  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.
