A novel integrated robust control synthesis methodology is presented here which combines a traditional sensitivity theory with relatively new advancements in bilinear matrix inequality (BMI) constrained optimization problems. The proposed methodology is demonstrated using a numerical example of integrated control design problem for combine harvester header linkage. The integrated design methodology presented is compared with a traditional sequential design method and the results show that the proposed methodology provides a viable alternative for robust controller synthesis and often times offers even a better performance than competing methods.
Issue Section:
Research Papers
References
1.
Bodden
, D.
, and Junkins
, J.
, 1985
, “Eigenvalue Optimization Algorithms for Structure/Controller Design Iterations
,” J. Guid., Control, Dyn.
, 8
(6), pp. 697
–706
.10.2514/3.200442.
Onoda
, J.
, and Haftka
, R. T.
, 1987
, “An Approach to Structure/Control Simultaneous Optimization for Large Flexible Spacecraft
,” AIAA J.
, 25
(8), pp. 1133
–1138
.10.2514/3.97543.
Padula
, S.
, Sandridge
, C.
, Walsh
, J.
, and Haftka
, R.
, 1992
, “Integrated Controls-Structures Optimization of a Large Space Structure
,” Comput. Struct.
, 42
(5
), pp. 725
–732
.10.1016/0045-7949(92)90184-24.
Zeiler
, T.
, and Gilbert
, M.
, 1993
, “Integrated Control/Structure Optimization by Multilevel Decomposition
,” Struct. Optim.
, 6
(2
), pp. 99
–107
.10.1007/BF017433425.
Khot
, N.
, 1995
, “Optimum Structural Design and Robust Active Control Using Singular Value Constraints
,” Comput. Mech.
, 16
(3
), pp. 208
–215
.10.1007/BF003697826.
Tsujioka
, K.
, Kajiwara
, I.
, and Nagamatsu
, A.
, 1996
, “Integrated Optimum Design of Structure and H-Control System
,” AIAA J.
, 34
(1
), pp. 159
–165
.10.2514/3.130367.
Khot
, N.
, and Öz
, H.
, 1998
, “Structural–Control Optimization With H2-and H-Norm Bounds
,” Optim. Control Appl. Methods
, 18
(4
), pp. 297
–311
.10.1002/(SICI)1099-1514(199707/08)18:4<297::AID-OCA604>3.0.CO;2-A8.
Lu
, J.
, and Skelton
, R.
, 2000
, “Integrating Structure and Control Design to Achieve Mixed H2/H Performance
,” Int. J. Control
, 73
(16
), pp. 1449
–1462
.10.1080/002071700501633239.
Bozca
, M.
, Muğan
, A.
, and Temeltaş
, H.
, 2008
, “Decoupled Approach to Integrated Optimum Design of Structures and Robust Control Systems
,” Struct. Multidiscip. Optim.
, 36
(2
), pp. 169
–191
.10.1007/s00158-007-0208-110.
Fu
, K.
, and Mills
, J.
, 2005
, “A Convex Approach Solving Simultaneous Mechanical Structure and Control System Design Problems With Multiple Closed-Loop Performance Specifications
,” ASME J. Dyn. Syst., Meas., Control
, 127
(1
), pp. 57
–68
.10.1115/1.187649311.
Pil
, A.
, and Asada
, H.
, 1996
, “Integrated Structure/Control Design of Mechatronic Systems Using a Recursive Experimental Optimization Method
,” IEEE/ASME Trans. Mechatronics
, 1
(3
), pp. 191
–203
.10.1109/3516.53704212.
Wu
, F.
, Zhang
, W.
, Li
, Q.
, and Ouyang
, P.
, 2002
, “Integrated Design and PD Control of High-Speed Closed-Loop Mechanisms
,” ASME J. Dyn. Syst., Meas., Control
, 124
(4), pp. 522
–528
.10.1115/1.151317913.
Krishnaswami
, P.
, and Kelkar
, A.
