Time optimal current control for PMSM drives

Previous article Next article The Closed-Loop Time Optimal Control. II: StabilityPavol BrunovskýPavol Brunovskýhttps://doi.org/10.1137/0314013PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractThe problem, to which extent does the closed-loop time-optimal control of a linear system fulfill its task if the system is subject to small perturbations, is studied.[1] Pavol Brunovský, The closed-loop time-optimal control. I. Optimality, SIAM J. Control, 12 (1974), 624–634 MR0355719 (50:8193) 0301.49004 LinkISIGoogle Scholar[2] Pavol Brunovský, On the best stabilizing control under a given class of perturbations, Czechoslovak Math. J., 15 (90) (1965), 329–369 MR0181518 (31:5747) 0154.10005 Google Scholar[3] H. Hermes, J. Hale and , J. LaSalle, Discontinuous vector fields and feedback controlDifferential Equations and Dynamical Systems (Proc. Internat. Sympos., Mayaguez, P. R., 1965), Academic Press, New York, 1967, 155–165 MR0222424 (36:5476) 0183.15905 Google Scholar[4] T. Ważewski, On an optimal control problem, Differential Equations and Their Applications (Proc. Conf., Prague, 1962), Publ. House Czechoslovak Acad. Sci., Prague, 1965, 229–242 MR0201758 (34:1640) 0133.06005 Google Scholar[5] B. N. Pšeničnyj, Line jny je differencial'ny je igry, Avtomat. i Telemeh., (1968), 65–78 Google Scholar[6] A. F. Filippov, On certain questions in the theory of optimal control, Vestnik Moskov. Univ. Ser. I Mat. Meh., (1959), 25–32, English transl., this Journal, 1 (1962), pp. 76–84 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Discrete and Continuous Dynamical Systems, Vol. 35, No. 9 | 2015 Cross Ref Measurement stability of time-optimal feedback control of two-input strictly normal linear systemsJournal of Differential Equations, Vol. 86, No. 1 | 1 Jul 1990 Cross Ref Local Time-Optimal Feedback Control of Strictly Normal Two-Input Linear SystemsSIAM Journal on Control and Optimization, Vol. 27, No. 1 | 14 July 2006AbstractPDF (3497 KB)Sensitivity Analysis of Time Optimal Control SystemsIFAC Proceedings Volumes, Vol. 17, No. 2 | 1 Jul 1984 Cross Ref Multivalued mappingsJournal of Soviet Mathematics, Vol. 24, No. 6 | 1 Mar 1984 Cross Ref Stability with regime switchingJournal of Economic Theory, Vol. 29, No. 1 | 1 Feb 1983 Cross Ref Measurement stability of third-order time-optimal control systemsJournal of Differential Equations, Vol. 36, No. 1 | 1 Apr 1980 Cross Ref Discontinuous differential equations, IIJournal of Differential Equations, Vol. 32, No. 2 | 1 May 1979 Cross Ref Volume 14, Issue 1| 1976SIAM Journal on Control and Optimization1-188 History Submitted:20 July 1973Published online:03 August 2006 InformationCopyright © 1976 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0314013Article page range:pp. 156-162ISSN (print):0363-0129ISSN (online):1095-7138Publisher:Society for Industrial and Applied Mathematics

A new instantaneous torque-control strategy is presented for high-performance control of a permanent magnet (PM) synchronous motor. In order to deal with the torque pulsating problem of a PM synchronous motor in a low-speed region, new torque estimation and control techniques are proposed. The linkage flux of a PM synchronous motor is estimated using a model reference adaptive system technique, and the developed torque is instantaneously controlled by the proposed torque controller combining a variable structure control (VSC) with a space-vector pulse-width modulation (PWM). The proposed control provides the advantage of reducing the torque pulsation caused by the nonsinusoidal flux distribution. This control strategy is applied to the high-torque PM synchronous motor drive system for direct-drive applications and implemented by using a software of the digital signal processor (DSP) TMS320C30. The simulations and experiments are carried out for this system, and the results demonstrate the effectiveness of the proposed control.

Time optimal control method for quadruped walking robots are developed and installed into a practical robot system. Each leg is modeled as a two link manipulator whose time optimal control theory has already been established by Bobrow. However, in legged robot systems, each leg supports their body weight, and the reaction forces from its ground must be inside of their friction corn. Moreover, the ZMP (zero moment point) of the robot is constrained for stable walk. Therefore, time optimal control inputs must be designed considering these constraints. SONY ERS-7 is used as a quadruped walking robot and a fundamental experiment is done. From the experimental results, the effectiveness of the developed control algorithm is verified

Comparison of model-free and model-based methods for time optimal hit control of a badminton robot

To mitigate the computational complexity inherent in permanent magnet synchronous motor (PMSM) control systems, this paper presents a dual-vector model predictive current control (DV-MPCC) strategy integrated with an improved exponential reaching law-based sliding mode controller (IEAL-SMC). A voltage phase angle decision-making mechanism is introduced to alleviate computational load and enhance the accuracy of voltage vector selection: this mechanism enables rapid determination of optimal control sectors and facilitates efficient screening of candidate vectors within the finite control set (FCS). To further boost the system’s disturbance rejection capability, a modified SMC scheme employing a softsign function-based exponential reaching law is developed for the speed loop. By adaptively tuning the smoothing parameters, this modified SMC achieves a well-balanced trade-off between fast dynamic response and effective chattering suppression—two key performance metrics in PMSM control. Experimental validations indicate that, in comparison with the conventional DV-MPCC approach, the proposed strategy not only improves the efficiency of voltage vector selection but also demonstrates superior steady-state precision and dynamic responsiveness across a broad range of operating conditions.

