Prototype Angle Domain Repetitive Control: Design and Robustness

Angle-domain repetitive disturbances refer to disturbances that are periodic in a generic angle variable which is monotonically increasing with time but not uniformly. This paper extends the classical prototype repetitive control methodology for time periodic disturbances to this situation. Instead of using an internal model approach to derive the control, an affine parameterization approach is adopted which reduces the control design methodology to one of estimating and canceling the disturbance. While the resulting control architectures are similar to the classical time-domain periodic case, the stability conditions are different and depend on the choice of signal norms. Compensator design for non-minimum phase plants also need to be modified. Robustness is also considered in the L₂ setting and an affine Q-filter concept is introduced to achieve robust stability.