Coupling and Controllability in Optimal Design and Control.

Abstract

So-called ‘smart’ products have the potential to improve life dramatically from the smallest scale, such as biological micro-electrical mechanical sensors for health monitoring, to the largest scale, such as electrical grids and transportation networks. All of these technologies require the design of both an artifact and a controller, and one can assert that optimal artifact and controller designs are required in order to realize their full benefit. The problem of combined design of artifact and controller is termed co-design. Coupling between the artifact and controller design problems has been demonstrated to be critical in the co-design of many such systems. It is necessary, then, to be able to identify coupling in these systems and to choose an optimization method that can optimize a coupled system particularly with respect to its controllability. This is the focus of the present dissertation. Relationships are derived between known coupling metrics and the controllability Grammian matrix of the system. These relationships represent a first a priori determination of coupling, namely, assessment of coupling between design and control decisions prior to system optimization. Previous work had focused on coupling metrics that require knowledge of the system optimum to compute coupling strength and choose an appropriate system design method. This dissertation introduces the Control Proxy Function (CPF) concept. A CPF is defined as a measure of the system’s ease of control. CPFs are derived for certain classes of problems, and examples are presented. For a co-design problem with a derived CPF, a sequential system design process can be effected, with the CPF augmenting the original artifact objective function. The optimal design and control problems can then be solved in sequence, while preserving system optimality. Conditions are derived under which the method is effective, and guidelines for the choice of a CPF are provided. The method is demonstrated in the co-design of a MEMS actuator. Results show that this method can be used to co-design systems effectively, allowing a designer to realize system optimal, or near-optimal, results with the simplicity of a sequential design process.Ph.D.Mechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/75943/1/dlpeters_1.pd

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