A comparison of fixed point designs and time-varying observers for scheduling repetitive controllers

This paper presents two distinct methods of designing scheduled repetitive controllers for the case where the frequency of the disturbance is slowly varying and when it is rapidly varying. In both cases the plant is subjected to random and periodic disturbances. The first method uses set points to design a family of controllers and then interpolates between them online. The conditions for designing sub-optimal gains are given. The second method utilizes results from time-varying Riccati equations to design a time-varying observer. It is shown via simulation that the time-varying Riccati method is superior but at a greater computational cost.