1. Introduction
With the advent of new power devices, microcontrollers, and integrated circuits, permanent magnet synchronous motors (PMSMs) have gained significant traction in emerging fields like new energy vehicles. In the field-oriented control of PMSMs, accurate rotor position estimation plays a vital role. Traditionally, mechanical or electronic sensors have been employed to obtain position information, offering a straightforward and effective approach. However, sensor-based methods come with certain limitations. Environmental conditions such as temperature and electromagnetic interference can adversely affect sensor performance, leading to substantial errors in position estimation. Furthermore, the high cost associated with sensor implementation is a notable drawback. To overcome these challenges, extensive research has been conducted on sensorless control strategies [
1,
2]. Moreover, in specific high-speed PMSM applications where precise control is paramount, there is an increasing demand for high-performance processors or microcontrollers. Consequently, there is a pressing need for cost-effective yet high-precision control systems, which have become a focal point of research [
3].
In the realm of sensorless control algorithms for PMSMs, two distinct categories exist based on the applicable motor speed range: methods suitable for low-speed or zero-speed control and methods suitable for medium to high-speed control. For position estimation at medium to high speed, various methods are currently employed that extract rotor position and speed information from the motor’s back electromotive force. Commonly used methods include direct computation, model reference adaptive control [
4], observer-based methods, extended Kalman filtering [
5,
6,
7], and artificial intelligence algorithms [
8]. Ref. [
9] proposed an extended back electromotive force method that decouples the DC and AC components of the inductances on the
and
axes of salient-pole motors. This method incorporates the AC component into the stator winding’s back electromotive force, enabling rotor position estimation. Sliding mode control theory was utilized in the observer for sensorless control in reference [
10]. Additionally, researchers have proposed methods such as variable sliding mode gains and speed adaptive sliding mode control to enhance the accuracy of position and speed estimation based on the basic sliding mode observer [
11,
12,
13]. Kalman filtering has been successfully applied to the sensorless control of PMSMs, effectively suppressing measurement errors and noise interference. However, its implementation requires a high computational complexity and processor requirements [
14]. Furthermore, reference [
15] introduced a method that utilizes high-frequency signal injection to estimate the speed of permanent magnet synchronous motors, enabling position observation at zero or low speeds. Ref. [
16] proposed a high-frequency square wave signal injection method based on oversampling, reducing the rotor position error and position update delay. For low-speed operation (including stationary states), reference [
17] employed a sliding-mode-based phase-locked loop observer defined by a complex switching function to observe the rotor angle. Ref. [
18] presented a sensorless control method for PMSMs based on low-frequency current signal injection, enabling precise position servo control. High-speed sliding mode observer technology was utilized in reference [
19] to assess the stability of a permanent magnet synchronous motor drive, enhancing control robustness. Ref. [
20] proposed a sensorless control method based on the static error between the discrete d-axis current and the corresponding reference value. This method accurately compensates for the estimated rotor position of the motor under high-speed and low-load-ratio conditions, improving sensorless control accuracy.
In the references above, the position observation algorithms for high-speed conditions are based on back electromotive force, while, for low-speed conditions, the position observation algorithms rely on the salient pole effect. This distinction arises because the motor’s back EMF differs at high and low speeds, making it impractical to employ back-EMF-based algorithms for position observation across the entire speed range. Therefore, if control is desired throughout the entire speed range, an additional switching algorithm from low to high speeds needs to be implemented. This increases the complexity of the control algorithm and places higher demands on the processor’s performance. To address this issue, we recognized that the magnetic flux linkage of the rotor remains consistent across high and low speeds, making it applicable throughout the entire velocity range. Therefore, we adopted a nonlinear observer based on the magnetic flux linkage model. This approach was initially proposed in references [
21,
22]. In this method, the accuracy of the control gain parameters and state variables is crucial to the algorithm’s performance. However, the original references provide a limited treatment of these aspects. When dealing with motors that have significant parameter variations, adjusting the parameters during debugging becomes challenging. Additionally, there is no specific handling of zero-speed or low-speed conditions, leading to significant disturbances from environmental factors. Hence, this paper aims to improve the nonlinear magnetic flux linkage observer algorithm to enhance its robustness and address these issues.