This paper aims to study the fast finite-time (FFT) tracking control strategy for permanent magnet synchronous motor (PMSM). The design of FFT tracking controller for PMSM faces many difficulties due to the coupling between current and rotational speed, as well as the nonlinear characteristics of motor torque. To overcome the difficulty, we utilize a novel coordinate transformation to establish the mathematical models of PMSM in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha -\beta $ </tex-math></inline-formula> coordinate system and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d-q $ </tex-math></inline-formula> coordinate system. Based on the obtained PMSM model, novel FFT tracking control strategy including FFT direct axis current tracking controller and FFT position tracking controller is developed. Superior to the existing control schemes of PMSM, the new FFT tracking control strategy ensures that the states error of the system can be quickly stabilized in a limited time with faster convergence speed and stronger anti-interference. Finally, the effectiveness of the proposed control method is illustrated by simulation results.

The Permanent Magnet Synchronous Motor (PMSM) is widely used in many fields. Aiming at nonlinearity, strong coupling and uncertainty of the PMSM, this paper proposes a nonlinear multi-input multi-output (MIMO) decoupling PMSM algorithm based on Active Disturbance Rejection Control (ADRC). A Lower-Upper matrix factorization approach is introduced to solve a general inverse of the measured time-varying matrix in real-time decoupling ADRC. This PMSM is based on the vector control. First, the PMSM model and vector control are simulated. Then, a first-order ADRC is introduced and used to replace the PID controller in the d and q axis of PMSM respectively. The simulation shows that the replaced system has a smaller fluctuation, faster response and better stability. Finally, the nonlinear MIMO decoupling ADRC and its inverse matrix method are deduced. Then, the decoupling PMSM control based on ADRC is verified. The simulation shows that this system has a better static and dynamic performance, and it conforms to the PMSM characteristics better. All this shows that the nonlinear MIMO decoupling ADRC is a better strategy for the PMSM. The presented algorithm also has advantage in method compared with some recent results of decoupling PMSM control.

To solve the problems of slow response speed of the permanent magnet synchronous motor (PMSM) system when the external interference occurs and the poor anti-interference ability, this paper proposes a double model predictive control (MPC) strategy for PMSM to control speed and current. To be specific, firstly, the mathematical model of PMSM is established under the two-phase synchronous rotation coordinate system. Secondly, we propose the double MPC strategy where MPC controller is used in the speed outer loop and deadbeat prediction controller is used in the current inner loop. Finally, By comparing the traditional control strategy (speed outer loop PI controller and current inner loop deadbeat prediction controller) with the double MPC strategy, the simulation results show that the double MPC has no overshot, better steady-state performance, faster dynamic response and stronger anti-load disturbance capability, which proves the effectiveness of the proposed strategy.

The field-oriented control (FOC) strategy of a permanent magnet synchronous motor (PMSM) in a simplified form is based on PI-type controllers. In addition to their low complexity (an advantage for real-time implementation), these controllers also provide limited performance due to the nonlinear character of the description equations of the PMSM model under the usual conditions of a relatively wide variation in the load torque and the high dynamics of the PMSM speed reference. Moreover, a number of significant improvements in the performance of PMSM control systems, also based on the FOC control strategy, are obtained if the controller of the speed control loop uses sliding mode control (SMC), and if the controllers for the inner control loops of id and iq currents are of the synergetic type. Furthermore, using such a control structure, very good performance of the PMSM control system is also obtained under conditions of parametric uncertainties and significant variations in the combined rotor-load moment of inertia and the load resistance. To improve the performance of the PMSM control system without using controllers having a more complicated mathematical description, the advantages provided by reinforcement learning (RL) for process control can also be used. This technique does not require the exact knowledge of the mathematical model of the controlled system or the type of uncertainties. The improvement in the performance of the PMSM control system based on the FOC-type strategy, both when using simple PI-type controllers or in the case of complex SMC or synergetic-type controllers, is achieved using the RL based on the Deep Deterministic Policy Gradient (DDPG). This improvement is obtained by using the correction signals provided by a trained reinforcement learning agent, which is added to the control signals ud, uq, and iqref. A speed observer is also implemented for estimating the PMSM rotor speed. The PMSM control structures are presented using the FOC-type strategy, both in the case of simple PI-type controllers and complex SMC or synergetic-type controllers, and numerical simulations performed in the MATLAB/Simulink environment show the improvements in the performance of the PMSM control system, even under conditions of parametric uncertainties, by using the RL-DDPG.

