Feedback control of flexible structures with non-uniform rods

A new method of noncollocated controller design for non-uniform flexible structures, governed by the wave equation, is proposed. First, an exact infinite dimensional transfer function, relating the actuation and measurement points, with general boundary conditions, is derived. A key element in that part is the existence of time delays due to the wave motion. These delays play a major role in the controller design, which consists of two stages. In the first one, an inner rate loop is closed in order to improve the system dynamic behavior. It uses rate feedback from both ends and 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 is closed to obtain feedback from the variable of interest. It has the structure of an observer-predictor control scheme to compensate for the response delay. The resulting overall transfer function is second order, with arbitrarily assigned dynamics, plus delay.