Gain selection method for robustness enhancement in sliding mode control combined with decoupled disturbance compensator with unknown inertia in industrial servo systems

This paper presents a method to enhance robustness in sliding mode control (SMC) combined with decoupled disturbance compensator (DDC). More specifically, a gain selection method for the DDC in industrial servo systems with unknown inertia is developed. The SMC with DDC method is a well-known robust control method which is effective for slowly-varying and bounded disturbances. However, when the gain of the DDC is improperly selected, a large error of the inertia parameter can lead to poor performance such as a large overshoot in the motor position. This paper shows that the disturbance caused by an uncertain inertia can produce a pair of complex conjugate eigenvalues of the error dynamics in the z-domain, which results in the overshoot in both position and velocity. In addition, utilizing this analysis, a gain selection method of DDC is proposed when the ratio of the actual inertia to the nominal inertia is assumed to be bounded. The analytical results are further supported using experiments performed on industrial servo systems with a ball-screw load and a belt load.