## 1 Introduction  
Inertially stabilized platforms (ISPs) are installed on moving carriers, such as aircraft and ships. ISPs provide stable direction for the photoelectric equipment inside the platform in inertial space. They are used extensively in airborne remote sensing, photoelectric detection, target tracking, navigation, and optical communication [1]. Generally, the stable platform is composed of three orthogonal mechanical frames: outer, middle, and inner frames. The photoelectric device and gyroscope sensor are often installed in the inner frame. The gyroscope directly measures the photoelectric equipment inertial angular velocity, and achieves inertial stable imaging by controlling the torque motor rotation in each frame. The platform compensates for the carrier attitude influence, external environment disturbance, and internal disturbance of the system [2]. When the photoelectric equipment operates with a small field of view, the system needs a higher degree of stability accuracy to obtain clearer images. Therefore, designing an effective control method is significant for improving the overall system performance. Currently, the most commonly used control schemes in research and engineering utilize a gyroscope to calculate the photoelectric equipment angular velocity error in inertial space and to achieve closed-loop feedback control [3,4]. This scheme is simple and effective; however, to achieve high-precision control, feedforward control is also needed in addition to feedback control. The feedforward controller comes from the control command. However, because of the limitation of gyro location, the control command is zero in the process of inertial stabilization, making it difficult to design a feedforward controller. This limitation prevents further system performance improvements. Besides being installed in the inner frame, the gyroscope can also be installed on the platform base to measure its attitude change. The encoder sensor on the motor can be used to achieve the strapdown inertial stabilization with reverse compensation [5,6]. This scheme is directly sensitive to base rotation. It can effectively use the base motion information to construct the feedforward controller and achieve perfect tracking via the reverse motion of each motor. In theory, it can achieve zero-error control performance for some bandwidths [7]. Nevertheless, environmental and mechanical structural factors cause the platform to be disturbed by multi-source disturbances, which include the platform base attitude change, external environment disturbances, and internal system disturbances. Among them, the internal system disturbances, such as nonlinear friction, wire-wound torque, mass unbalance, and model uncertainty, are more complex. In addition, they seriously affect the stability accuracy of the line of sight (LOS). To deal with these disturbances, a variety of methods have been independently proposed and applied in related fields [8]. These include disturbance observer control (DOBC) [9], active disturbance rejection control (ADRC) [10,11], disturbance accommodation control [12], and nonlinear disturbance observer control (NDOBC) [13]. However, most control methods focus on one type of disturbance or they consider multiple disturbances as an equivalent disturbance. This may lead to conservative disturbance compensation in the presence of multiple disturbances [14,15]. For multi-source disturbances, composite hierarchical anti-disturbance control (CHADC) is an important means to address the above-mentioned problems. The idea is to design multiple loops to compensate for the different types of disturbances, so that high-precision disturbance compensation can be achieved. Furthermore, \(H_{\infty}\) control [16], sliding mode control (SMC) [17,18], or adaptive control [19] is integrated with the disturbance compensation method to achieve tracking performance and for disturbance attenuation.