# Dynamic High-Type Interval Type-2 Fuzzy Logic Control for Photoelectric Tracking System
## 1 Introduction  
Photoelectric servo tracking equipment is widely used in beam control systems, such as adaptive optics, free-space communication, line of sight stabilization, etc., and has important application value in military and civilian fields [1, 2, 3]. Its tracking performance is the most important index to evaluate the control system. Commonly used tracking control methods include PID [4, 5], speed/acceleration lag compensation [6, 7], and disturbance observer based on a multi-loop feedback control [8]. Among them, the PID method is simple in design, stable in performance, and the most widely used. However, due to itsslow dynamic response speed and low steady-state accuracy, it is difficult to adapt to the situation where the target volume becomes smaller, and the maneuverability becomes stronger in the current environment [9]. As early as the 1990s, the United States' Launch Area Theodolite System applied dynamic high-type control technology (DHTC), which has achieved great tracking accuracy and a wide range [10]. Dynamic high-type technology refers to dynamically connecting and disconnecting one or more integrators based on the original multi-loop feedback system to improve the response speed and steady-state accuracy while ensuring that the system does not have integral saturation. However, the research on DHTC in academia is still in its infancy. [PERSON] constructed a PID-I system and added an integrator to the PID controller to achieve high-type control [1], and [PERSON] et al. constructed the explicit analytical PID tuning rules for the design of type-III control loops based on the principle of the symmetrical optimum criterion [11], but they did not achieve the goal of changing the type in real time according to the system status, and there is a hidden danger of integral saturation. At present, in the research of dynamic high-type switching, the method of type switching relies on manual operation, and the switching moment will bring greater chattering to the system, which is far from meeting the needs of practical applications. In recent years, the fuzzy logic control (FLC) method has developed rapidly, which provides a breakthrough for the realization of DHTC. As a rule-based nonlinear controller, the FLC provides a systematic method in which experts construct language information and transform it into a control strategy. It can solve many complex control problems that cannot be established for precise mathematical models. Therefore, FLC is an effective method to control uncertainties and inaccuracy in the system [12]. Later, researchers applied it to many practical systems in the control field. In [13], the two-level fuzzy feedback scheduling scheme is designed to adjust the task priority and period according to the combined effects of the response time and packet loss of cyber-physical systems for robot control, proving that fuzzy control has fast and accurate response performance in real-time systems. In [14], according to the characteristics of the actual reaction of the continuous stirred tank reactor, the T-S fuzzy model is used to study the problem of fault detection. In addition, the fuzzy controller is also used in the medical field, such as the fuzzy control-based energy aware routing protocol (EARP) applied in wireless body area networks (WBANs) [15] and combined with sliding mode control applied in gyroscope control systems [16; 17]. In the study of DHTC, [PERSON] et al. used T1 FLC to construct the T1 FLC-DHTC structure, which realized automatic switching of system types [18], but the control parameters of T1 FLC completely relied on artificial settings, and in the real unstructured dynamic environment and many specific applications, the traditional T1 FLC will face many uncertainties, mainly including measurement noise, friction, and rule base differences, etc. [19; 20; 21; 22]. As an extension of the type-1 fuzzy logic system (T1 FLS), the type-2 fuzzy logic system (T2 FLS) was proposed.