## 1 Introduction
The disturbance compensation loop based on CHADC is designed inside the velocity loop; the velocity loop focuses on tracking the performance, and the compensation loop focuses on the disturbance separately [20]. Recently, several researchers have proposed a variety of methods to handle disturbances in IS/SISPs. The traditional design controller method focuses on feedback loops. The proportional integral derivative (PID) control method has been widely used in industrial control systems owing to its simple structure and parameter adjustment capabilities. A SMC has been proposed to achieve a better steady-state accuracy than PID control [21]. As the system is affected by matched and unmatched uncertainties, a modified feedforward-based extended state observer has also been proposed to achieve high tracking performance [22]. Owing to nonlinear factors, such as friction, wire-wound restraint, sensor noise, un-modeled parts, or the varying system parameter, the system stability accuracy cannot be guaranteed by using the velocity loop. To address this problem, a novel discrete-time direct model reference adaptive control based on nonlinear friction compensation has been introduced into the original PI control system [23]. A stable control method based on ADRC and a noise reduction method based on the disturbance observer (DOB) have been proposed to handle the system disturbance and to improve the anti-disturbance capability in a strapdown inertially stabilized platform (SISP) [24]. To achieve better disturbance compensation, the main disturbance needs to be analyzed. Then, an effective control method should be designed on the basis of the model. The primary nonlinear disturbance in the SISP system with a harmonic drive is friction caused by the transmission mechanism relative motion. The traditional friction compensation method measures the relative angular velocity and fits the friction model. The feedback controller contains the negative friction compensation on the basis of the model [25]. The work in [26] adopted a LuGre model-based friction compensation method to design the controller. The disadvantage of this method is the existence of a delay in the sampling period in the control system. As the nonlinear friction torque forms the feedback loop, the instability problem is apparent [27]. In addition to multi-source disturbances, we found that SISP systems supported by light bases will vibrate when using a PI feedback controller only. The vibration of the closed-loop control system seriously affects the performance of the system, and so does adding a disturbance compensation controller or other advanced controllers. Therefore, we need to design a controller to suppress the vibration before disturbance compensation. To suppress the vibration, the model of this system should be analyzed carefully. The conventional system dynamics model employs motor rotor and load only, without considering the stator, or it implicitly assumes a fixed stator. The base of the SISP is connected with the motor stator, and the control system command emerges from the base movement, that is, the motor stator movement, in the inertial space. The control value corresponds to the motor output torque, it acts on the rotor and load, and the reaction torque also acts on the base. The reason for the vibration is that the influence of the light base support and the control on the dynamic characteristics of the whole system is not considered. This is highlighted by the location of the gyroscope in the SISP. To solve the multi-source disturbance and vibration problem, we first consider the motor stator (platform base), motor rotor, and load as three rigid bodies and establish a multi-body dynamics model by the Euler method, which is commonly used in robotics [28; 29]. This model can describe the interaction of the system better.