introduction
PMSM (Power Mitigation System) is widely used in aerospace, electric vehicles, and industrial servo applications due to its inherent characteristics such as high torque-to-inertia ratio, high energy density, and high efficiency. With the development of high-performance magnetic materials, power electronics, microelectronics, and modern control theory, especially the emergence of high-performance control strategies such as vector control and direct torque control, PMSM speed control systems have experienced rapid development. PMSM vector control, mimicking DC motors, achieves excellent dynamic and static performance through decoupling control of torque and excitation components. This breaks the monopoly of DC speed control systems in the high-performance electric drive field and gradually usheres in the era of AC speed control systems.
High-performance PMSM control systems rely on reliable sensor devices and precise detection technology. Traditional control systems often use mechanical sensors such as photoelectric encoders and rotary transformers to obtain rotor position information. However, mechanical sensors are difficult to install and maintain, increasing the complexity of the system's mechanical structure and affecting its dynamic and static performance, thus reducing its robustness and reliability. The performance of PMSM vector control systems is often limited by the accuracy and response speed of mechanical sensors, while high-precision, high-resolution mechanical sensors are expensive, increasing the cost of the drive control system and limiting the application of the drive device under harsh conditions. The fundamental solution to the inherent contradiction of low cost, high accuracy, and high reliability of mechanical sensors is to eliminate mechanical sensors and adopt sensorless technology. Therefore, research on sensorless PMSM control technology has rapidly become a hot topic.
Current Status of PMSM Research at Home and Abroad
Research on sensorless control technology began abroad in the 1970s. Over the following two decades, scholars both domestically and internationally conducted extensive research on sensorless operation of AC motors and proposed numerous methods. These research findings have enabled the application of sensorless motor drive systems in a wider range of industrial sectors.
The development of sensorless PMS technology has mainly gone through two stages: The first generation of AC motors using sensorless vector control technology has appeared on the market after nearly 10 years of research and prototype testing. However, the speed control accuracy of the first-generation sensorless motors was not high, and the range of speeds that could operate normally was limited. At low speeds and zero speeds, the mechanical characteristics were very soft and the error became large, making speed control impossible. The first-generation sensorless technology was still far from perfect, thus limiting its application. Currently, the second-generation sensorless technology is under development, and it is expected to have higher accuracy and complete torque control even at zero speed, comparable to traditional vector control technology. The expected application areas for the second-generation sensorless technology are basically the same as those of the first generation, but with better dynamic characteristics.
Overview of PMSM sensorless control technology
Since gaining widespread attention from scholars both domestically and internationally, sensorless PMSM technology has progressed rapidly, achieving phased results and with some technologies already in practical application. From in-depth exploration of the characteristics of PMSM itself to the application of numerous modern control theories, the theory of sensorless PMSM control is constantly evolving. A review of the mainstream theories of sensorless PMSM control is presented below.
Based on PMSM Fundamental Electromagnetic Relationship Estimation Method
The fundamental control principle of PMSM (Polarization-Modulation-Morphology) is to achieve field-oriented control. Whether controlling voltage, current, or frequency, the quality of control performance ultimately depends on the effectiveness of magnetic field control. Sensorless technology based on the fundamental electromagnetic relationships of PMSM focuses on the PMSM stator flux linkage space vector equation and stator voltage vector equation. It estimates rotor position by detecting motor current and voltage to obtain physical quantities containing rotor information, such as flux linkage and induced electromotive force. Sensorless methods based on the fundamental electromagnetic relationships of PMSM can be either open-loop or closed-loop. The method that estimates the induced electromotive force using the stator voltage vector equation and then estimates the rotor position using the arctangent function is typically an open-loop method. The method that uses the stator flux linkage space vector equation first calculates the stator flux linkage vector using voltage vector integration, then calculates the equivalent synchronous inductance through rapid iteration, and then estimates the rotor position information can also be either open-loop or closed-loop. Its advantages are low computational complexity, simplicity, and ease of implementation. However, since this method is based on the PMSM mathematical model, although different mathematical models can be selected, all models involve motor parameters. Motor parameters such as stator resistance and inductance vary with temperature and motor load, as well as magnetic circuit saturation, all of which affect the accuracy of the estimation. Therefore, this method is best applied in conjunction with online identification of motor parameters.
Assuming the rotating coordinate method
Assuming the rotating coordinate method focuses on the voltage equations of the PMSM mathematical model in a two-phase rotating coordinate system, a controllable reference coordinate is proposed for sensorless control; this coordinate is called the estimated coordinate. It is not a synchronous rotating coordinate, but rather oriented to a known estimated position, and can automatically adjust itself according to a defined control law. Specifically, the position deviation is estimated by detecting voltage and current, and the estimated position deviation is adjusted through a PLL regulator to make the dummy rotor position nearly consistent with the actual rotor position. The core of this method's estimation accuracy is accurately estimating the position deviation. Although the mathematical model is precise, the estimation accuracy is still affected by changes in motor parameters and the accuracy of current detection. Although closed-loop control is used, it still does not completely eliminate dependence on motor parameters. This method is essentially an estimation method based on back EMF. Therefore, it is difficult to apply to sensorless control in stationary and low-speed operation. Nevertheless, the control system constructed by this method is relatively simple. Due to the use of a PLL regulator, the estimation accuracy and stability of the system are improved, and good steady-state performance can be obtained.
