On control of flexible structures

A new method of noncollocated controller design for flexible structures, governed by the wave equation, is proposed. First a transfer function, relating arbitrary actuation and measurement points, with general boundary conditions, is derived and its properties are investigated. A key element in that part is the existence of time delays due to the wave motion. Those delays play a major role in the controller design, which consists of two stages. In the first one, an inner collocated rate loop is closed in order to improve the system dynamic behavior. It is shown that there exists a controller that leads to a finite dimensional plus delay inner closed loop, which is the equivalent plant for the outer loop. In the second stage an outer noncollocated loop, with an observer-predictor structure, is closed. The resulting overall transfer function is second order, with arbitrarily assigned dynamics, plus delay.