For permanent magnet synchronous motors (PMSMs) supplied with a voltage source inverter, current control strategies are commonly implemented under the synchronously rotating reference frame. In order to simplify the system structure, three-phase currents can be measured with a single DC-link current sensor using the phase current reconstruction technique. However, it still needs to follow the conventional AC current control approach. In this paper, a DC-link current control method for PMSMs is proposed to further simplify the control system. The problem of phase current control was separated into the problems of amplitude control and phase control. Then, amplitude control was achieved using a closed-loop controller directly tracking the DC-link current; while phase control was achieved by AC-side pulse width modulation (PWM) following the phase angle of back electromotive force. The compensation for nonlinear distortion of the inverter was taken into account during the control process. Finally, the proposed method realized three-phase current control with a single current sensor and controller, and achieved the purpose of electromagnetic torque control. Experimental results demonstrate the effectiveness of the proposed method.

The shaftless rim-driven propulsion system (RDPS) is a new lightweight and efficient aviation electric propulsion system to meet the needs of energy-saving, low-carbon and green aviation for the future. In order to solve the problems of slow response speed, electromagnetic torque oscillation and poor robustness of high-speed permanent magnet synchronous motor (PMSM) in shaftless RDPS, this paper studied and compared the response of three control strategies including Id = 0, maximum torque per ampere (MTPA) and d-axis current flux-weaken based on field-oriented control (FOC) under high speed and time-varying load conditions. In addition, the verification analysis of three drive control strategies is carried out under the actual fan operating condition. The results showed that the electromagnetic torque of low-speed motor could follow the load torque under the three control strategies. The MTPA and d-axis current flux-weaken control strategies solved the problem of electromagnetic torque oscillation of high-speed PMSM under the Id = 0 method, and effectively shorten the response time of motor. Actual operating conditions of shaftless RDPS also verified that the PMSM had the best response speed and robustness under the d-axis current flux-weaken control strategy.KeywordsAviation electric propulsionFlux-weakenField-oriented controlPermanent magnet synchronous motorRim propulsionShaftless driven

The objective of this paper is to control the speed of Permanent Magnet Synchronous Motor (PMSM) over wide range of speed by consuming minimum time and low cost. Therefore, comparative performance analysis of PMSM on basis of speed regulation has been done in this study. Comparison of two control strategies i.e. Field oriented control (FOC) without sensor less Model Reference Adaptive System (MRAS) and FOC with sensor less MRAS has been carried out. Sensor less speed control of PMSM is achieved by using estimated speed deviation as feedback signal for the PI controller. Performance of the both control strategies has been evaluated in in MATLAB Simulink software. Simulation studies show the response of PMSM speed during various conditions of load and speed variations. Obtained results reveal that the proposed MRAS technique can effectively estimate the speed of rotor with high exactness and torque response is significantly quick as compared to the system without MRAS control system.

Field-Oriented Control (FOC) is widely recognized as a standard framework for Permanent Magnet Synchronous Motor (PMSM) drives. Linear control techniques are commonly employed in designing controllers for this strategy. However, traditional control methods often exhibit performance limitations and reduced robustness, particularly under harsh operating conditions, which makes the FOC structure less appealing and less effective. To address and overcome these challenges, this study proposes a Second-order Non-singular Terminal Sliding (SNTS) mode approach to achieve fast, accurate, and robust tracking for the FOC control structure applied to PMSM drives. The SNTS method combines the benefits of non-singular terminal sliding mode and second-order control laws. This approach ensures rapid and precise tracking while minimizing steady-state errors by using a nonlinear terminal sliding mode surface instead of a linear one. Furthermore, the system state transitions smoothly along the sliding mode surface with continuous functions, which reduces chattering around the sliding surface. The second-order control law incorporated into this method helps mitigate chattering and achieve fast convergence. The Lyapunov stability theory is employed to verify the stability of the SNTS technique designed for the PMSM system. Simulation and experimental validation on a hardware platform confirm the effectiveness and superiority of the proposed SNTS method, demonstrating its capability to enhance the performance of speed controllers for PMSM drives.

In this paper, a new development in the time optimal control theory in sliding mode control systems for multi-quadrant buck converters with a variable load is presented. In general, the closed-loop time optimal control system is applied to multi-quadrant buck converters for output regulation, so that an optimal switching surface is obtained. Moreover, an adjusted optimal sliding mode controller is suggested which adjusts the controller parameters to give an optimal switching surface. In addition, a description of the transient response of the closed-loop system is proposed and used to damp any output or input disturbances in minimum time. Numerical simulations and experimental results are employed to demonstrate that the output regulation time and transient performances of dc/dc converters using the proposed technique are improved effectively when compared to the classical sliding mode control method.

This chapter describes the sliding-mode control of permanent magnet synchronous motor (PMSM) servo systems. The typical structure of the systems consists of the position, velocity, and current control loops. The design of three controllers, position controller, speed controller, and current controller, and a filter in speed loop has been described respectively, aimed at reaching high-performances of PMSM servo systems, such as fast response, strong robustness, and high precision. The digitization of terminal sliding-mode (TSM) controllers of PMSM servo system has been discussed for the purpose of practical implementation.