Analysis of disturbance observer-based control systems via spherical polynomials

Robustness analysis of disturbance observer (DOB)-based control systems under parametric uncertainty is addressed in this study. A spherical polynomial family-based approach is adopted to analyse how much uncertainty can be tolerated, and to capture a unified framework for different cases including non-minimum phase plant and different nominal and perturbed plant structures. Results are validated using the value set concept for spherical polynomial families. The study has shown that if the relative degrees of the perturbed plant and the nominal plant are equal, then robustness is achievable even if the plant model is low order. Although non-minimum phase zeros limit the selection of DOB bandwidth, the robustness margin can be exactly determined for a given DOB bandwidth. Furthermore, it is shown that when the plant numerator and denominator have uncertain parameters, the robustness margin is not increased as with the DOB filter bandwidth in general.