TY - GEN
T1 - Analysis and use of several generalized H(∞ mixed sensitivity frameworks for stable multivariable plants subject to simultaneous output and input loop breaking specifications
AU - Puttannaiah, Karan
AU - Echols, Justin A.
AU - Mondal, Kaustav
AU - Rodriguez, Armando
N1 - Publisher Copyright:
© 2015 IEEE.
PY - 2015/2/8
Y1 - 2015/2/8
N2 - In this paper, we present and examine three generalized mixed-sensitivity control design frameworks for linear time invariant (LTI) plants for trading off properties at distinct multivariable loop-breaking points, while being able to handle a broad class of closed loop (e.g. H(∞, H2, frequency- and time domain) specifications. Multiobjective tradeoff paradigms are developed and analysed for ill-conditioned plants having large relative gain array entries - plants that have received considerable attention in the literature without yielding a direct systematic design methodology. We provide insight into the effectiveness of each approach and discuss the trading-off of properties at distinct loop-breaking points. This is done by exploiting the Youla-Jabr-Bongiorno-Kucera-Zames (YJBKZ) parameterization, the resulting convexification, and efficient state-of-the-art convex solvers that can be applied to smooth as well as non-differentiable problems. Moreover, we also show how our approach can be applied to multivariable infinite-dimensional plants. Specifically, by using finite dimensional approximants that converge in the uniform topology, we obtain near-optimal finite dimensional controllers for the infinite dimensional plant. Illustrative examples are provided for a thermal PDE and a retarded time delay system.
AB - In this paper, we present and examine three generalized mixed-sensitivity control design frameworks for linear time invariant (LTI) plants for trading off properties at distinct multivariable loop-breaking points, while being able to handle a broad class of closed loop (e.g. H(∞, H2, frequency- and time domain) specifications. Multiobjective tradeoff paradigms are developed and analysed for ill-conditioned plants having large relative gain array entries - plants that have received considerable attention in the literature without yielding a direct systematic design methodology. We provide insight into the effectiveness of each approach and discuss the trading-off of properties at distinct loop-breaking points. This is done by exploiting the Youla-Jabr-Bongiorno-Kucera-Zames (YJBKZ) parameterization, the resulting convexification, and efficient state-of-the-art convex solvers that can be applied to smooth as well as non-differentiable problems. Moreover, we also show how our approach can be applied to multivariable infinite-dimensional plants. Specifically, by using finite dimensional approximants that converge in the uniform topology, we obtain near-optimal finite dimensional controllers for the infinite dimensional plant. Illustrative examples are provided for a thermal PDE and a retarded time delay system.
KW - Algorithm design and analysis
KW - Control design
KW - Convex functions
KW - Electrical engineering
KW - Optimization
KW - Sensitivity
KW - Silicon
UR - http://www.scopus.com/inward/record.url?scp=84962038041&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84962038041&partnerID=8YFLogxK
U2 - 10.1109/CDC.2015.7403261
DO - 10.1109/CDC.2015.7403261
M3 - Conference contribution
AN - SCOPUS:84962038041
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 6617
EP - 6622
BT - 54rd IEEE Conference on Decision and Control,CDC 2015
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 54th IEEE Conference on Decision and Control, CDC 2015
Y2 - 15 December 2015 through 18 December 2015
ER -