OPTIMAL CONTROLLER FOR DITHERED SYSTEMS WITH BACKLASH OR HYSTERESIS

Dither is a high-frequency signal introduced into a nonlinear system t o improve the system performance. A nonlinearity with memory (backlash , hysteresis) is considered in this paper; a dither of a given amplitu de is being injected at the input of the nonlinearity. The dither can effectively eliminate memory of the nonlinearity. The significance of the dither frequency lies in its effect on the deviation of the dither ed system from its corresponding model, the smoothed system, in which the nonlinearity is a smooth function. The deviation amount can be imp roved as the dither frequency increases. If the dither has a sufficien tly high frequency, the outputs of the smoothed system and the dithere d system can be made as close as desired. This enables us to predict t he stability of the dithered system by establishing the stability of t he smoothed system.