Stability of Digital Robust Motion Control Systems with Disturbance Observer

In this paper, new stability analysis methods are proposed for digital robust motion control systems implemented using a Disturbance Observer (DOb). The proposed methods utilise time domain and traditional frequency domain analysis techniques, and the same stability constraints on the free control parameters of the digital DOb are established through analysis. This paper demonstrates that the observer gain of the digital DOb (aka digital DOb's bandwidth) is constrained by the stability of the observer, in addition to its limitation by noise sensitivity. As the gain of the digital observer is increased, the disturbance estimation accuracy can be enhanced for a limited bandwidth range, and the DOb becomes unstable when the observer gain exceeds the stability constraint derived in the paper. It is also shown that the observer gain's stability constraint changes when disturbances are cancelled through the use of estimated disturbances in an inner-loop. The nominal plant model of the servo system, along with the gain of the digital DOb, must be carefully tuned to ensure good performance and robust stability. The stability constraints identified in this paper can be utilised to effectively adjust the observer gain and nominal plant model of a servo system in DOb-based digital robust motion control, facilitating good performance in practical engineering applications. Results from simulations are presented to verify the novel stability analysis methods.