, 2003
, “Optimal Design of Controlled Multibody Dynamic Systems for Performance, Robustness, and Tolerancing
,” Eng. Comput.
, 19
, pp. 26
–34
.10.1007/s00366-002-0246-14.
Carrigan
, J.
, Kelkar
, A.
, and Krishnaswami
, P.
, 2005
, “Integrated Design and Minimum Sensitivity Design of Controlled Multibody Systems
,” ASME
Paper No. DETC2005-85429. 10.1115/DETC2005-8542915.
Bode
, H.
, 1952
, Network Analysis and Feedback Amplifier Design
(Bell Telephone Laboratories Series
, Vol. 8), Van Nostrand-Reinhold, New York
.16.
Horowitz
, I.
, 1963
, Synthesis of Feedback Systems
, Academic Press
, New York.17.
Tomović
, R.
, 1963
, Sensitivity Analysis of Dynamic Systems
, McGraw-Hill
, New York.18.
Bradt
, A.
, 1968
, “Sensitivity Functions in the Design of Optimal Controllers
,” IEEE Trans. Autom. Control
, 13
(1
), pp. 110
–111
.10.1109/TAC.1968.109882619.
Sobral
, M. J.
, 1968
, “Sensitivity in Optimal Control Systems
,” Proc. IEEE
, 56
(10
), pp. 1644
–1652
.10.1109/PROC.1968.670020.
Sannuti
, P.
, Cruz
, J.
, Lee
, I.
, and Bradt
, A.
, 1968
, “A Note on Trajectory Sensitivity of Optimal Control Systems
,” IEEE Trans. Autom. Control
, 13
(1
), pp. 111
–113
.10.1109/TAC.1968.109878221.
Eslami
, M.
, 1994
, Theory of Sensitivity in Dynamic Systems: An Introduction
, Springer-Verlag
, Berlin.22.
Fleming
, P.
, 1973
, Trajectory Sensitivity Reduction in the Optimal Linear Regulator
, The Queen's University of Belfast
, Belfast, UK.23.
Fleming
, P.
, and Newmann
, M.
, 1977
, “Design Algorithms for a Sensitivity Constrained Suboptimal Regulator
,” Int J. Control
, 25
(6
), pp. 965
–978
.10.1080/0020717770892228224.
Frank
, P.
, 1978
, Introduction to System Sensitivity Theory
, Academic Press
, New York.25.
Yedavalli
, K.
, and Skelton
, R.
, 1982
, “Controller Design for Parameter Sensitivity Reduction in Linear Regulators
,” Optim. Control Appl. Methods
, 3
(3
), pp. 221
–240
.10.1002/oca.466003030226.
Youla
, D.
, Jabr
, H.
, and Bongiorno
, J. J.
, 1976
, “Modern Wiener-HOPF Design of Optimal Controllers—Part II: The Multivariable Case
,” IEEE Trans. Autom. Control
, 21
(3
), pp. 319
–338
.10.1109/TAC.1976.110122327.
Zames
, G.
, and Francis
, B.
, 1983
, “Feedback, Minimax Sensitivity, and Optimal Robustness
,” IEEE Trans. Autom. Control
, 28
(5
), pp. 585
–601
.10.1109/TAC.1983.110327528.
Tulpule
, P.
, and Kelkar
, A.
, 2012
, “Robust Optimal Control Design Using Sensitivity Dynamics and Youla Parameterization
,” ASME
Paper No. DSCC2012-MOVIC2012-8741. 10.1115/DSCC2012-MOVIC2012-874129.
Boyd
, S.
, El Ghaoui
, L.
, Feron
, E.
, and Balakrishnan
, V.
, 1994
, Linear Matrix Inequalities in System and Control Theory
, Vol. 15
, Society for Industrial Mathematics
, Philadelphia, PA.30.
El Ghaoui
, L.
, and Niculescu
, S.