Model Reference Adaptive System
The basic idea of a Model Reference Adaptive System (MRAS) is to use an equation without unknown parameters as a reference model and an equation with estimated parameters as an adjustable model. Both models have the same input and output with the same physical meaning. They operate simultaneously, using the difference in output parameters to adjust the estimated parameters in real time according to a suitable adaptive law, achieving the goal of the adjustable model tracking the reference model. Depending on the choice of the reference model and the adjustable model, various speed identification models for Model Reference Adaptive Systems can be constructed. The most commonly used method is the back-EMF-based MRAS algorithm, whose advantage is that the system's integrity depends entirely on the reference model. However, its disadvantage is that at low speeds, it is sensitive to stator resistance, leading to inaccurate speed identification or even divergence, and thus cannot solve the low-speed problem.
Location identification methods based on observer technology
An observer is essentially a state reconstruction, that is, reconstructing a system using directly measurable variables from the original system as its input signals, and ensuring that the reconstructed state is equivalent to the original system state under certain conditions. The principle of equivalence is that the error between the two systems asymptotically and stably approaches zero during dynamic changes. This system used to achieve reconstruction is called an observer.
Observers are classified into deterministic and stochastic observers based on signal type, and into linear and nonlinear observers based on system type. The basic structure of an observer consists of a state estimation equation derived from the mathematical model of the motor, plus a correction element; these two elements form a closed-loop state estimate, i.e., the observer. Electrical engineers have drawn upon theoretical achievements from numerous scientific fields worldwide, creatively integrating cutting-edge ideas from various disciplines into observer theory, resulting in many valuable observers with diverse control concepts. In sensorless PMS technology, adaptive full-order observers, extended Kalman filters (EKF), and sliding mode observers (SMO) are commonly used.
(1) Adaptive full-order observer
Adaptive observers are sensorless technologies that integrate adaptive control with observer theory. The basic idea is to introduce adaptive control into the correction stage of the observer structure to achieve adaptive speed control. The PMSM adaptive full-order observer first constructs a current observer using the voltage equations in the two-phase rotating coordinate system of the PMSM. Then, a standardized PMSM mathematical model is used as a reference model. The constructed current observer serves as an adjustable model, and the output error of the two models drives the adaptive mechanism. Under the action of the adaptive law, the parameters to be estimated can be continuously corrected so that the output error of the two models tends to zero. Adaptive observers can not only be used to estimate the rotor position and speed of the PMSM, but also identify motor parameters based on Popov stability theory, reducing the impact of parameter variations and improving the robustness of the system.
(2) Extended Kalman filter
The Kalman filter is also a type of observer, applying the Kalman filtering concept to observer theory. Like other observers, the Extended Kalman Filter (EKF) tracks the system state, but unlike others, it is nonlinear and stochastic. EKF state estimation consists of two main stages: prediction and correction. In the prediction stage, the predicted value for the next estimate is derived from the previous estimate. In the correction stage, the deviation between the actual output and the predicted output is used to correct the predicted value. Essentially, Kalman filtering is about feedback correction of the predicted value. Therefore, it not only has optimization and adaptive capabilities but also better suppresses measurement noise and system noise. However, a drawback of the EKF filter is the unknown nature of system measurement noise and system noise, making it difficult to select the covariance matrix in the EKF filter using a deterministic method. Generally, a trial-and-error method is used to select the covariance matrix, which is related to the system's dynamic performance and stability. Therefore, determining the covariance matrix is crucial to the system's stability.
(3) Sliding mode observer
The sliding mode observer is an application of sliding mode variable structure control in observer theory. Its characteristics include performance entirely determined by its sliding hyperplane, no overshoot during transient response, and strong robustness to changes in its own parameters and external disturbances. The basic idea is to first establish a sliding mode current observer based on the PMSM mathematical model. The deviation between the observed current and the actual current is chosen as the sliding hyperplane. This deviation is controlled by a popping control to estimate the induced electromotive force (EMF) containing higher harmonics, forming the system closed loop. The induced EMF containing higher harmonics is then filtered to calculate the position and speed. The presence of higher harmonics in the estimated variables is a drawback of the sliding mode observer, affecting its application in high-performance servo systems. Although filtering can be performed, conventional filtering methods can cause phase deviations. As mentioned earlier, the Kalman filter can account for the impact of noise on the system. Therefore, the sliding mode observer and Kalman filter can be effectively combined to leverage the strengths of the Kalman filter and create a more complete observer.
