This paper proposed the simulation model of the servo system with three-stage reducer and presented the result of frequency analysis of the servo system considering backlash ratios and motor input voltage. By virtue of this work, we realized that if the motor input voltage of the system was large, the influence of each stage backlash ratio could be minimized or removed. Besides, we also found that if the motor input voltage was small, this created an optimal backlash ratio combination which could maximize the anti-resonance and resonance frequency of the servo system. This paper could be useful for determining each stage backlash ratio in designing a three-stage geared servo system with fast response.

In this study, a super-twisting sliding mode controller with a non-linear disturbance observer for a ball-screw servo system was designed to obtain a precise motion and fast convergent control performance. Unknown dynamics of the servo system were approximated into pre-assumed diagonal constants for rapid controller design in the real industry to avoid expensive and time consuming experimental identification process. Moreover, uncertainties due to nonlinear friction, axis misalignment and dead zone were estimated by a nonlinear disturbance observer, which is combined with the designed super-twisting controller. The designed controller and observer systems were applied to the 2-axis ball screw servo system to verify the efficacy of the proposed control system via simulation and experiment.

This paper investigated the influence of the backlash ratio on frequency response characteristic in servo systems with twostage gear reducer, according to the change of magnitude of motor input voltage. The backlash ratio is defined as the ratio of the first gear stage backlash magnitude in relation to total backlash magnitude. This paper presents that the maximum anti-resonance and resonance frequency of the system can take place at the maximum backlash ratio if the motor input voltage of the system is large. On the other hand, if the motor input voltage is small, the maximum anti-resonance and resonance frequency of the system will occur at an arbitrary backlash ratio. In order to develop the geared servo system with fast response, it is effective to increase the maximum allowable motor input voltage and to reduce the magnitude of backlash on the second gear reduction stage.