Discrete-Time Analysis and Synthesis of Disturbance Observer-Based Robust Force Control Systems

This paper analyses Disturbance Observer- (DOb-) based robust force control systems in the discrete-time domain. The robust force controller is implemented using velocity and acceleration measurements. A DOb is employed in an inner-loop to achieve robustness, and another DOb, viz. Reaction Force Observer (RFOb), is employed in an outer-loop to estimate interaction forces and improve the performance of force control. First, the inner-loop is analysed. It is shown that the DOb works as a phase-lead/lag compensator tuned by the nominal design parameters in the inner-loop. The phase margin of the inner-loop controller and the bandwidth of the velocity-based (i.e., conventional) DOb are constrained not only by noise-sensitivity but also by the waterbed effect. This explains why we observe unstable responses as the bandwidth of the conventional DOb increases in practice. To eliminate the design constraint due to the waterbed effect, this paper proposes an acceleration-based DOb. Then, the robust force controller is analysed. It is shown that the design parameters of the RFOb have a notable effect on the stability of the robust force control system. For example, the robust force controller has a non-minimum phase zero (zeros) when the RFOb is not properly tuned. This may cause severe stability and performance problems when conducting force control applications. By using the stability and robustness analyses, this paper proposes new design tools which enable one to synthesize a high-performance robust force control system. Simulations and experiments are presented to validate the proposed analysis and synthesis methods.