A Guide to Design Disturbance Observer

TL;DR

This paper analytically derives the bandwidth constraints of disturbance observers, clarifies their robustness limits, and proposes new design methods to improve robustness and performance in control systems.

Contribution

It provides the first analytical formulation of DOB bandwidth constraints using Bode and Poisson formulas and introduces new design methods for robust DOB-based control.

Findings

Bandwidth of DOB has upper and lower bounds for robustness.

Higher-order DOB can improve performance but may reduce robustness.

Proposed methods achieve good robustness and predefined performance.

Abstract

The goal of this paper is to clarify the robustness and performance constraints in the design of control systems based on disturbance observer (DOB). Although the bandwidth constraints of a DOB have long been very well-known by experiences and observations, they have not been formulated and clearly reported yet. In this regard, the Bode and Poisson integral formulas are utilized in the robustness analysis so that the bandwidth constraints of a DOB are derived analytically. In this paper, it is shown that the bandwidth of a DOB has upper and lower bounds to obtain good robustness if the plant has non-minimum phase zero(s) and pole(s), respectively. Besides that the performance of a system can be improved by using a higher-order disturbance observer (HODOB); however, the robustness may deteriorate, and the bandwidth constraints become more severe. New analysis and design methods, which provide good robustness and predefined performance criteria, are proposed for the DOB based robust control systems. The validity of the proposals are verified by simulation results.