Sensorless Speed Control of PMSM via Extended State Observer

This article presents a Permanent Magnet Synchronous Motor (PMSM) sensorless control system using backstepping control. The Extended State Observer (ESO) is also used to perform the sensorless control, and to estimate the load torque which is considered an external disturbance of the control system. Starting from the classic Field Oriented Control (FOC) type PMSM control structure, the classic PI speed and current controllers i <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> , i <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> are replaced by a backstepping control structure. The main blocks used for the implementation and numerical simulation in the Matlab/Simulink graphical programming environment are presented. The very good static and dynamic performance obtained through numerical simulations even at high speeds, step variations of the value of the load torque, uniformly distributed noise, and variations of the PSMS nominal parameters can be explained by the fact that the backstepping control is applied to the non-linear system of the PMSM and by the step-by-step method of achieving each iqref, ud and uq control by using a Lyapunov-type function. Future articles propose the approach of real-time implementation of the PMSM sensorless control by using the backstepping control.

In the permanent magnetic synchronous motor (PMSM) system with active disturbance rejection controller (ADRC), the estimation accuracy of extended state observer (ESO) will decrease when the ADRC does not depend on the system model completely. In order to improve the estimation accuracy, this paper proposes an improved ADRC approach by adding a model compensation term. Furthermore, the rotor inertia and viscous friction coefficient in the model compensation term is identified by the model reference adaptive identification (MRAI) algorithm. The load torque is estimated according to the mechanical equation of PMSM system. Then the identification values of rotor inertia, viscous friction coefficient, and load torque make up the compensation term of the ESO. Simulation results indicate that this improved ADRC approach has the better parameter robustness and anti-load-disturbance performance.

This paper presents a robust sixth-order Discrete-time Extended Sliding Mode Observer (DESMO) for sensorless control of PMSM in order to estimate the currents, speed, rotor position, load torque and stator resistance. The satisfying simulation results on Simulink/Matlab environment for a 1.6 kW PMSM demonstrate the good performance and stability of the proposed ESMO algorithm against parameter variation, modeling uncertainty, measurement and system noises.

Sensorless technologies for the field-oriented control of the permanent magnet synchronous motors (PMSMs) are being actively developed today. Recently, a robust, nonlinear and globally convergent position observer for the surface-mount permanent magnet synchronous motor (SPMSM) has been proposed in [4]. The key feature of the robust observer is estimation of the rotor position requiring only the knowledge of the stator currents, voltages, resistance and inductance. However, the resistance and inductance of the stator may change during operation as a result of overheating, mechanical wear and environmental impacts. Thus, the aim of this study is to develop adaptive algorithms for the stator windings' parameters, which can be used for this position observer improvement. In this paper the authors propose four adaptive observers for estimation of the resistance and inductance at low motor speeds. It is assumed, that only currents and voltages of the stator windings are known. The other state variables and parameters of PMSM are unknown. The main idea of the synthesis of identification algorithms is linear filtering, which allows us to eliminate the unknown terms obtained by the mathematical transformations. Requirements to the external load, which ensure successful identification of the PMSM stator parameters, are given for each observer. The proposed adaptive observers for the stator resistance and inductance can be applied in case, when at low speeds, the field-oriented control of PMSM is carried out by means of Hall sensor, while at higher speeds, the sensorless control algorithms are used. A distinctive feature of the proposed estimation algorithms is that the resistance and inductance identification can be implemented during PMSM operation.

In this paper, a Square root Cubature Kalman filter (SCKF) is applied for speed and position estimation in the control of Interior Permanent Magnet Synchronous Motor (IPMSM). Cubature Kalman filter avoids the linearization errors prevailing in the Extended Kalman filter algorithm, and is much easier to tune than the Unscented Kalman filter. The square root version of the Cubature Kalman filter gives an increased numerical stability in the digital implementation of the observer. With an augmented state space model of the system, the proposed observer facilitates joint parameter estimation, wherein load torque and stator resistance are also estimated. Estimated load torque is used in the speed control loop and the estimated resistance is used in tuning the PI controllers for current adaptively. The proposed observer's robustness to parameter variations is demonstrated through the simulations.

This paper deals with the problem of global sensorless speed control of permanent magnet synchronous motors in which the speed and load torque are not available. The key problem in sensorless speed control is the design of the observer that is used to estimate the speed and load torque. The major difficulty in the design of the observer results from the presence of the quadratic term of the speed and direct axis current in the quadrature axis current equation. We first view the quadratic term as a disturbance term. Then we design an adaptive feedback law in the direct axis current equation to reject the influence of the disturbance term on the observer. On the basis of the observation, we propose an observer-based adaptive global control method for the speed control of the motor. The method can ensure that all signals in the closed loop system are bounded and that the speed tracking error converges to zero. Simulations of a motor are performed to show the utility of the control method.

