Robust Stability and Performance Analysis of the Control Systems with Higher Order Disturbance Observer: Frequency Approach

The Disturbance Observer (DOB) is widely used in many robust control applications such as robotics and industrial automation due to its simplicity and efficiency. The DOB estimates and compensates the system disturbances by using an inner-feedback loop in the range of its bandwidth. It includes the inverse of the nominal system model and a low pass filter (LPF) which determines the bandwidth of the DOB. The dynamic characteristic and bandwidth of the LPF directly affect the robust stability and performance of the system. The dynamic characteristic of the LPF can be adjusted by using Higher Order Disturbance Observers (HODOB). The bandwidth of the DOB is demanded to be as high as possible to suppress the system disturbances in a wide frequency range. However, it is bounded by the noise and robustness of the system. The conventional robustness analysis method which is based on the Small Gain theorem and unstructured uncertainties, unnecessarily limits the bandwidth of the DOB due to conservatism. The conservatism can be decreased by using the structured uncertainty based robustness analysis methods. In this paper, the robust stability and performance of the system with DOB/HODOB is analyzed by using the conventional analysis method and Singular Structured Values (SSV) that is based on the structured uncertainties. The pros and cons of these methods are shown. A general second order system model is analyzed and simulation results are given to show the validity of the proposed methods.