The paper analyzes how the frequency bandwidth of a servo system is affected by the input voltage of its motor and the magnitude of the total backlash. The bandwidth of the system is defined as the set of antiresonance frequencies, which appears in the frequency-response characteristic. The change in the frequency-response characteristics is investigated depending on motor input voltage and the magnitude of the total backlash. It is shown that at infinite motor input voltage, the servo system has a bandwidth equivalent to that of a backlash-free system. The amount of the system's bandwidth reduction due to the backlash changes greatly with the motor input voltage. It becomes possible then to determine the necessary maximum input voltage of the motor and the admissible magnitude of the total backlash to satisfy the desired bandwidth for a servo system with a gear reducer.
IntroductionIntelligent systems such as autonomous vehicles, unmanned airplanes and guided missiles require rapid responsiveness and outstanding adaptability to environments. Such requirements call for automatic servo devices with fast response. Therefore, servo systems with servomotors have been used extensively in many fields.In the case of servomotors, various direct drive motors that do not need gear reducers have been developed with the recent advances of motor technology. However, direct drive-type motors are larger in volume and weight compared to servo systems with gear reducers and have relatively low output torque. Consequently, servo systems with gear reducers have been widely used in fields where there are limitations on space and weight. The size and weight of servo systems installed on flying objects such as guided missiles are very important as their increase shortens the range of the object at given amount of fuel.The velocity control bandwidth and responsiveness of servo systems are greatly limited by the anti-resonance and resonance frequencies appearing in the motor angular velocity output to the motor torque input, [1,2]. The anti-resonance frequency is defined as the servo system's velocity control bandwidth. It is necessary to increase the system's anti-resonance frequency to achieve faster tracking and higher responsiveness, [1]. To this end, it is necessary to expand the bandwidth without increasing the weight of the system at the design revision stage.In related research, it was reported that the stiffness of driving linkages such as shafts greatly affects the bandwidth of a system, [3]. It was determined that the backlash affected the antiresonance and resonance frequencies of a system, [4]. Experimental verification showed that an increase of the backlash magnitude reduced the bandwidth, [5]. These studies showed also that the bandwidth reduction of the system due to backlash is small.