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

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.