We present a design approach for robust controller synthesis using a -synthesis procedure, which returns a controller in an observor/state-feedback form with physically meaningful states. We are also able to (approximately) retain this physical meaning when using balanced truncation to (significantly) reduce the controller order, as is often necessary in practice. The advantages of this physics-based approach are illustrated by a detailed outline of the controller design for Woodward Governor’s GS16 Turbine Gas Metering Valve.
Issue Section:
Research Papers
1.
Costello
, D. J.
, and Gawthrop
, P. J.
, 1997, “Physical-Model Based Control: Experiments With a Stirred-Tank Heater
,” Chem. Eng. Res. Des.
0263-8762, 75
(3
), pp. 361
–370
.2.
Doyle
, J.
, Glover
, K.
, Khargonekar
, P.
, and Francis
, B.
, 1989, “State Space Solutions to H2 and H∞ Control Problems
,” IEEE Trans. Autom. Control
0018-9286, 34
(8
), pp. 831
–847
.3.
Zhou
, K.
, Doyle
, J.
, and Glover
, K.
, 1996, Robust and Optimal Control
, Prentice-Hall
, Englewood Cliffs, NJ
.4.
Balas
, G.
, Doyle
, J.
, Glover
, K.
, Packard
, A.
, and Smith
, R.
, 1991, “The μ Analysis and Synthesis Toolbox
,” MathWorks and MUSYN.5.
Xu
, L.
, and Yao
, B.
, 2001, “Output Feedback Adaptive Robust Precision Motion Control of Linear Motors
,” Automatica
0005-1098, 37
, pp. 1029
–1039
.6.
Wu
, Y. K.
, Hartman
, S.
, and Mikhailov
, S. F.
, 2003, “A Physics Based Control System for the Duke Storage Ring
,” Proceedings of the Particle Accelerator Conference
, pp. 2482
–2484
.7.
An
, C. H.
, Atkeson
, C. G.
, and Hollerbac
, J. M.
, 1988, “Model-Based Control of a Direct Drive Arm. II. Control
,” Proceedings of the 1988 IEEE International Conference on Robotics and Automation
, pp. 1386
–1391
.8.
Hashimoto
, K.
, Kimoto
, T.
, Kawabata
, M.
, and Kimura
, H.
, 1991, “H∞ Model-Based Robust Control of a Manipulator
,” Proceedings of Intelligent Robots and Systems
, Vol. 3
, pp. 1597
–1602
.9.
Haylock
, J. A.
, Mecrow
, B. C.
, Jack
, A. G.
, and Atkinson
, D. J.
, 1999, “Enhanced Current Control of High Speed PM Machine Drives Through the Use of Flux Controllers
,” IEEE Trans. Ind. Appl.
0093-9994, 35
, pp. 1030
–1038
.10.
Skogestad
, S.
and Postlethwaite
, I.
, 1996, Multivariable Feedback Control
, Wiley
, New York
.11.
Young
, P. M.
, 1996, “Controller Design With Real Parametric Uncertainty
,” Int. J. Control
0020-7179, 65
, pp. 469
–509
.12.
Redheffer
, R.
, 1959, “Inequalities for a Matrix Riccati Equation
,” J. Math. Mech.
0095-9057, 8
(3
), pp. 349
–367
.13.
Doyle
, J.
, 1982, “Analysis of Feedback Systems With Structured Uncertainty
,” IEE Proc.-D: Control Theory Appl.
0143-7054, 129
(6
), pp. 242
–250
.14.
Safonov
, M.
, 1982, “Stability Margins for Diagonally Perturbed Multivariable Feedback Systems
,” IEE Proc.-D: Control Theory Appl.
0143-7054, 129
, pp. 251
–256
.15.
Young
, P. M.
, Newlin
, M. P.
, and Doyle
, J. C.
, 1995, “Computing Bounds for the Mixed μ Problem
,” Int. J. Robust Nonlinear Control
1049-8923, 5
, pp. 573
–590
.16.
Glover
, K.
, and Doyle
, J.
, 1988, “State Space Formulae for All Stabilizing Controllers That Satisfy an H∞ Norm Bound and Relations to Risk Sensitivity
,” Syst. Control Lett.
0167-6911, 11
, pp. 167
–172
.17.
Safonov
, M. G.
, Limebeer
, D. J. N.
, and Chiang
, R. Y.
, 1990, “Simplifying the H∞ Theory Via Loop Shifting, Matrix Pencil and Descriptor Concepts
,” Int. J. Control
0020-7179, 50
, pp. 2467
–2488
.Copyright © 2008
by American Society of Mechanical Engineers
You do not currently have access to this content.
