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

This article analyses the robust stability and performance of the disturbance observer (DOb) based digital motion control systems in the 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 the upper and lower bounds due to robust stability and performance constraints as well as the noise sensitivity. The constraints on the design parameters of the DOb change when the digital motion controller is synthesized by measuring different states of a servosystem. For example, the bandwidth of the DOb is limited by the noise sensitivity and waterbed effect when the 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 generalized Bode integral theorem in discrete time. The proposed design constraints allow one to systematically synthesize a high-performance DOb-based digital robust motion controller. The experimental results are given to verify the proposed analysis and synthesis methods.