Discrete-time disturbance observer design for systems with time delay

In many engineering systems, time delay is present or can be used to approximate phase loss at high frequencies. In such situations, existing disturbance observer design techniques encounter difficulties due to bandwidth limitations or relative degree restrictions on disturbance observer filtering. These problems can be avoided by a straightforward inclusion of time delay in the nominal plant model. As a result, the disturbance observer sensitivity function is degraded, but this is offset by the fact that higher bandwidth low pass filtering can be used. Importantly, input-output characteristics of the disturbance observer loop better approximate the nominal plant model, thus improving noise rejection and simplifying the subsequent design of outer loop compensation and feedforward filtering. The technique is applied one axis of a high speed X-Y table. Simulation and experimental results demonstrate the effectiveness of the technique.