Design guidelines for disturbance observer's filter in discrete time

Control by using disturbance observer is one of the widely recognized servomotor robust control techniques. It is generally known that higher robustness is achieved by higher bandwidth of the low-pass filter, which is used in the disturbance observer. However, the control engineers in practice face problems with realization of the high bandwidth filter. It was considered that the high frequency noise, which is amplified by the time derivative in the observer, causes instability. However, in our paper we show that the vibration and instability of the control system are rather caused by inappropriate sampling time than by the generated noise. We study both, the low pass filter and the disturbance observer in discrete time, and give the guidelines to set the filter's cut-off frequency, nominal parameters of the observer, and gain of the speed loop controller, all in relation to the sampling time, to achieve stable and non-vibrational response. Results are verified by simulation and experiments.