In order to achieve a higher-precision control of PMSMs, extensive research has been conducted on control systems. In reference [
23], researchers implemented an integrated control of the PMSM drive system and regenerative braking system based on the principle of vector control. They utilized a Field Programmable Gate Array (FPGA) as the central processor, which improved the real-time performance and stability of the PMSM control system. Ref. [
24] implemented a dynamic parameter speed controller using a generalized regression neural network on a TI Digital Signal Processor (DSP) platform to control the PMSM. In reference [
25], a parallel and pipeline design principle was adopted, and a compensation controller based on an extended Kalman filter was constructed on an FPGA. This design improved the execution speed of the control algorithm and the tracking performance of the system. Ref. [
26] employed an FPGA-based real-time sampling and update strategy to reduce the update delay of pulse width modulation. Ref. [
27] proposed an optimized multi-axis control system for permanent magnet synchronous motors based on a system-on-chip, achieving an execution time of only a few microseconds while reasonably utilizing system resources. Ref. [
28] implemented sensorless sliding mode observer control of PMSMs on an FPGA using hardware optimization algorithms such as pipeline and resource sharing. This implementation demonstrated good robustness and a high performance. In reference [
29], a PMSM control scheme based on a Luenberger disturbance observer was implemented on a Zynq System-on-Chip(SoC). Therefore, it can be observed that, due to the inability of certain general-purpose processors to meet the required performance standards, such as speed, the high-precision control of PMSMs in the references above is implemented on an FPGA or DSP. This significantly increases the implementation cost and results in poor portability between different platforms, along with an increased complexity in application.
In summary, the current sensorless control algorithms for PMSMs still have deficiencies as they are challenging to apply simultaneously under both low-speed and high-speed conditions. Moreover, for the high-precision control of high-speed PMSMs, the performance of general-purpose processors cannot meet the requirements of complex control algorithms at the same cost. Therefore, this paper fills these research gaps. The main contributions of this paper are as follows:
An improved nonlinear flux observer model was proposed, enhancing the robustness of position observation and exhibiting an excellent performance in both low-speed and high-speed conditions while reducing computational complexity;
The improved nonlinear flux observer for position estimation was implemented in hardware circuitry;
An SOC designed for PMSMs, based on the ARM Cortex-M0 core, was introduced. It adopts a combined software and hardware approach, ensuring algorithmic execution efficiency while maintaining flexibility in software implementation. Additionally, it significantly reduces implementation costs and is suitable for the high-precision control of high-speed PMSMs, achieving a high performance and low cost in permanent magnet synchronous motor control.
The organization of this paper is as follows: In
Section 2, an introduction to the basic nonlinear flux observer is provided, followed by its improvements, including a variable gain model and a compensation model for the state variables. The improved algorithm is then subjected to fixed-point processing. In
Section 3, the hardware implementation of the improved position observer is discussed, where it is implemented as a hardware IP and integrated into an SOC designed based on the ARM Cortex-M0 core for PMSM applications. In
Section 4, the improved nonlinear flux observer is validated through simulation, and the performance of the position observer and the functionality of the SOC are tested for an actual system. Finally, conclusions are presented in
Section 5.
5. Conclusions
In this paper, the nonlinear flux position observer was analyzed, and a variable gain model and a compensation model for the state variables were proposed. The improved position observer demonstrates an excellent observation performance, reaching a convergent state after one electrical cycle since its activation. The error between the observed and actual angle is less than 0.2 rad, with an error fluctuation of less than 0.05 rad. When the target velocity switches, the observed angle does not exhibit significant divergence and quickly converges. Additionally, fixed-point processing was performed on the improved algorithm, and the circuit was implemented and synthesized using the SMIC 180 nm process. Next, an SOC was designed based on the ARM Cortex-M0 core, and the aforementioned nonlinear flux position observer circuit was incorporated as a hardware IP of the SOC. We validated the SOC prototype on a Xilinx FPGA. The experiments indicate that the designed SOC balances the high efficiency of hardware implementation with the flexibility of software implementation. When running a sensorless control algorithm for a PMSM, it achieves a 30.3% increase in execution efficiency.
Therefore, significant improvements in accuracy and stability are achieved by the newly proposed nonlinear flux observer in this study, filling the research gap in the field of nonlinear flux observer for position estimation. Furthermore, addressing the lack of high-performance motor controllers, this study introduced a sensorless control SOC specifically designed for high-speed PMSMs, which combines software and hardware to control the motor. This approach enhances the convergence of the observer angles and improves the efficiency of algorithm execution. The contribution fills the research gap in high-speed PMSM control systems, specifically in terms of control efficiency and accuracy, and provides a new solution for high-performance motor control in practical applications. In the future, this work is intended to be expanded as follows:
The improved position observer and the designed SOC will be subjected to extensive experimental validation to expand their application scope in different domains;
Research will be conducted on how to further reduce the complexity and cost of hardware circuits to achieve a more efficient and cost-effective motor control system.