A discrete-time design and analysis of perturbation observer

In disturbance observers, the design of low pass filter (so-called Q-filter) has been a central issue. However, the effect of the Q-filter on the performance and robust stability has not been clarified yet, specifically in discrete-time domain. In this paper, we investigate this problem considering general order of discrete Q-filter and the inertia perturbation as a structured model uncertainty, through which a practical guideline on the performance and robustness trade-off is suggested. Our results make it transparent how the performance and robustness of the perturbation observer loop are affected according to the variation of Q-filter parameters (filter order and cut-off frequency) and the model parameter (i.e. inertia) perturbation in discrete control systems with changeable sampling frequency. Furthermore, the robust stability condition with respect to the inertia uncertainty extends the results on the time-delayed controllers. Also, the validity of the analysis and the effectiveness of the discrete perturbation observer are shown through comparative experiments.