A distributed delay based controller for simultaneous periodic disturbance rejection and input-delay compensation

The paper presents a controller design for systems suffering from multi-harmonic periodic disturbance and substantial input time-delay. It forms an alternative approach to Repetitive Control where the goal is to stabilize a close-loop that encapsulates an explicit time-delay model of the periodic signal. The proposed controller design is based on the Internal Model Control (IMC) framework, and it consists of the inverse system model and a tuneable distributed delay with an overall length related to the period of the disturbance. The properness of the controller can be ensured by utilizing a low-pass filter, however, such a component is shown to be unnecessary when the relative order of the system model is one. This fact makes the alternative approach especially suitable for systems approximated by a first-order model with input time-delay, leading to a straightforward controller design thanks to its simple structure and attainable conditions. Stability of the configuration is guaranteed by an ideal IMC framework. For further performance and robustness requirements for the non-ideal case the tuning of the controller is posed as a weighted-7-infinity optimization problem where frequency-, spectral-and time-domain requirements are formulated as constraints. The overall control design is experimentally verified on a laboratory setup that has high-order dynamics approximated by a first-order model with input delay.