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Technical Brief

Robust Reliability Based Optimal Design of H Control of Parametric Uncertain Systems

[+] Author and Article Information
Shu-Xiang Guo

Professor
Faculty of Mechanics,
College of Science,
Air Force Engineering University,
Xi'an 710051, China
e-mail: guoshuxiang66@163.com

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received April 14, 2013; final manuscript received October 23, 2013; published online December 9, 2013. Assoc. Editor: Fu-Cheng Wang.

J. Dyn. Sys., Meas., Control 136(2), 024504 (Dec 09, 2013) (7 pages) Paper No: DS-13-1159; doi: 10.1115/1.4025862 History: Received April 14, 2013; Revised October 23, 2013

An efficient nonprobabilistic robust reliability method for H robust controller design of parametric uncertain systems is presented by describing the uncertain parameters as interval variables. Design optimization of H robust controller is carried out by solving a robust reliability based optimization problem, by which the disturbance attenuation, control cost, and robust reliability can be taken into account simultaneously. By the method, a robust reliability measure of an uncertain control system satisfying required H robust performance can be obtained, and the robustness bounds of uncertain parameters such that the control cost of the system is guaranteed can be provided. The presented formulations are in the framework of linear matrix inequality and thus can be carried out conveniently. The presented method provides an essential basis for reasonable tradeoff between reliability and control cost in controller design of uncertain systems. Active control design of vehicle suspension is employed for illustrating the effectiveness and feasibility of the presented method.

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References

Boyd, S., Ghaoui, L. E., Feron, E., and Balakrishnan, V., 1994, Linear Matrix Inequalities in System and Control Theory, Vol. 15, SIAM Studies in Applied Mathematics, Philadelphia, PA.
Xie, L., Fu, M., and Souza, C. E., 1992, “H Control and Quadratic Stabilization of Systems With Parameter Uncertainty via Output Feedback,” IEEE Trans. Autom. Control, 37(8), pp. 1253–1256. [CrossRef]
Sun, C.-C., Chung, H.-Y., and Chang, W.-J., 2005, “H2/H Robust Static Output Feedback Control Design via Mixed Genetic Algorithm and Linear Matrix Inequalities,” ASME J. Dyn. Syst. Meas. Control, 127, pp. 715–722. [CrossRef]
Boulet, B., Francis, B. A., Hughes, P. C., and Hong, T., 1997, “Uncertainty Modeling and Experiments in H Control of Large Flexible Space Structures,” IEEE Trans. Control Syst. Technol., 5(5), pp. 504–519. [CrossRef]
Du, H., Lam, J., and Sze, K. Y., 2005, “Design of Non-Fragile H Controller for Active Vehicle Suspensions,” J. Vib. Control, 11, pp. 225–243. [CrossRef]
Chen, H., and Guo, K.-H., 2005, “Constrained Control of Active Suspensions: An LMI Approach,” IEEE Trans. Control Syst. Technol., 13(3), pp. 412–421. [CrossRef]
Calafiore, G. C., and Campi, M. C., 2006, “The Scenario Approach to Robust Control Design,” IEEE Trans. Auto. Control, 51(5), pp. 742–753. [CrossRef]
Guo, S. X., and Zhang, L., 2006, “Robust Reliability-Based Optimal Design of Robust H Controller for Time-Delay Systems With Parametric Uncertainty,” Control Theory Appl., 23(6), pp. 981–985.
Guo, S. X., 2010, “Robust Reliability as a Measure of Stability of Parametric Uncertain Systems,” J. Vib. Control, 16(9), pp. 1351–1368. [CrossRef]
Guo, S. X., 2011, “Stability Analysis and Design of Time-Delay Uncertain Systems Using Robust Reliability Method,” J. Syst. Eng. Elec., 22(3), pp. 493–499.
Taflanidis, A. A., Scruggs, J. T., and Beck, J. L., 2010, “Robust Stochastic Design of Linear Controlled Systems for Performance Optimization,” ASME J. Dyn. Syst. Meas. Control, 132(5), p. 051008. [CrossRef]
Crespo, L. G., and Kenny, S. P., 2005, “Reliability-Based Control Design for Uncertain Systems,” J. Guid. Control Dyn., 28, pp. 649–658. [CrossRef]
Taflanidis, A. A., Scruggs, J. T., and Beck, J. L., 2008, “Reliability-Based Performance Objectives and Probabilistic Robustness in Structural Control Applications,” J. Eng. Mech., 134, p. 291C301. [CrossRef]
Chakraborty, S., and Roy, B. K., 2011, “Reliability Based Optimum Design of Tuned Mass Damper in Seismic Vibration Control of Structures With Bounded Uncertain Parameters,” Probab. Eng. Mech., 26, p. 215C221. [CrossRef]
Li, J., Peng, Y. B., and Chen, J. B., 2011, “Probabilistic Criteria of Structural Stochastic Optimal Controls,” Probab. Eng. Mech., 26, p. 240C253. [CrossRef]
Elishakoff, I., 1995, “Essay on Uncertainties in Elastic and Viscoelastic Structures: From A.M. Freudenthal's Criticisms to Modern Convex Modeling,” Comput. Struct., 56, pp. 871–895. [CrossRef]
Ben-Haim, Y., 1996, Robust Reliability in the Mechanical Sciences, Springer-Verlag, Berlin.

Figures

Grahic Jump Location
Fig. 1

Quarter-car model with active suspension

Grahic Jump Location
Fig. 2

Bump responses and the corresponding input control forces of the uncertain system with uncertain parameters generated randomly

Grahic Jump Location
Fig. 3

Relation between robust reliability and disturbance attenuation lever

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