Frequency domain adaptive control: Band-wise compensation

The idea of band-wise compensation is extended to the design of parametric model-based controllers. Given an (LTI) unknown plant and a frequency domain specification, one first choses a frequency set where the open-loop compensation is required. Then, for each frequency band, one represents the plant by a lower- (first- or second-) order transfer function, and designs a band-compensator. This procedure allows the reduction of a high-dimensional problem (pole placement, LQG, etc.) to a set of lower-dimensional problems, avoiding the problem of singularity arising in most adaptive control by using the certainty equivalence. A numerical example is included to illustrate this idea.