Design of Feedforward Input for Output-Settling Control With Dual-Stage Actuators

The settling problem is an output transition problem, i.e., given an initial state x(0), the goal is to bring the output to a desired value y(t
_f
) = y macr and hold it constant after the end of settling, t > t
_f
. This article develops the direct solution to the optimal-output-transition (OOT) problem for settling, and develops a method to use postactuation inputs to optimize the settling cost. The approach is illustrated with simulations on an example dual-stage system model. Simulations are also used to illustrate the reduction in the computational burden for online implementation by using linear combinations of precomputed inputs.