The design of low-order controllers using the Frobenius-Hankel norm
Ramaker, Russell Allen
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https://hdl.handle.net/2142/23085
Description
Title
The design of low-order controllers using the Frobenius-Hankel norm
Author(s)
Ramaker, Russell Allen
Issue Date
1990
Doctoral Committee Chair(s)
Perkins, William R.
Department of Study
Electrical Engineering
Discipline
Electrical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Language
eng
Abstract
The problem of determining robust, low order controllers which achieve stability and disturbance attenuation is considered. This is an important problem for the control of very high order structures where a full order controller is inappropriate.
To address this problem, an approach using the Frobenius-Hankel (FH) norm is developed. The FH norm is shown to lead to attractive robustness and performance properties. A parameter optimization method is developed which provides an iterative method for determining the FH optimal parameters of a dynamic system using a gradient approach.
Two distinct controller design methods are presented which make use of the FN optimization procedure. The first approach determines a controller which minimizes the FH norm of the closed loop system. While the solution method is iterative, the procedure proves to be straightforward to apply.
"The second approach uses projective controls as a first step in the design. This allows the designer to take advantage of the attractive features of projective controls. Design parameters in the controllers are then determined by solving the FH optimization problem called the ""auxiliary minimization problem."""
Examples of each approach are given, including a full design problem for the control of a flexible structure using the projective controls approach. The resulting improvement in the disturbance attenuation of the system using only second order controllers points to the effectiveness of this design procedure.
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