Simple and effective optimization based FIR repetitive controller design and conversion to learning control using initial condition updates

In many control applications, the same task is performed repeatedly producing the same error every time. Repetitive control (RC) and iterative learning control (ILC) aim to eliminate such errors. ILC applies when each run starts from the same initial conditions. RC aims for zero tracking error following a periodic command, or with a periodic disturbance. The research reported here develops new optimization based methods that are simple to use, in designing effective RC and ILC designs.; The ideal RC or ILC law would use the system inverse as a compensator to cancel the system dynamics. However, this usually results in instability. First, a time domain method is developed to create a, stable FIR approximation of the system inverse for RC. Then, an improved method is developed using optimization in the frequency domain. This method is shown to be very easy to use and very effective. It produces a simple FIR compensator design that can closely approximate the inverse of the system frequency response using a small number of control gains. The resulting optimized designs are interpreted in terms of the resulting compensator pole and zero locations. The design can use frequency response data and does not need a model.; Lack of robustness to parasitic poles is a difficulty in RC applications. An effective approach to robustification uses a zero-phase filter to make a learning cutoff. Here a parallel design process develops non-causal zero-phase low-pass FIR filters for use in real time RC. The approach allows one to tune the filter for the RC objectives for the specific problem at hand. Then the RC design and the filter are integrated to produce a simple to use and effective robust RC law.; ILC and RC are very similar. The effective results developed here for RC are converted to apply to ILC. A new mathematical structure for ILC is developed, which not only iterates on the command input from repetition to repetition, but also makes iterative updates on the initial conditions used each iteration, in order to produce stability in ILC.