Robust stability anaylsis of the system with disturbance observer: The real parametric uncertainity approach I

The Disturbance Observer (DOB) guarantees the robustness of the system if the disturbances stay within the bandwidth of the DOB. Thus, high bandwidth is demanded to compensate the disturbances in a wide frequency range. The bandwidth of the DOB is limited by the noise and robustness of the system. The noise limitation depends on the measurement plant and sampling rate. The robustness limitation depends on the robustness analysis method. Conventionally, the robustness of the system with DOB is analyzed using the unstructured uncertainty and Small Gain theorem. Due to the nature of the Small Gain theorem, the conventional analysis includes conservatism. The conservatism unnecessarily limits the bandwidth of the DOB to obtain robust stability. However, the bandwidth of the DOB is demanded to be as high as possible to increase the performance of the system. In this paper the robust stability of the system with DOB is analyzed in the presence of the real parametric uncertainties. This analysis is not conservative and it gives a lower bound on the bandwidth of the DOB to obtain robust stability. The lower bound on the bandwidth of the DOB is derived for the interval and affinely linear polynomials and it shows us that the system with DOB is robustly stable if its bandwidth is higher than the lower bound in the presence of the real parametric uncertainties. The proposed method is applied to a general second order system model with the real parametric uncertainties and the simulation results are given to show the validity of the proposed method.