# Sensorless HSPMSM Control of an Improved SMC and EKF Based on Immune PSO  
[PERSON]  
1 College of Energy and Power Engineering, Inner Mongolia University of Technology, Hohhot 010080, China; doi:10.10051/12-2  
system operating efficiency, saving energy and reducing consumption. HSPMSMs generally use mechanical sensors such as photoelectric encoders to accurately monitor rotor position and speed. The integration of mechanical sensors inevitably increases system wiring, which directly affects the overall stability of the flywheel energy storage system (FESS). In addition, high-frequency pulses interfere with the power output signal, exacerbate system instability, and increase system cost. Therefore, sensorless vector control technology in HSPMSMs has become a popular solution [2]. Sensorless technology in HSPMSMs can be divided into two main technical routes [3]. The first is a calculation method based on the current and voltage equation of the motor; i.e., the method is based on the fundamental wave estimation of the counterexample force, which requires high parameter accuracy and performs inadequately at low speeds. The second is a signal injection method based on magnetic circuit asymmetry; i.e., the method involves extracting position and velocity signals after injecting high-frequency signals using the convex pole rate of the motor. The high-frequency signal injection method [4] can achieve favorable estimation results in low- and zero-speed ranges, but it is not directly practical for hidden pole motors with low salient pole rates, and the construction of filters leads to a complicated algorithm [5; 6]. Fundamental wave estimation methods based on the inverse electric potential can be categorized as open-loop or closed-loop. The open-loop method uses the voltage, current, and mechanical equations of the motor to find the rotor position directly. This method is fast and simple but offers low stability and poor dynamic responsiveness and lacks an error adjustment mechanism. The closed-loop method uses a state observer to observe the back electromotive force or estimate the position state. This method has an error adjustment mechanism and offers better dynamic performance and stability than the open-loop method [7]. Commonly used closed-loop methods include state observers, EKFs, model-reference adaptive observers, and sliding mode observers (SMOs) [8; 9; 10; 11; 12]. Each method has its own advantages and disadvantages. For example, an SMO handles external disturbances and parameter changes well and is simple to compute. However, the output quantity of the SMO contains high-frequency jitter signals, which requires the addition of a low-pass filter to filter out high-frequency clutter, resulting in phase lag and thus requiring additional phase compensation. An EKF performs similarly to a real system model in terms of system and measurement noise and can accurately estimate the rotor position. However, an EKF approximates a linear system after considering the first-order truncation of the nonlinear system model. Neglecting the higher-order terms leads to an increased estimation error and low observer stability when strong noise and nonlinearity are involved. Traditional EKFs require repeated trial and error to select noise optimal covariance parameters, which is often time-consuming and interferes with achieving favorable results. If the noise covariance is not selected properly, an EKF system may converge too slowly, jitter too much, or even completely diverge. Therefore, there have been many attempts to select optimal EKF noise covariance matrices [13; 14; 15; 16; 17]. [PERSON] et al. [13] used the particle swarm optimization (PSO) algorithm to optimize the covariance matrix of an EKF. The optimized system can adequately suppress noise and shorten the selection time of the covariance matrix, but the basic PSO algorithm has weak searchability and a slow search speed. [PERSON] et al.