Aimed at the nonlinear friction,disturbance torque and load variation in typical mechanical-electrical servo systems,by considering discrete-time output signals of angular position sensor as the observer input,the design of an angular acceleration boundary observer design is presented using sliding-mode control method.Based on the analysis of the structure of the boundary observer,we propose a method to determine the control input by designing the sliding mode.Furthermore,the key performance parameters and the design principle are provided.For a practical mechanics system,the designed angular acceleration observer exhibits the excellent dynamical performance under the nonlinear disturbance.