A Guide to Design Disturbance Observer-based Motion Control Systems in Discrete-time Domain

TL;DR

This paper provides a comprehensive analysis and synthesis framework for disturbance observer-based motion control systems in discrete-time, highlighting the limitations of continuous-time methods and offering new design constraints for digital controllers.

Contribution

It introduces discrete-time analysis methods for DOb-based controllers, deriving stability and performance constraints specific to digital implementations.

Findings

Discrete-time analysis explains digital controller behavior better than continuous-time methods.

Proposed design constraints enable systematic synthesis of high-performance digital controllers.

Simulations verify the effectiveness of the proposed analysis and synthesis approach.

Abstract

This paper analyses and synthesises the Disturbance Observer (DOb) based motion control systems in the discrete-time domain. By employing Bode Integral Theorem, it is shown that continuous-time analysis methods fall-short in explaining the dynamic behaviours of the DOb-based robust motion controllers implemented by computers and microcontrollers. For example, continuous-time analysis methods cannot explain why the robust stability and performance of the digital motion controller deteriorate as the bandwidth of the DOb increases. Therefore, unexpected dynamic responses (e.g., poor stability and performance, and high-sensitivity to disturbances and noise) may be observed when the parameters of the digital robust motion controller are tuned by using continuous-time synthesis methods in practice. This paper also analytically derives the robust stability and performance constraints of the DOb-based motion controllers in the discrete-time domain. The proposed design constraints allow one to systematically synthesise a high-performance digital robust motion controller. The validity of the proposed analysis and synthesis methods are verified by simulations.