Finite dimensional robust repetitive controller for tracking periodic reference input

The presented work demonstrates in steps the way of development and deployment of Finite Dimensional Robust Repetitive Controller (FDRRC) starting from the conventional Repetitive Controller (RC) which is actually an infinite dimensional system. By the virtue of being infinite dimensional RC can track any periodic reference input but many times degrading stability due to the small period mismatch between controller period and actual period of disturbance and also in high frequency applications. To minimize the problem of instability in high frequency, a low pass filter is introduced in the RC loop which in turn limits the infinite dimensional RC in to Finite Dimensional RC (FDRC) and to deal with small period uncertainties, an attempt is taken to explore the design and implementation of multiple loops Robust Repetitive Controller (RRC). Combination of the said strategies results in FDRRC. The new idea of FDRRC is utilized and experienced through the a 1st order system in this paper and every time a comparison is carried out to show the necessity of development in the considered controller models. Finally the paper tries to emphasise over the effectiveness of the FDRRC based on results obtained.