## 1 Introduction  
An opto-electric stable platform (OESP) is an opto-mechanic device for long-distance target observation. Through an infrared detector or charge-coupled device (CCD) mounted on an OESP, the image of the target can be presented to the operator, as can be seen in Figure 1. OESPs usually work on moving objects such as airplanes or vehicles, and so both optimal low speed performance and inertial stability accuracy are necessary for OESPs in maintaining image quality. The opto-electric servomechanism (OES) is the key component of the OESP to achieve accurate motion. However, the torque disturbance commonly existing in the opto-electric servomechanism (OES) and the low signal-to-noise ratio(SNR) speed signal differentiated by the encoder make it difficult to achieve satisfactory servo performances. For the purpose of suppressing torque disturbance of an OES, a torque or speed closed loop using a PI controller is always considered. The principle and implementation of a proportional-integral (PI) controller are simple. However, since the PI belongs to the linear control scheme, it seems difficult to effectively deal with the nonlinear torque disturbances, such as friction and torque ripple. Another well-known approach is to build a torque disturbance observer and perform disturbance compensation according to the output of the observer. Depending on how the observer is built, this approach can be divided into two categories. The first category is to establish dynamic models for each torque disturbance mainly existing in the OES, and to suppress these disturbances one after another using these models. Obviously, an accurate model can compensate for the corresponding torque disturbance quite well. However, if there are multiple types of torque disturbances coexisting in the OES, this method will become complicated; additionally, unless the dynamic model is sufficiently precise, it will lead to a more serious impact on the motion performances of the OES [1; 2; 3]. Therefore, this method is suitable for servomechanisms under simple working conditions. Another category is to design a disturbance observer based on the nominal model of the OES. Among all the nominal-model-based observers, disturbance observer(DOB) is the most widely used [4]. However, the performance of DOB is subject to the cut-off frequency of its Q filter. If the cut-off frequency is set too high, a severe chattering may happen, causing the OES to not work properly. Additionally, if the cut-off frequency is set too low, the disturbance cannot be effectively observed, resulting in an unsatisfactory disturbance suppression effect. Since the cut-off frequency of the Q filter needs to be determined in reference to the actual characteristics of the OES, it is difficult for the DOB to obtain an optimal observation for the servomechanisms whose parameters change drastically, thus it is usually necessary to combine DOB with other advanced controllers, such as sliding mode controller(SMC) [5], to get a better motion performance. Due to the limited size and mass of the platform, the OES rarely configures a tachometer for axial speed measurement. Instead, the axial speed is mainly obtained by finite-differentiating the angular data from the encoder mounted on the output side of the OES. However, due to the limited resolution of the encoder, there is a significant quantization error in the obtained speed signal. In order to deal with this problem, a low-pass filter (LPF) is commonly used to handle the differential signal of the encoder [6]. However, the linear LPF brings a severe phase lag and decreases the stability margin while suppressing the noise. [PERSON] et al. proposed a first-order adaptive windowing method (FOAW), which achieves a tradeoff between the noise suppression and the output rapidity by adaptively adjusting the differential step size of encoder data [7; 8]. [PERSON] et al. proposed a parabolic sliding mode filter (PSMF) as well as the adaptive tuning methods for PSMF parameters [9; 10; 11; 12; 13; 14].