THESIS
2009
xii, 124 p. : ill. ; 30 cm
Abstract
Despite much progress in the robust control area, the robust performance problem in the face of plant uncertainty is still awaiting for a complete analytical solution. Consequently, some simpler related problem which may yield insights into solving the problem are considered. This thesis is mainly concerned with a special optimal H
2 control problem under robust stability and controller degree constraint. Given an n-th order proper plant P(s), we would like to find a controller with degree no larger than n, which satisfies the robust stability constraint and gives the best transient performance....[
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Despite much progress in the robust control area, the robust performance problem in the face of plant uncertainty is still awaiting for a complete analytical solution. Consequently, some simpler related problem which may yield insights into solving the problem are considered. This thesis is mainly concerned with a special optimal H
2 control problem under robust stability and controller degree constraint. Given an n-th order proper plant P(s), we would like to find a controller with degree no larger than n, which satisfies the robust stability constraint and gives the best transient performance.
Firstly, the very useful Youla parametrization is used to reduce the original problem to a suboptimal Nehari problem so that we could characterize all the stabilizing suboptimal controllers in a set C
β by solving the Nehari problem. Then we will give the set of all strictly proper suboptimal controller with degree constraint Ĉ
β,n which is a subset of C
β based on results in literature. We also develop a polynomial solution to a nominal performance controller called the central controller, which is proved to be an element of the set Ĉ
β,n during the derivation of this polynomial solution.
Next, we parameterize the controller set Ĉ
β,n for a strictly proper plant over R
2n and do H
2 optimization in this parameter set to find the controller that minimizes ║T
wy║
2. Based on the property of the quadratic map, we choose the central controller to be the initial condition and use Newton's method to solve the nonlinear equations. The optimization strategy is quite standard and is performed using MATLAB and the Control System Toolbox. An unconstraint optimization is utilized to obtain the controller for any given parameter in R
2n. Then we state our algorithm to find the solution to the special mixed H
2/H
∞ control problem, and compare our controllers with those obtained by other approaches.
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