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Delay-Based Controller Design for Continuous-Time and Hybrid Applications

Lavaei, Javad and Sojoudi, Somayeh and Murray, Richard M. (2010) Delay-Based Controller Design for Continuous-Time and Hybrid Applications. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechCDSTR:2010.002

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Abstract

Motivated by the availability of different types of delays in embedded systems and biological circuits, the objective of this work is to study the benefits that delay can provide in simplifying the implementation of controllers for continuous-time systems. Given a continuous-time linear time-invariant (LTI) controller, we propose three methods to approximate this controller arbitrarily precisely by a simple controller composed of delay blocks, a few integrators and possibly a unity feedback. Different problems associated with the approximation procedures, such as finding the optimal number of delay blocks or studying the robustness of the designed controller with respect to delay values, are then investigated. We also study the design of an LTI continuous-time controller satisfying given control objectives whose delay-based implementation needs the least number of delay blocks. A direct application of this work is in the sampled-data control of a real-time embedded system, where the sampling frequency is relatively high and/or the output of the system is sampled irregularly. Based on our results on delay-based controller design, we propose a digital-control scheme that can implement every continuous-time stabilizing (LTI) controller. Unlike a typical sampled-data controller, the hybrid controller introduced here -— consisting of an ideal sampler, a digital controller, a number of modified second-order holds and possibly a unity feedback -— is robust to sampling jitter and can operate at arbitrarily high sampling frequencies without requiring expensive, high-precision computation.


Item Type:Report or Paper (Technical Report)
Additional Information:This research was supported by ONR MURI N00014-08-1-0747 "Scalable, Data-driven, and Provably-correct Analysis of Networks," ARO MURI W911NF-08-1-0233 "Tools for the Analysis and Design of Complex Multi-Scale Networks," and the Army's W911NF-09-D-0001 Institute for Collaborative Biotechnology.
Group:Control and Dynamical Systems Technical Reports
Record Number:CaltechCDSTR:2010.002
Persistent URL:http://resolver.caltech.edu/CaltechCDSTR:2010.002
Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format with proper citation.
ID Code:28139
Collection:CaltechCDSTR
Deposited By: Imported from CaltechCDSTR
Deposited On:15 Jun 2010
Last Modified:26 Dec 2012 14:31

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