Abstract
An integrated approach to the design of a minimum weight structure with optimum robust control is presented. The two control design approaches used for illustration are based on the LQR and the H 2 – H ∞ theory for multi-input multi-output systems. The problem is formulated as a nonlinear optimization problem with structural design and control design variables being treated as independent design quantities. In the LQR control design approach, a constraint is imposed on the spectral radius of the closed loop transfer matrix. In the H 2 – H ∞ control design approach, constraints are imposed on the singular values of the transfer function. For both control design approaches, constraints are also imposed on the structural frequency distribution. The application of the integrated approach is illustrated by designing two idealized structures. The actuators and sensors are assumed to be collocated and embedded in structural elements. The structural design variables are the cross-sectional areas of bar elements and the thicknesses of membrane elements. The control design variables are the elements of the weighting matrix of the controller and the matrices used in the parameterization of uncertainties.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
A. L. Hale, “Integrated Structural/Control Synthesis Via Set - Theoretic Methods,” AIAA./ASME/ASCE/AHS 26th SDM Conference, Orlando FL, 85-0806-CP, April, 1985.
M. Salama, J. Garba, and L. Demesetz, “Simultaneous Optimization of Controlled Structures,” Computational Mechanics, Vol. 3, pp. 275–282, 1988.
R. T. Haftka, A. Martinovic and W. L. Hallauer, Jr., “Enhanced Vibration Controllability by Minor Structural Modifications,” AIAA Journal, Vol. 23, No. 8, August 1985, pp. 1260–1266.
N. S. Khot, “Structures/Control Optimization to Improve the Dynamic Response of Space Structures,” Computational Mechanics, Vol. 3, 1988, pp. 179–186.
H. Oz and N. S. Khot, “Optimization for Efficient Structure-Control Systems,” Proc. of the 5th NASA-DOD Conference on Control-Structure Interactions, Lake Taho NV, March 1992.
S. S. Rao, “Combined Structural and Control Optimization of Flexible Structures,” Engineering Optimization, Vol. 13, 1988, pp. 1–16.
R. V. Lust and L. A. Schmit, “Control Augmented Structural Synthesis,” AIAA Journal Vol. 26, No. 1, 1988, pp. 86–95.
W. K. Belvin and K. C. Park, “Computer Implementation of Analysis and Optimization Procedures for Control-Structure Interaction Problems,” AIAA Dynamics Specialist Conference, Long Beach CA, April 2-4, 1990, pp. 32–41.
S. E. Woodward, S. L. Padula, P. C. Graves, and B. B. James, “An Optimization Method for Controlled Space Structures with Variable Actuator Mass,” Proceedings of the Fourth NASA/DOD Controls/Structures Interaction Technology Conference, WL- TR-91-3013, U.S. air Force, January 1991, pp. 411–428.
P. G. Maghami, S. M. Joshi and E. S. Armstrong, “An Optimization-Based Integrated Controls-Structures Design Methodology for Flexible Space Structures,” NASA Technical Paper 3283, January 1993.
K. B. Lim and J. L. Junkins, “Robust Optimization of Structural and Controller Parameters,” J. Guidance, Vol. 12, January 1989, pp. 89–96.
D. W. Rew, J. L. Junkins, and J. N. Juang, “Robust Eigenstructure Assignment by a Projection Method: Applications Using Multiple Optimization Criteria,” Proceedings of the AAS/AIAA Astrodynamics Conference, Kalispell MT, August 1987.
R. V. Grandhi, I. Haq and N. S. Khot, “Enhanced Robustness in Integrated Structural/Control Systems Design,” AIAA Journal Vol. 29, July 1991, 1168–1173.
N. S. Khot and D. E. Veley, “Robustness Characteristics of Optimum Structural/ Control Design,” Journal of Guidance, Control and Dynamics, Vol. 15, Jan-Feb 1992, pp. 81–87.
N. S. Khot, “Consideration of Robustness in Optimum Structural and Control Design,” Presented at the Fourth AIAAAJSAF/NASA/OAI Symposium on Multidisciplinary Analysis and Optimization, Cleveland OH, Sep 1992.
N. S. Khot and H. Oz, “Structural-Control Optimization with H2 and H∞ Constraints,” Presented at the 34th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, La Jolla CA, April 1993, pp. 1429–1436.
Y. Juang, T. Kuo and C. Hsu, 1987, “New Approach to Time–Domain Analysis for Stability Robustness of Dynamic Systems,” Intl. J. of Systems Science. Vol. 8, No. 7, pp. 1363–1376.
R. K. Yedavalli, S. S. Banda, and D. B. Ridgely, 1985, “Time Domain Stability Robustness Measures for Linear Regulators,” Journal of Guidance, Control and Dynamics, Vol. 8, No. 4, pp. 520–525.
S. S. Banda, H. H. Yeh and S. A. Heise, “A Surrogate system Approach to Robust Control Design,” Proceedings 1989 AIAA Guidance, Navigation and Control Conference, Boston MA, 1989, pp. 576–582.
N. S. Khot and D. E. Veley, “Robustness Characteristics of Optimum Structural/ Control Design,” Proceedings 1990 AIAA Guidance, Navigation and Control Conference, Portland OR, 1990, pp. 394–403.
R. Thareja and R. T. Haftka, “NEWSUMT-A: A Modified Version of NEWSUMT for Inequality and Equality Constraints,” Virginia Polytechnic Institute and State University, Blacksburg, March 1986.
A. D. Belegundu, L. Berke and S. N. Patniak “An Optimization Program Based on Method of Feasible Directions - Theory and User’s Guide,” NASA Report, June 1993.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Khot, N.S., Veley, D.E. (1995). Optimum Structural/Control Design with Robustness Constraints. In: Batra, R.C. (eds) Contemporary Research in Engineering Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80001-6_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-80001-6_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-80003-0
Online ISBN: 978-3-642-80001-6
eBook Packages: Springer Book Archive