Stability and Robustness of the Disturbance Observer-based Motion Control Systems in Discrete-Time Domain

This paper analyses the robust stability and performance of the Disturbance Observer- (DOb-) based digital motion control systems in discrete-time domain. It is shown that the phase margin and the robustness of the digital motion controller can be directly adjusted by tuning the nominal plant model and the bandwidth of the observer. However, they have upper and lower bounds due to robust stability and performance constraints as well as noise-sensitivity. The constraints on the design parameters of the DOb change when the digital motion controller is synthesised by measuring different states of a servo system. For example, the bandwidth of the DOb is limited by noise-sensitivity and waterbed effect when velocity and position measurements are employed in the digital robust motion controller synthesis. The robustness constraint due to the waterbed effect is removed when the DOb is implemented by acceleration measurement. The design constraints on the nominal plant model and the bandwidth of the observer are analytically derived by employing the generalised Bode Integral Theorem in discrete-time. The proposed design constraints allow one to systematically synthesise a high-performance DOb-based digital robust motion controller. Experimental results are given to verify the proposed analysis and synthesis methods.