Abstract
This paper is focused on characterization of easily controllable plants in practical control applications rather than to design an optimal or a robust controller for a give plant. After explaining the background and the motivation of the research topic, we first provide two notions, namely finite frequency positive realness (FFPR) and Condition (π), which represent desirable phase/gain properties for easily controllable plants. We then show closed-form analytical expressions of best achievable \( {\cal H}_2 \) tracking and regulation performances, and we provide the connection between Condition (π) and the achievable robust performance based on \( {\cal H}_\infty \) loop shaping design procedure.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bakhtiar, T., Hara, S.: H 2 Regulation Performance Limitations for SIMO Linear Time-invariant Feedback Control Systems. Automatica (to appear, 2007)
Chen, J., Hara, S., Chen, G.: Best tracking and regulation performance under control energy constraint. IEEE Trans. on Automatic Control 48(8), 1320–1336 (2003)
Freudenberg, J.S., Looze, D.P.: Right half plane zeros and poles and design tradeoffs in feedback systems. IEEE Trans. on Automatic Control 30(6), 555–565 (1985)
Hara, S.: A unification of analytical expressions for control performance limitations via reciprocal transform. In: SSSC 2007. 3rd IFAC Symp. on System, Structure and Control (submitted, 2007)
Hara, S., et al.: The Best Achievable H 2 Tracking Performances for SIMO Feedback Control Systems. J. of Control Science and Engineering (2007)
Hara, S., Kanno, M., Onishi, M.: Finite frequency phase property versus achievable control performance in \( {\cal H}_\infty \) loop shaping design. In: Proc. of SICE-ICASE Int. Joint Conf. 2006, Busan, Korea, pp. 3196–3199 (October 2006)
Iwasaki, T., Hara, S., Yamauchi, K.: Dynamical system design from a control perspective: Finite frequency positive-realness approach. IEEE Trans. on Automatic Control 48(8), 1337–1354 (2003)
Kanno, M., Hara, S., Onishi, M.: Characterization of Easily Controllable Plants Based on the Finite Frequency Phase/Gain Property. In: Proc. of American Control Conference 2007, New York, pp. 5816–5821 (July 2007)
Kanno, M., et al.: Parametric optimization in control using the sum of roots for parametric polynomial spectral factorization. In: Proc. Int. Symposium on Symbolic and Algebraic Computation, Waterloo, Ontario, Canada, pp. 211–218 (July-August 2007)
Kanno, M., Hara, S., Anai, H., Yokoyama, K.: Sum of Roots, Polynomial Spectral Factorization, and Control Performance Limitations. In: IEEE Conf. on Decision and Control, New Orleans (to be presented, December 2007)
McFarlane, D.C., Glover, K.: Robust Controller Design Using Normalized Coprime Factor Plant Descriptions. Lecture Notes in Control and Inf. Sciences, vol. 138. Springer, Heidelberg (1990)
Middleton, R.H.: Trade-offs in linear control systems design. Automatica 27(2), 281–292 (1991)
Seron, M.M., Braslavsky, J.H., Goodwin, G.C.: Fundamental Limitations in Filtering and Control. Springer, London (1997)
Skogestad, S., Postlethwaite, L.: Multivariable Feedback Control: Analysis and Design, 2nd edn. Wiley, Chichester (2005)
Vinnicombe, G.: Uncertainty and Feedback — \( {\cal H}_\infty \) Loop-shaping and the υ-gap Metric. Imperial College Press, London (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hara, S., Kanno, M. (2008). When Is a Linear Continuous-time System Easy or Hard to Control in Practice?. In: Blondel, V.D., Boyd, S.P., Kimura, H. (eds) Recent Advances in Learning and Control. Lecture Notes in Control and Information Sciences, vol 371. Springer, London. https://doi.org/10.1007/978-1-84800-155-8_8
Download citation
DOI: https://doi.org/10.1007/978-1-84800-155-8_8
Publisher Name: Springer, London
Print ISBN: 978-1-84800-154-1
Online ISBN: 978-1-84800-155-8
eBook Packages: EngineeringEngineering (R0)