## 1 Introduction  
The tracking control system (TCS) is widely used in long-distance communication, astronomical observation, target tracking and other scientific fields [1; 2; 3; 4; 5]. However, when applied to practical programs, the TCS suffers from some external interferences from atmosphere, ground or movable platforms such as vehicles, airplanes and ships [1; 6]. In the TCS, gyroscopes and position detectors are generally used as sensors to implement a dual-loop feedback control (DFC) to stabilize the controlled platforms [7; 8] Gyroscopes with a small delay are used to build a high-bandwidth inner loop and the tracking performance of the TCS mainly depends on the position information from position detectors such as a charge-coupled device (CCD). Control bandwidth and disturbance suppression ability are two significant factors for evaluating the closed-loop performance of the TCS. However, control bandwidth and disturbance suppression ability are limited by the mechanical resonance and the sensors' performance such as the drift and time delay caused by the low sampling frequency [9; 10]. In order to improve the performance of control bandwidth and disturbance suppression, the micro-electro-mechanical system (MEMS) accelerometer has been widely recommended for the TCS due to its high bandwidth, small size and low weight [11; 12; 13; 14; 15]. The MEMS accelerometer can compensate for the mechanical resonance in the acceleration feedback control loop, and is therefore utilized to enhance the stiffness of the controlled object. [PERSON] implemented a dual-loop control by using the MEMS accelerometer and the CCD with a high bandwidth to improve control bandwidth [16]. In 2016, [PERSON] proposed a multi-loop feedback control method (MFC) with the MEMS accelerometer, MEMS gyroscope and CCD, which successfully improved the disturbance suppression performance [17]. The overall disturbance suppression ability is the product of each single loop, hence the disturbance suppression ability of MFC is naturally better than that of DFC [18]. Moreover, the research about the disturbance suppression of the TCS is based on MFC for obtaining better performance. To improve the performance of the TCS, the feedforward method based on direct measurement is also introduced as it can suppress most of the theoretical external disturbances [19; 20]. However, it involves additional cost for another sensor and specific environments with low measurable noise. As a result, the implementation feedforward method is limited in more complex conditions due to its disadvantages. In order to avoid the extra cost and application limitations, 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. This feedforward method was first presented by [PERSON] in the 1980s and was named the disturbance observer (DOB) method [21; 22; 23]. It has been applied to several engineering processes, such as robot control, the hard disk, the magnetic hard drive servo system and permanent magnet synchronous motor control [24; 25; 26; 27; 28; 29]. Beyond this, [PERSON] recommended the disturbance observer for an acceleration feedback control loop with a MEMS accelerometer, which improved disturbance suppression ability only at intermediate frequency [30]. Disturbance suppression is still a large obstacle for the good tracking performance of the TCS. One problem that has not been handled by the afore-mentioned method is that there is considerable drift caused by the MEMS accelerometer due to its insensitivity at low frequency. As a result, the drift leads to integral saturation when feedforward methods are used to suppress disturbance [30]. As such, it is hard to improve disturbance suppression performance at low frequency with the MEMS accelerometer.