Analysis and use of several generalized ℋ(∞ mixed sensitivity frameworks for stable multivariable plants subject to simultaneous output and input loop breaking specifications

• Published in: 2015 54th IEEE Conference on Decision and Control (CDC) pp. 6617 - 6622
• Main Authors: Puttannaiah, Karan, Echols, Justin A., Mondal, Kaustav, Rodriguez, Armando A.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.12.2015
• Subjects: Algorithm design and analysis; Control design; Convex functions; Electrical engineering; Optimization; Sensitivity; Silicon
• DOI: 10.1109/CDC.2015.7403261

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 ∞ , ℋ 2 , 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.