additional cost and weight and increased complexity of the drive system. For these reasons, the development of alternative indirect methods for speed and position control becomes an important research topic. Many advantages of sensorless control such as reduced hardware complexity, low cost, reduced size, cable elimination, increased noise immunity, increased reliability and decreased maintenance. The key problem in sensorless vector control of ac drives is the accurate dynamic estimation of the stator flux vector over a wide speed range using only terminal variables (currents and voltages). The difficulty comprises state estimation at very low speeds where the fundamental excitation is low and the observer performance tends to be poor. The reasons are the observer sensitivity to model parameter variations, unmodeled nonlinearities and disturbances, limited accuracy of acquisition signals, drifts, and dc offsets. Poor speed estimation at low speed is attributed to data acquisition errors, voltage distortion due the PWM inverter and stator resistance drop which degrading the performance of sensorless drive. Moreover, the noises of system and measurements are considered other main problems. This paper presents a comprehensive study of the different methods of speed and position estimations for sensorless PMSM drives. A deep insight of the advantages and disadvantages of each method is investigated. Furthermore, the difficulties faced sensorless PMSM drives at low speeds as well as the reasons are highly demonstrated. Keywords: permanent magnet, synchronous motor, sensorless control, speed estimation, position estimation, parameter adaptation

Advanced Mathematics and Computational Applications in Control Systems Engineering

Control system engineering is a multidisciplinary discipline that applies automatic control theory to design systems with desired behaviors in control environments. Automatic control theory has played a vital role in the advancement of engineering and science. It has become an essential and integral part of modern industrial and manufacturing processes. Today, the requirements for control precision have increased, and real systems have become more complex. In control engineering and all other engineering disciplines, the impact of advanced mathematical and computational methods is rapidly increasing. Advanced mathematical methods are needed because real-world control systems need to comply with several conditions related to product quality and safety constraints that have to be taken into account in the problem formulation. Conversely, the increment in mathematical complexity has an impact on the computational aspects related to numerical simulation and practical implementation of the algorithms, where a balance must also be maintained between implementation costs and the performance of the control system. This book is a comprehensive set of articles reflecting recent advances in developing and applying advanced mathematics and computational applications in control system engineering

Finite-Time Chaos Control of a Complex Permanent Magnet Synchronous Motor System

This paper investigates the finite-time chaos control of a permanent magnet synchronous motor system with complex variables. Based on the finite-time stability theory, two control strategies are proposed to realize stabilization of the complex permanent magnet synchronous motor system in a finite time. Two numerical simulations have been conducted to demonstrate the validity and feasibility of the theoretical analysis