, 2000
, Advances in Linear Matrix Inequality Methods in Control
, Vol. 2
, Society for Industrial Mathematics
, Philadelphia, PA.31.
Scherer
, C.
, Gahinet
, P.
, and Chilali
, M.
, 1997
, “Multiobjective Output-Feedback Control Via LMI Optimization
,” IEEE Trans. Autom. Control
, 42
(7
), pp. 896
–911
.10.1109/9.59996932.
Iwasaki
, T.
, and Skelton
, R.
, 1994
, “All Controllers for the General [H]∞ Control Problem: LMI Existence Conditions and State Space Formulas
,” Automatica
, 30
(8
), pp. 1307
–1317
.10.1016/0005-1098(94)90110-433.
Pipeleers
, G.
, Demeulenaere
, B.
, Swevers
, J.
, and Vandenberghe
, L.
, 2009
, “Extended LMI Characterizations for Stability and Performance of Linear Systems
,” Syst. Control Lett.
, 58
(7
), pp. 510
–518
.10.1016/j.sysconle.2009.03.00134.
Tuan
, H.
, and Apkarian
, P.
, 2000
, “Low Nonconvexity-Rank Bilinear Matrix Inequalities: Algorithms and Applications in Robust Controller and Structure Designs
,” IEEE Trans. Autom. Control
, 45
(11
), pp. 2111
–2117
.10.1109/9.88763635.
Goh
, K.
, Safonov
, M.
, and Papavassilopoulos
, G.
, 1995
, “Global Optimization for the Biaffine Matrix Inequality Problem
,” J. Global Optim.
, 7
(4
), pp. 365
–380
.10.1007/BF0109964836.
VanAntwerp
, J. G.
, Braatz
, R. D.
, and Sahinidis
, N. V.
, 1997
, “Globally Optimal Robust Control for Systems With Time-Varying Nonlinear Perturbations
,” Comput. Chem. Eng.
, 21
, pp. S125
–S130
.10.1016/S0098-1354(97)87490-X37.
El Ghaoui
, L.
, Oustry
, F.
, and AitRami
, M.
, 1997
, “A Cone Complementarity Linearization Algorithm for Static Output-Feedback and Related Problems
,” IEEE Trans. Autom. Control
, 42
(8
), pp. 1171
–1176
.10.1109/9.61825038.
Kanev
, S.
, Scherer
, C.
, Verhaegen
, M.
, and De Schutter
, B.
, 2004
, “Robust Output-Feedback Controller Design Via Local BMI Optimization
,” Automatica
, 40
(7
), pp. 1115
–1127
.10.1016/j.automatica.2004.01.02839.
Yim
, S.
, and Park
, Y.
, 2011
, “Design of Rollover Prevention Controller With Linear Matrix Inequality-Based Trajectory Sensitivity Minimisation
,” Veh. Syst. Dyn.
, 49
(8
), pp. 1225
–1244
.10.1080/00423114.2010.50727540.
Tulpule
, P.
, and Kelkar
, A.
, 2013
, “BMI Based Robust Optimal Control Synthesis Via Sensitivity Minimization
,” 6th Annual Dynamic Systems and Control Conference, Palo Alto, CA, October 21–23.41.
Xie
, Y.
, Alleyne
, A.
, Greer
, A.
, and Deneault
, D.
, 2011
, “Fundamental Limits in Combine Harvester Header Height Control
,” American Control Conference (ACC)
, San Francisco, CA, June 29–July 1, pp. 5279
–5285
.42.
Xie
, Y.
, and Alleyne
, A.
, 2012
, “Two Degree of Freedom Controller on Combine Harvester Header Height Control
,” ASME
Paper No. DSCC2012-MOVIC2012-8576. 10.1115/DSCC2012-MOVIC2012-857643.
Clairaut
, A.
, 1734
, Histoire Acad. R. Sci. Paris
, pp. 196
–215
.Copyright © 2014 by ASME
You do not currently have access to this content.
