Controller Improvement via Frequency Response Function Estimates

With knowledge of the internal stability of a closed-loop system with an unknown plant P and a known controller C1, we search for a controller better than the currently stabilizing controller in the sense of a certain performance measure. This searching procedure is formulated in the form of an optimization problem. Nonparametric identification of P or other transfer functions is performed with known error bounds from a limited amount of signal data collected from experiments on the closed-loop system with the currently stabilizing controller excited by designed reference signals and corrupted by disturbances and, then, the optimization problem is built in terms of these estimates. In order to reduce the numerical difficulty of the optimization problem, we employ a controller parameterization and propose an algorithm that may not produce the optimal controller but has fast computation ability. A focus of the study is to understand what can be achieved and under what assumptions for controller redesign using such limited identified system data.