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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(tf) = y macr and hold it constant after the end of settling, t > tf. 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.
Date of Publication: Dec. 2007