This project investigates the application of model reference adaptive system (MRAS) for the speed sensorless control of an induction motor. The rotor speed can be accurately estimated by employing the closed-loop observer named reactive MRAS. Therefore, this observer eliminates the need of a speed sensor for the control of the motor speed. The method is robust to stator and rotor resistance variations due to change of temperature. The dynamic system equations of the induction machines are formulated, and the motor control system performance is studied. Both scalar voltage-to-frequency (V/f) control and vector field oriented control (FOC) schemes, implemented using digital signal processor (DSP), are investigated. The design of the speed sensorless DSP-based controller is completed. Software packages have been developed to implement the design. An experimental system using the proposed controller has been built. Various tests have been conducted to verify the technical feasibility of the control technique. The experimental results confirm the feasibility of the proposed speed sensorless V/f control scheme using MRAS speed estimator. The designed V/f profile has been tested. Even with step change of the load or that of the command speed, the system can achieve the correct steady state after a short transient operation. The experimental results also confirm the feasibility of the proposed speed sensorless FOC control scheme using MRAS speed estimator. The current regulators meet the design requirements. Both the flux-producing current component and the torque-producing current component can be controlled separately. In the implementation, digital signal processor (DSP) TMS320 FL2407 and voltage source inverter (VSI) Skiip 342GD120-316CTV are employed. The modular strategy is adopted to develop the software package.

With the widespread application of permanent magnet synchronous motors (PMSMs), drive control technology for these motors has gradually become a focal point of research. To overcome the drawbacks associated with installing separate sensors, sensorless drive control technology has attracted significant attention. This paper presents a sensorless flux linkage estimation method for permanent magnet synchronous motors (PMSMs) utilizing a nonlinear observer. In the absence of a position sensor, this method employs a Nonlinear Extended State Observer (ESO) along with advanced flux linkage techniques to accurately estimate the stator flux linkage. By integrating a voltage-current hybrid model, the approach facilitates adaptive switching between the voltage and current models, effectively addressing issues such as DC offset and integrator saturation that are common in first-order integration of the voltage model. Furthermore, the Nonlinear Extended State Observer is utilized to estimate and compensate for noise and disturbances in the voltage model, ensuring precise determination of the stator flux linkage during motor operation. Finally, a phase-locked loop (PLL) is implemented to estimate the rotor angle and speed, thereby enhancing the accuracy of these estimations and improving the overall performance of sensorless control in PMSMs.

In order to optimize the speed-control performance of the permanent-magnet synchronous motor (PMSM) system with different disturbances and uncertainties, a nonlinear speed-control algorithm for the PMSM servo systems using sliding-mode control (SMC) and load torque compensation techniques is developed in this paper. A SMC strategy is designed based on field oriented control (FOC) theory, which is adopted in the speed loop of PMSM system. Meanwhile, considering the SMC need providing large gain to restrain disturbances resulting in large chattering, an adaptive extended sliding mode torque observer (ESMO) is proposed to estimate and compensate load torque. Through torque estimation for feed-forward compensation, one new composite SMC algorithm has been proposed to take a smaller value of switching gain without large chattering. The control scheme is verified by comprehensive simulation and experimental results.

This paper proposes a novel and robust method of sensorless speed control using a deadbeat observer for an interior permanent magnet synchronous motor (IPMSM). The proposed sensorless speed control method uses a deadbeat observer to estimate the extended electromotive force (EEMF) in a rotational coordinate system. The estimated EEMF is used in the IPMSM velocity estimation algorithm. The deadbeat EEMF observer (DEEMFO) shows greater robustness compared to the reconstructor, which estimates the EEMF by simply recalculating the voltage equation. Unlike a reconstructor, DEEMFO has a feedback component, so it can compensate for errors due to uncertainty in motor parameters and errors due to parameter fluctuations that may occur during use. By simulating and experimenting with speed, load torque, and parameter fluctuations, it is proved to be more robust and precise than the reconstructor. The simulation is performed with MATLAB/Simulink, and the experiments were carried out using a DSP TMS320F28335 and a motor-generator set (M-G Set). The simulation and experiment results show the reliability and precision of the proposed sensorless control method.