Based on PMSM motor characteristic estimation method
Most sensorless PMSM technologies rely on induced electromotive force (EMF) to estimate rotor position. However, at very low or zero speeds, the induced EMF approaches zero, making it difficult, or even impossible, to accurately estimate the rotor pole position. High-frequency signal injection, based on the salient polarity characteristic of PMSM motors, offers significant advantages for observing rotor pole position. Its main methods include the rotating voltage vector method and the pulsating voltage vector method.
(1) Rotating voltage vector method
Rotating voltage injection involves injecting a three-phase symmetrical high-frequency sinusoidal voltage signal into a plug-in PMSM motor. This generates a constant-amplitude, high-speed rotating space voltage vector within the motor. This space voltage vector produces a rotating magnetic field within the motor, which is periodically modulated by the rotor's salient poles. The modulation result is naturally reflected in the current response, and the stator high-frequency current becomes a carrier current containing rotor position information. After demodulation processing, the relevant rotor position information can be extracted, thus forming various closed-loop control systems to achieve sensorless vector control or direct torque control. This is currently a highly promising sensorless control method.
(2) Pulsating voltage vector method
The pulsating voltage injection method injects a pulsating voltage vector into a permanent magnet synchronous motor. The pulsating voltage vector is superimposed on the excitation magnetic field, which changes the saturation level of the excitation magnetic circuit and gives the excitation magnetic circuit salient polarity. This salient polarity modulates the pulsating voltage vector. This modulation effect changes as the pulsating voltage deviates from the excitation magnetic pole axis. This change is reflected in the high-frequency current response, and therefore, this current response will carry information about the rotor position estimation error.
Both methods utilize the salient pole characteristics of the motor for modulation, but the salient pole of the rotating voltage injection method is structural salient, meaning it is applied to insert-type PMSMs. The salient pole of the pulsed voltage injection method, on the other hand, is mainly saturated salient, and structural salient poles have a weak effect on high-frequency voltage modulation. The pulsed voltage injection method can be applied to surface-mounted PMSMs, while the rotating voltage injection method cannot. Both methods are suitable for low-speed estimation and initial position estimation, utilizing the salient pole of the PMSM without relying on the motor's mathematical model and parameters. The pulsed voltage input method is characterized by its independence from motor parameters and operating state, allowing it to operate across the entire speed range, even at zero speed.
Estimation methods based on artificial intelligence theory
The rotor position estimation method based on neural network artificial intelligence theory was proposed against the backdrop of MRAS (Model Reference System). Its aim is to leverage the simplicity and stability of MRAS's model reference adaptive system to improve speed estimation accuracy in the low-speed range and enhance its sensitivity to motor parameters. With the continuous development and improvement of artificial intelligence theory, research is being conducted on sensorless technology applying neural network theory to replace the PMSM (Power Probe Model) current model rotor observer, and to replace proportional-integral adaptive system with an error direction propagation algorithm for position estimation. The network's input and output have clear physical meanings. The network weights are the motor parameters, and the network's learning process is the speed and position estimation process. This method is of great theoretical significance, but its theoretical research is still immature, and hardware implementation also presents certain difficulties. Currently, numerous papers have been published on the application of intelligent control theories such as neural networks, expert systems, and fuzzy control in the field of electric drives, but their industrialization is still some distance away.
Development Trends of PMSM Sensorless Control Technology
Sensorless control of PMSM (Power Management System) represents the current development direction of PMSM control theory, and its theoretical achievements have broadened the application fields of PMSM. The basic idea of sensorless PMSM control is to estimate rotor information by detecting voltage and current and applying corresponding control theories. However, no single sensorless PMSM control method can yet achieve full-speed operation of the PMSM system. On the one hand, the absolute advantage of high-frequency signal injection in the zero-speed and low-speed domain makes it a promising method for full-speed operation of PMSM systems. However, some problems inherent in the high-frequency signal injection method require further research, making it a focus for many scholars. On the other hand, based on observer analysis methods, modern control theories such as adaptive control, variable structure control, and nonlinear control have been introduced to form numerous sensorless control methods. Each control method has its own advantages and disadvantages; a single control method is unlikely to achieve ideal control results. Exploring the mutual penetration and combination of various control methods to better improve sensorless control performance is the future development direction of sensorless control technology.
Conclusion
This paper reviews the current development status of PMSM sensorless control technology, analyzes and compares the advantages and disadvantages of various PMSM sensorless control methods, points out the research focus and problems to be solved in PMSM sensorless control technology, and predicts the future development direction of PMSM sensorless control technology: one is the research direction of expanding from the zero-low speed field to the full speed field using the high-frequency signal injection method; the other is the research direction of combining and integrating various modern control theories based on observers.
