Page 890 - The Mechatronics Handbook

0066_Frame_C30 Page 1 Thursday, January 10, 2002 4:43 PM

30

Control System Design

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Via H Optimization

30.1 Introduction
30.2 General Control System Design Framework
Central Idea: Design Via Optimization • The
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Signals • General H Optimization Problem • Generalized
Plant • Closed Loop Transfer Function
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Matrices • Overview of H Optimization Problems to Be
Considered
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30.3 H Output Feedback Problem
Hamiltonian Matrices
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30.4 H State Feedback Problem
Generalized Plant Structure for State Feedback • State
Feedback Assumptions
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30.5 H Output Injection Problem
Generalized Plant Structure for Output Injection •
Armando A. Rodriguez Output Injection Assumptions
Arizona State University 30.6 Summary

30.1 Introduction
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This chapter addresses control system design via H (quadratic) optimization. A unifying framework
based on the concept of a generalized plant and weighted optimization permits designers to address state
feedback, state estimation, dynamic output feedback, and more general structures in a similar fashion.
The framework permits one to easily incorporate design parameters and/or weighting functions that may
be used to influence the outcome of the optimization, satisfy desired design specifications, and systematize
the design process. Optimal solutions are obtained via well-known Riccati equations; e.g., Control
Algebraic Riccati Equation (CARE) and Filter Algebraic Riccati Equation (FARE). While dynamic weight-
ing functions increase the dimension of the Riccati equations being solved, solutions are readily obtained
using today’s computer-aided design software (e.g., MATLAB, robust control toolbox, µ-synthesis tool-
box, etc.).
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In short, H optimization generalizes all of the well-known quadratic control and filter design
methodologies:
• Linear Quadratic Regulator (LQR) design methodology [7,11],
• Kalman–Bucy Filter (KBF) design methodology [5,6],
• Linear Quadratic Gaussian (LQG) design methodology [4,10,11].
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H optimization may be used to systematically design constant gain state feedback control laws, state
estimators, dynamic output controllers, and much more.

©2002 CRC Press LLC