Assuming that for AC electrical machines, the only measurable variables are the currents and the voltages, the mathematical models of the synchronous and induction motors are used to study their respective observability property. If this property is satisfied and under some necessary conditions introduced later, observers are designed to estimate the non-measurable variables of the electric machines. First, some definitions and an introduction to the Nonlinear Observers design are developed. Next, a classification in terms of the convergence rate of two classes of observers is studied: (1) Observers with an asymptotic convergence. (2) Observers with a finite-time convergence. Furthermore, as for nonlinear systems there are no canonical forms, several observer structures are introduced to be next applied to AC machines. From the mathematical model of the PMSM, rewritten in the form of two interconnected subsystems, an adaptive interconnected observer can be designed to estimate the rotor speed, rotor position, and load torque. Some assumptions are considered in order to ensure its asymptotic convergence of the observer. Because the stator resistance depends on the temperature which introduces a variation with respect to its nominal value, then in order to determine its real value, an adaptive interconnected observer is designed to estimate the stator resistance and simultaneously the rotor speed, rotor position, and non-measured load torque. Sufficient conditions are obtained to ensure the asymptotic convergence. Then, a super-twisting observer for a class of nonlinear systems is considered. The advantages of this observer are robustness with respect to parametric uncertainties and finite-time convergence which allows to guarantee that the separation principle can be satisfied when a controller is next applied. Similarly, from the IMPSM mathematical model, an adaptive interconnected observer is designed to estimate the rotor position, rotor speed, load torque, and stator resistance. Finally, for the induction motor, an adaptive interconnected observer is designed to simultaneously estimate the rotor speed, the fluxes, and the load torque. To guarantee the robustness property, an extension of the above observer under parametric uncertainties is developed and, by using practical stability concepts, the practical stability of the estimation error is ensured.

This paper presents an anti-windup composite adaptive speed controller (AW-CASC) for permanent-magnet synchronous motors (PMSMs) operating under parameter uncertainties, external load torque, and input saturation. The proposed AW-CASC integrates three components, an adaptive compensation control (ACC) term, an adaptive proportional-integral (API) controller, and an anti-windup (AW) mechanism, and is therefore referred to as AW[API-ACC]. The ACC compensates for unknown disturbances using an adaptive law that relies only on measurable feedback signals, ensuring robust operation of the composite controller without requiring disturbance observers. The API employs a nonlinear adaptive gain algorithm based on exponential and fractional functions of the velocity error, enabling fast transient response and improved tracking accuracy without the need for fuzzy logic or gain scheduling. To suppress overshoot caused by integrator windup under large step-speed commands, a lightweight AW strategy is integrated directly into the Lyapunov-based control framework. Stability analysis confirms that all closed-loop signals are uniformly ultimately bounded. The proposed AW[API-ACC] method is implemented and experimentally validated under various speed profiles, incorporating parameter uncertainties, external load torque, and current saturation conditions. Compared with a conventional PI controller with disturbance observer (PI-OB), an adaptive optimal control (AOC) strategy, and adaptive sliding mode control combined with an extended state observer (ASMC-ESO), the AW[API-ACC] method achieves up to a 61% reduction in RMS speed error (sinusoidal), 33% and 31% reductions in overshoot and maximum tracking error (ramp), a 70% faster recovery under load torque disturbances, and an 8.8% improvement in settling time (step). These results highlight the improved robustness and tracking performance of the proposed method.

In permanent magnetic synchronous motor (PMSM) speed regulation system, the tracking performance and disturbance rejection property of the system are coupled when using conventional active disturbance rejection control (ADRC) controller, which complicates the parameter setting of the controller. A decoupled ADRC controller with position feedback is proposed in this paper. Extended state observer (ESO) is modified to make disturbance rejection property of the system independent of the proportional coefficient, which affects both the tracking performance and the disturbance rejection property in the conventional ADRC control system. Using the modified ESO, the tracking performance and disturbance rejection property can be adjusted by the proportional coefficient and the bandwidth of ESO respectively, thus simplifies the parameter setting of the controller. Extensive experiments are performed on dSPACE DS1103 to verify the validity and practicality of the proposed algorithm.

The Permanent Magnet Synchronous Motor (PMSM) are emerging as one of the most important categories of AC machine drives. Therefore, different control methods are used for speed control of PMSM. In this paper, sliding mode and Extended state observer (ESO) are used to improve the speed control of the PMSM drive system. A sliding mode controller is employed in the outer speed control loop for tracking the speed of PMSM. Load torque disturbance is estimated using ESO. Performance evaluation of the sliding mode controller with ESO is compared with the conventional speed controller using PI. Better speed tracking accuracy is obtained for sliding mode controller than conventional PI controller

This paper presents a sensorless controller design to speed tracking problem for a Permanent Magnet Synchronous Motor (PMSM). The technique of passivity requires knowing the load torque, this is estimated with a reduced-order extended state observer, a traditional reduced-order observer and an online algebraic estimator. The speed and position of the rotor are estimated using the currents and voltages of the motor, avoiding the rotor's sensor. The efficiency of the controller is illustrated by the simulation results with Matlab-Simulink/PSIM.