Research Papers

Integrated Robust Optimal Design Using Bilinear Matrix Inequality Approach Via Sensitivity Minimization

[+] Author and Article Information
Punit J. Tulpule

Department of Mechanical Engineering,
Iowa State University,
Ames, IA 50011
e-mail: ptulpule@iastate.edu

Atul G. Kelkar

ASME Fellow
Department of Mechanical Engineering,
Iowa State University,
Ames, IA 50011
e-mail: akelkar@iastate.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received March 2, 2013; final manuscript received October 10, 2013; published online February 19, 2014. Assoc. Editor: Fu-Cheng Wang.

J. Dyn. Sys., Meas., Control 136(3), 031012 (Feb 19, 2014) (8 pages) Paper No: DS-13-1092; doi: 10.1115/1.4026132 History: Received March 02, 2013; Revised October 10, 2013

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.

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Bodden, D., and Junkins, J., 1985, “Eigenvalue Optimization Algorithms for Structure/Controller Design Iterations,” J. Guid., Control, Dyn., 8(6), pp. 697–706. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Zeiler, T., and Gilbert, M., 1993, “Integrated Control/Structure Optimization by Multilevel Decomposition,” Struct. Optim., 6(2), pp. 99–107. [CrossRef]
Khot, N., 1995, “Optimum Structural Design and Robust Active Control Using Singular Value Constraints,” Comput. Mech., 16(3), pp. 208–215. [CrossRef]
Tsujioka, K., Kajiwara, I., and Nagamatsu, A., 1996, “Integrated Optimum Design of Structure and H-Control System,” AIAA J., 34(1), pp. 159–165. [CrossRef]
Khot, N., and Öz, H., 1998, “Structural–Control Optimization With H2-and H-Norm Bounds,” Optim. Control Appl. Methods, 18(4), pp. 297–311. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Krishnaswami, P., and Kelkar, A., 2003, “Optimal Design of Controlled Multibody Dynamic Systems for Performance, Robustness, and Tolerancing,” Eng. Comput., 19, pp. 26–34. [CrossRef]
Carrigan, J., Kelkar, A., and Krishnaswami, P., 2005, “Integrated Design and Minimum Sensitivity Design of Controlled Multibody Systems,” ASME Paper No. DETC2005-85429. [CrossRef]
Bode, H., 1952, Network Analysis and Feedback Amplifier Design ( Bell Telephone Laboratories Series, Vol. 8), Van Nostrand-Reinhold, New York.
Horowitz, I., 1963, Synthesis of Feedback Systems, Academic Press, New York.
Tomović, R., 1963, Sensitivity Analysis of Dynamic Systems, McGraw-Hill, New York.
Bradt, A., 1968, “Sensitivity Functions in the Design of Optimal Controllers,” IEEE Trans. Autom. Control, 13(1), pp. 110–111. [CrossRef]
Sobral, M. J., 1968, “Sensitivity in Optimal Control Systems,” Proc. IEEE, 56(10), pp. 1644–1652. [CrossRef]
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. [CrossRef]
Eslami, M., 1994, Theory of Sensitivity in Dynamic Systems: An Introduction, Springer-Verlag, Berlin.
Fleming, P., 1973, Trajectory Sensitivity Reduction in the Optimal Linear Regulator, The Queen's University of Belfast, Belfast, UK.
Fleming, P., and Newmann, M., 1977, “Design Algorithms for a Sensitivity Constrained Suboptimal Regulator,” Int J. Control, 25(6), pp. 965–978. [CrossRef]
Frank, P., 1978, Introduction to System Sensitivity Theory, Academic Press, New York.
Yedavalli, K., and Skelton, R., 1982, “Controller Design for Parameter Sensitivity Reduction in Linear Regulators,” Optim. Control Appl. Methods, 3(3), pp. 221–240. [CrossRef]
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. [CrossRef]
Zames, G., and Francis, B., 1983, “Feedback, Minimax Sensitivity, and Optimal Robustness,” IEEE Trans. Autom. Control, 28(5), pp. 585–601. [CrossRef]
Tulpule, P., and Kelkar, A., 2012, “Robust Optimal Control Design Using Sensitivity Dynamics and Youla Parameterization,” ASME Paper No. DSCC2012-MOVIC2012-8741. [CrossRef]
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.
El Ghaoui, L., and Niculescu, S., 2000, Advances in Linear Matrix Inequality Methods in Control, Vol. 2, Society for Industrial Mathematics, Philadelphia, PA.
Scherer, C., Gahinet, P., and Chilali, M., 1997, “Multiobjective Output-Feedback Control Via LMI Optimization,” IEEE Trans. Autom. Control, 42(7), pp. 896–911. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Goh, K., Safonov, M., and Papavassilopoulos, G., 1995, “Global Optimization for the Biaffine Matrix Inequality Problem,” J. Global Optim., 7(4), pp. 365–380. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
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.
Xie, Y., and Alleyne, A., 2012, “Two Degree of Freedom Controller on Combine Harvester Header Height Control,” ASME Paper No. DSCC2012-MOVIC2012-8576. [CrossRef]
Clairaut, A., 1734, Histoire Acad. R. Sci. Paris, pp. 196–215.


Grahic Jump Location
Fig. 1

Schematic diagram of combine harvester

Grahic Jump Location
Fig. 2

Schematic diagram of combine header. Pin joint location in the body centered coordinate system is the design parameter. Sensitivity is also computed with respect to this parameter.

Grahic Jump Location
Fig. 3

Schematic of dynamics included in the system

Grahic Jump Location
Fig. 4

Comparison between only controller design and integrated controller/structure design. (a) Comparison between performance. (b) Comparison between sensitivities. (c) Comparison between control inputs.




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