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Research Papers

Determination of Most Desirable Nominal Closed-Loop State Space System Via Qualitative Ecological Principles

[+] Author and Article Information
Nagini Devarakonda

Department of Mechanical
and Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210
e-mail: ndevarak@gmail.com

Rama K. Yedavalli

Department of Mechanical
and Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210
e-mail: yedavalli.1@osu.edu

1Present address: General Motors, Milford Proving Grounds, MI 48708

2Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received December 22, 2014; final manuscript received October 27, 2015; published online December 4, 2015. Assoc. Editor: Srinivasa M. Salapaka.

J. Dyn. Sys., Meas., Control 138(2), 021001 (Dec 04, 2015) (10 pages) Paper No: DS-14-1544; doi: 10.1115/1.4031957 History: Received December 22, 2014; Revised October 27, 2015

This paper addresses the issue of determining the most desirable “nominal closed-loop matrix” structure in linear state space systems, from stability robustness point of view, by combining the concepts of “quantitative robustness” and “qualitative robustness.” The qualitative robustness measure is based on the nature of interactions and interconnections of the system. The quantitative robustness is based on the nature of eigenvalue/eigenvector structure of the system. This type of analysis from both viewpoints sheds considerable insight on the desirable nominal system in engineering applications. Using these concepts, it is shown that three classes of quantitative matrices labeled “target sign stable (TSS) matrices,” “target pseudosymmetric (TPS) matrices,” and finally “quantitative ecological stable (QES) matrices” have features which qualify them as the most desirable nominal closed-loop system matrices. In this paper, we elaborate on the special features of these sets of matrices and justify why these classes of matrices are well suited to be the most desirable nominal closed-loop matrices in the linear state space framework. Establishment of this most desirable nominal closed-loop system matrix structure paves the way for designing controllers which qualify as robust controllers for linear systems with real parameter uncertainty. The proposed concepts are illustrated with many useful examples.

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References

Devarakonda, N. , and Yedavalli, R. , 2011, “ Qualitative Robustness and Its Role in Robust Control of Uncertain Engineering Systems,” ASME Paper No. DSCC2011-6163.
Yedavalli, R. K. , and Devarakonda, N. , 2014, “ Determination of Most Desirable Nominal Closed Loop State Space System Via Qualitative Ecological Principles,” ASME Paper No. DSCC2014-6181.
Dorato, P. , and Yedavalli, R. K. , 1990, Recent Advances in Robust Control, IEEE Press, New York.
Yedavalli, R. K. , 2014, Robust Control of Uncertain Dynamic Systems: A Linear State Space Approach, Springer, New York.
Yedavalli, R. K. , 1993, “ Flight Control Application of New Stability Robustness Bounds for Linear Uncertain Systems,” AIAA J. Guid., Control Dyn., 16(6), pp. 1032–1037. [CrossRef]
Patel, R. V. , and Toda, M. , 1980, “ Quantitative Measures of Robustness for Multivariable Systems,” Joint American Control Conference.
Edelstein-Keshet, L. , 1988, Mathematical Models in Biology, McGraw-Hill, New York.
Hofbauer, J. , and Sigmund, K. , 1988, “ Growth Rates and Ecological Models: ABC on Ode,” The Theory of Evolutions and Dynamical Systems, Cambridge University Press, London, pp. 29–59.
Hogben, L. , 2007, Handbook of Linear Algebra (Discrete Mathematics and Its Applications), Chapman and Hall/CRC, New York.
Yedavalli, R. K. , and Devarakonda, N. , 2009, “ Qualitative Principles of Ecology and Their Implications in Quantitative Engineering Systems,” ASME Paper No. DSCC2009-2621.
Yedavalli, R. K. , and Devarakonda, N. , 2010, “ Sign Stability Concept of Ecology for Control Design With Aerospace Applications,” AIAA J. Guid. Control Dyn., 33(2), pp. 333–346. [CrossRef]
Devarakonda, N. , and Yedavalli, R. K. , 2010, “ Engineering Perspective of Ecological Sign Stability and Its Application in Control Design,” American Control Conference, Baltimore, MD, June 30–July 2, pp. 5062–5067.
Yedavalli, R. K. , 2006, “ Qualitative Stability Concept From Ecology and Its Use in the Robust Control of Engineering Systems,” American Control Conference, Minneapolis, MN, June 14–16, pp. 5097–5102.
Jeffries, C. , 1974, “ Qualitative Stability and Digraphs in Model Ecosystems,” Ecology, 55(6), pp. 1415–1419. [CrossRef]
Quirk, J. , and Ruppert, R. , 1965, “ Qualitative Economics and the Stability of Equilibrium,” Rev. Econ. Studies, 32(4), pp. 311–326. [CrossRef]
May, R. , 1973, Stability and Complexity in Model Ecosystems, Princeton University Press, Princeton, NJ.
Allesina, S. , and Tang, S. , 2012, “ Stability Criteria for Complex Ecosystems,” Nature, 483(7388), pp. 205–208. [CrossRef] [PubMed]
Allesina, S. , and Pascual, M. , 2008, “ Network Structure, Predator–Prey Modules, and Stability in Large Food Webs,” Theor. Ecol., 1(1), pp. 55–64. [CrossRef]
Brogan, W. L. , 1974, Modern Control Theory, Prentice Hall, Englewood Cliffs, NJ.
Devarakonda, N. , and Yedavalli, R. K. , 2010, “ A New Robust Control Design Method for Linear Systems With Norm Bounded Time Varying Real Parameter Uncertainty,” ASME Paper No. DSCC2010-4195.
Kaszkurewicz, E. , and Bhaya, A. , 2000, Matrix Diagonal Stability in Systems and Computation, Birkhauser, New York.
Franklin, G. , Powell, J. D. , and Naeini, A. E. , 2006, Feedback Control of Dynamic Systems, Prentice Hall, Upper Saddle River, NJ.

Figures

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Fig. 1

Types of interactions between species

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Fig. 2

A qualitative matrix and its corresponding digraph

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Fig. 3

(a) Interactions and (b) interconnections in an ecosystem

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Fig. 4

Set of best nominal matrices

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