Design Constraints of Disturbance Observer-based Motion Control Systems are Stricter in the Discrete-Time Domain

This paper shows that the design constraints of the Disturbance Observer (DOb) based robust motion control systems become stricter when they are implemented using computers or microcontrollers. The stricter design constraints put new upper bounds on the plant-model mismatch and the bandwidth of the DOb, thus limiting the achievable robustness against disturbances and the phase-lead effect in the inner-loop. Violating the design constraints may yield severe stability and performance issues in practice; therefore, they should be considered in tuning the control parameters of the robust motion controller. This paper also shows that continuous-time analysis methods fall-short in deriving the fundamental design constraints on the nominal plant model and the bandwidth of the digital DOb. Therefore, we may observe unexpected stability and performance issues when tuning the control parameters of the digital robust motion controllers in the continuous-time domain. To improve the robust stability and performance of the motion controllers, this paper explains the fundamental design constraints of the DOb by employing the generalised continuous and discrete Bode Integral Theorems in a unified framework. Simulation and experimental results are given to verify the proposed analysis method.