## 1 Introduction  
Fast steering mirror (FSM)-based laser-beam steering (LBS) systems are used in various optical tracking control systems, such as long-range laser communication, line-of-sight (LOS) stabilization, and adaptive optics [1; 2; 3; 4; 5]. In addition, these systems are increasingly mounted on moving platforms, such as spacecraft, satellites, airplanes, ships, and vehicles [6; 7; 8]. However, the LBS control system must maintain the aiming point in the target plane while minimizing factors that cause jitter in the presence of disturbances. In applications, jitter usually is caused by the vibration of the optical bench through which the laser beam travels [9]. The robustness design of FSM systems is typically approached as two separate cases. First, the design of structural parameters must be considered to satisfy the control requirements of the target platform. FSM systems require the flexible hinges as rigid elastic supports to meet structural stiffness and drive forces for a certain range of strokes. Flexible hinges have a simplified structure, integrated design, and machining to guarantee the transmission resolution and accuracy, as well as good rotational response, because they eliminate mechanical friction and non-linearity [10; 11]. In addition, the flexible hinges can be attenuated to the mechanical vibration, which leads to reduced rotational position error and increased precision performance [12]. A flexible hinge should approximate a mechanical structure with higher axial/torsional stiffness and lower rotational stiffness to ensure the desired flexible segment movement. Second, with high-precision control performance, it is necessary to design a control system with fast response characteristics and disturbance rejection control performance [13; 14; 15]. FSM systems typically use voice coil actuators or PZT actuators, with VCA having a longer stroke, while their response, output force, and resolution are primarily suitable for most applications. PZT actuators are also suitable for applications that require higher resolution and faster settling times than VCA. High-precision tip-tilt controllers for FSM systems are designed to ensure that the aforementioned VCA or PZT actuator maintains an extremely small rotational position in the presence of dynamic disturbances to satisfy the desired operating conditions. Therefore, several studies have been conducted to achieve high-precision control performance. A method to eliminate the vibration effect of PZT actuators has been proposed [16]. A notch filter was developed as an effective method to eliminate the main resonant mode of FSM systems [17; 18]. Furthermore, an input shape controller and an integral resonance controller were developed [19; 20]. In general, several methods can be adopted to improve the performance of the dynamic disturbance attenuation for high-precision motion control systems. Particularly, the iterative controllers and adaptive feedforward cancellation (AFC) schemes have been applied to cancel out the repeatable disturbances resulting from the operational condition of the target application [21; 22]. Iterative control algorithms are the most widely used for disturbance rejection, as either internal or external model-based controllers [23]. Discrete-time iterative controllers based on the internal model principle (IMP) have been analyzed [24]. As a disturbance-attenuation control system, an IMP-based control algorithm is commonly used in which a model of the disturbance-generating system is included in the feedback system. However, owing to the hardware limitations of the servo loop in our FSM control system, classical AFC schemes cannot be used to precisely control the rotational position. In order to avoid the above-mentioned problems, a basic idea to suppress disturbances emerges, which estimates the influences of external disturbances independently by using the disturbances observer and then eliminates the perturbation through the feedforward method.