A Practical Solution to the Deterministic Nonhomogeneous LQR Problem

[+] Author and Article Information
R. D. Hampton

Department of Engineering (Mechanical), McNeese State University, Lake Charles, LA 70609

C. R. Knospe, M. A. Townsend

Department of Mechanical, Aerospace, and Nuclear Engineering, University of Virginia, Charlottesville, VA 22903

J. Dyn. Sys., Meas., Control 118(2), 354-359 (Jun 01, 1996) (6 pages) doi:10.1115/1.2802329 History: Received July 15, 1993; Online December 03, 2007


A linear-quadratic-regulator-based (LQR) controller originates from a homogeneous set of state-space equations, and consists of a matrix of constant feedback gains. If the state equations are made nonhomogeneous by adding a vector of deterministic forcing terms, the standard LQR solution is no longer optimal. The present paper develops a matrix solution to this augmented (nonhomogeneous) LQR problem. The solution form consists of constant-gain feedback of the full-state vector, summed with a matrix preview (Duhamel integral) term. A practical and usable approximation is presented for the optimal preview term, having the form of a constant preview gain matrix. An example shows the improvement obtainable in controller performance with the use of this preview gain matrix, for exponentially decaying disturbances with a range of time constants.

Copyright © 1996 by The American Society of Mechanical Engineers
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