Collaborative Research: Integrated Parameter and Control Design

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Project SummaryMotivated by design problems i anotechnology and by key theoretical problems of interest,we consider a paradigm whereby the plant description depends on one or several parameters thatare subject to design.We propose a general framework for I tegrated Parameter and Controller(IPC)design that allows multiple performance requirements.We propose to address the problemof designing these parameters in conjunction with the feedback controller i order to achieve one ormore objectives.We then propose to address and solve the underlying optimization problem.Thetheoretical underpinnings will rely o ew results in the non-convex optimization literature thatutilize convex relaxation i order to get global optimal solutions.The potential of our approachto yield e .ective solutions to the resulting problems is demonstrated by our recent work thatapplies the proposed methods to the robust synthesis problem in 1 giving the only global optimalsolution to this important problem.Aside from its contribution to the theory of control design,the IPC design tools to be developed will be used to address several practical problems where thesimultaneous parameter and controller design can have a large and measurable impact.Speci .cally,we will address a signi .cant nanotechnology design problem i volving ultra-high resolution micro-cantilevers.This problem will take adva tage of existing expertise i the laboratory of the PIs andwill be conducted i close collaboration with the relevant industry.Based o the interdisciplinarytools eeded for IPC design theory,we also address educational goals that are made possible bythe proposed research.The intellectual merit of this proposal stems from the novel approach for a well recognizedunsolved problem of integrated parameter and controller (IPC)design.The proposal will contributesigni .cantly to optimization based methodologies in control theory solving hitherto unaddressedproblems that are of importance for practical control design.The proposal lays particular emphasison applying the theory developed to micro-cantilever based technologies in the context of IPCdesign.The theoretical paradigm is well suited and timely for furthering this technology.Apart from the theoretical impact the related technology to be developed will be applicableto practical problems i the two hundred million dollar scanning probe industry.The PIs havesigni .cant collaboration with industry and the technical knowhow developed will be guided andtransferred e .ectively to the industry.E .ort will be placed on integrating the software developedon a typical Matlab platform.This will enable wide use of the tools developed by the relatedcommunities.The main topic of the proposal provides a unique opportunity to expose the studentto the importance of plant structure that facilitates good overall plant-controller performance.Anovel course that builds o the ideas and results of this project to motivate the general philosophyand techniques of integrated parameter and control design will be developed.1