# Disturbance Observer-Based Anti-Shock Controller for Laser Beam Steering Systems
## 1 Introduction  
Fast-steering mirror (FSM)-based laser beam steering (LBS) systems are used extensively in various optical tracking control systems, such as line-of-sight stabilization, adaptive optics, and long-range laser communication [1; 2; 3]. Moreover, these systems are increasingly being mounted on mobile platforms such as spacecraft, satellites, airplanes, ships, and vehicles [4; 5]. Therefore, the control precision of LBS systems must be improved to maintain the aiming point in the target plane while minimizing factors that cause jitter even under dynamic disturbances [6]. The robust design of FSM systems is typically approached from two perspectives. First, the design of structural parameters is considered to satisfy the control requirements of the target platform. FSM systems require flexible hinges as rigid elastic supports to achieve the desired structural stiffness and sustain driving forces for a certain range of strokes. Flexible hinges are designed and assembled to guarantee the required transmission resolution and accuracy, as well as to facilitate substantial rotation, because such hinges eliminate mechanical friction and sources of nonlinearity such as backlash, hysteresis, and static resistance [7; 8]. In addition, flexible hinges do not require lubrication, have wide operating temperature ranges, and are more reliable than traditional bearings [9]. A flexible hinge should approximate a bearing connected to a mirror to ensure higher axial/torsional stiffness and lower rotational stiffness. However, the stiffness of flexible hinges in different directions is coupled, and therefore, axial/torsional stiffness cannot be considerably higher than rotational stiffness. In addition, reducing the rotational stiffness of a flexible hinge to expand its angular range inevitably reduces the axial/torsional stiffness. Second, to achieve high-precision control performance, it is necessary to design a control system with rapid response characteristics and strong disturbance-rejection control performance [10; 11]. FSM systems typically use long-stroke voice coil actuators (VCAs) or high-actuation resolution piezoelectric (PZT) actuators, and their response, output force, and resolution are suitable for most applications. In particular, PZT actuators are moresuitable than VCAs for use in applications that require higher actuation resolution and faster settling times. High-precision tip-tilt controllers for FSM systems are designed to ensure that the aforementioned VCAs or PZT actuators maintain an extremely small rotational position (under 10 \(\upmu\)rad rms) in the presence of dynamic disturbances to satisfy the desired operating conditions. Therefore, several studies have been conducted to realize High-precision control performance. For instance, a method to eliminate the vibration effect of PZT actuators was proposed [12]. A notch filter was developed to effectively eliminate the main resonant mode of FSM systems [13]. In other studies, an input shape controller and an integral resonance controller were developed [14]. Primarily, two types of disturbances hinder the tip-tilt control of FSM systems: periodic and nonperiodic disturbances. First, periodic disturbances occur owing to the spinning of cooling fan units on the target platform. To eliminate periodic disturbances, repetitive controllers and adaptive feedforward cancellation (AFC) schemes have been applied [15; 16]. Repetitive control technologies are the most widely used, either as internal or external model-based controllers [17]. Discrete-time repetitive controllers based on the internal model principle (IMP) have been synthesized and analyzed [18]. The most common approach is based on the IMP, which states that a model of the disturbance generation system must be included in the feedback system to realize disturbance cancellation. However, owing to hardware limitations of the servo loops used in FSM control systems, the classic AFC method cannot be used to precisely control rotational position.