Robust stability analysis of the system with disturbance observer: The real parametric uncertainty approach II

Several studies have been performed on the robustness of the systems with the disturbance observer (DOB). These studies are generally based on the frequency domain analysis which uses unstructured uncertainty and the Small Gain theorem. However, the frequency domain analysis can be easily implemented any kind of systems and it can properly define any kind of uncertainties of the system; it suffers by the conservatism due to the nature of the Small Gain theorem. The main drawback of the conservatism on the DOB based control system is that the bandwidth of the low pass filter (LPF) of DOB is unnecessarily limited by the conservatism. It was shown that the conservatism can be decreased by using the Structured Singular Values (SSV) method. However, this analysis is not suitable to define the constraints on the LPF of DOB in properly. The real parametric uncertainty based analysis shows us that if the bandwidth of the LPF of DOB is higher than its lower bound then the system with DOB becomes stable. The real parametric uncertainty based analysis does not suffer from conservatism however it can only consider the parametric uncertainties and the computational efficiency of this method highly depends on the system structure. These results were proved in the first paper of this research. In this paper, the stability margin of the system with DOB is analyzed and it is shown that as the bandwidth of the LPF of DOB increases the stability margin of the system also increases in the presence of the real parametric uncertainties. To show the validity of the proposed method, a general second order system with the real parametric uncertainties is analyzed and the simulation results are given.