Describing function analysis of an anti-backlash controller

We develop an anti-backlash controller for servo applications. This controller uses constant feedforward and feedback gains which can be chosen to set the level of control authority. We demonstrate this controller by means of two standard problems, namely, a pure backlash plant as well as a mechanical oscillator with position input through a deadzone. Using time domain analysis, we show that for both of these plants the compensator gains can be chosen to reduce the effects of backlash. Next, using a describing function analysis for the linearized frequency response, we show that the controller suppresses the effects of the nonlinearity in reducing phase delay and achieving unity gain in the servo response. While the describing function technique is classical, the analysis of the anti-backlash controller is nonstandard.