# An Overview of Position Sensorless Techniques for Switched Reluctance Machine Systems
## 3 An Overview of Recent Development in Position Estimation Methods of SRM
### Magnetic-Model-Based Position Sensorless Methods
#### 3.1.4 Observer-Based Methods  
Compared with intelligent algorithms, the development of modern control theory provides a new method of position control. The state equation of the system can be established, and the observer can be constructed to measure the physical quantity that is not convenient to measure directly. The flux observers, position observers, and sliding mode observers are also used to obtain the rotor position indirectly [114; 115; 116; 117]. Generally, such algorithms have the advantages of torque- and speed-independent control algorithms, no pre-stored large amounts of data, and wide applicability to speeds. More deeply, this kind of position estimation control needs to set more parameters, which is its disadvantage. \[\left\{ \begin{array}{l}\frac{d\Psi_{k}}{dt}=-R_{k}\dot{k}_{k}+U_{k}\\ \frac{d\omega}{dt}=-\frac{1}{J}D\omega-\frac{1}{J}\Psi_{k}{}^{T}\frac{d\textbf {L}_{k}^{-1}(\theta_{ph})}{d\theta_{ph}}\Psi_{k}\\ \frac{d\theta_{ph}}{dt}=\omega\\ i_{k}=\textbf{L}_{k}^{-1}(\theta_{ph})\Psi_{k}\end{array} \right. \tag{8}\]  
where \(J\) and \(D\) are the moment of inertia and viscous friction coefficient of the motor, respectively. \(w\) is the rotational speed. The basic equations satisfied by the SRM system are shown in (8). Hence, many studies will design different observers based on different control theories, such as sliding mode control and nonlinear state observers. This class of position sensorless methods is an application of modern control theory [37; 118]. The performance of advanced control algorithms is highlighted in the efficient aspects of speed regulation, torque regulation, and position estimation [118]. Based on the general nonlinear magnetizing model (GNMM) was applied to estimate the rotational speed and the position of the rotor [127]. With the introduction and development of sliding mode control theory, sliding mode observers have been designed and improved to improve performance [121; 122; 123; 124; 125; 126]. Early position estimation methods based on sliding mode observers used linear models, which limited their accuracy. With finite element modeling and nonlinear fitting improving the accuracy of flux linkage and torque calculations, a second-order inductance model based on the Fourier model is used in a typical second order sliding-mode observer to observe the rotor position. Later, scholars improved the performance by improving the approach control law to force the rotor posi  
Figure 8: Rotor position estimation principle based on neural network (**a**) Block diagram of SRM sensorless system based on neural network. (**b**) Artificial neural networks. tion estimation error to converge to the sliding mode surface [124; 126]. In order to solve the rotor position error caused by nonideal measurement noises and flux linkage calculation errors, as shown in Figure 9a, a nonlinear state observer (NSO) is designed to indirectly measure the rotor position with special position detection. In addition, a comparison between the linear observer and the proposed observations was made in terms of position estimation and speed estimation, as shown in Figure 9b [128]. The observer has outstanding performance in the medium- and high-speed range. The observer design is also more difficult, but it can reduce the need for motor parameters and is not limited by the speed range. The discovery of modern control theory is a direction full of potential opportunities. Methods that require the use of electromagnetic quantities are the most mentioned. It is obvious that this is an important direction for the future development of location-free methods. Through the above introduction, Table 1 shows the characteristics of these types, the current development, and the future development direction. The observer advantage here is huge due to the speed-independent torque control strategy. Due to the complex design of the artificial intelligence algorithm, it does not have an obvious advantage in rotor position estimation.