Integrated Actuator/Sensor Design for Control of Distributed Parameter Systems

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The dynamics of many systems depend  not only on time, but also on the spatial distribution of the system. Examples include: fluid flow, transmission networks, structural vibrations, acoustic noise. These systems are known as distributed parameter systems (DPS) and models involve partial differential equations. This is different from lumped parameter systems, such as circuits, where the models are ordinary differential equations. This introduces a number of complexities into estimator and controller design.***For  control and estimation of systems that vary in space, performance depends on the location of controller hardware, the sensors and actuators. The best locations may be different from those chosen based on physical intuition. Analysis is crucial, as it is often difficult to move hardware. For example, piezo-electric actuator/sensors are useful in structural control and estimation, but once placed, cannot be moved without damaging the structure. A mechatronic approach that  integrates controller/estimator design  with actuator/sensor location should be used. Sensor location in particular has many applications. These applications include sensor placement on structures, thermostat placement to improve building efficiency and sensor placement to study environmental changes in lakes. One question involves sensor selection: for a given budget, which choice yields better performance, a small number of quality sensors or a larger number of cheap sensors? What is the best control of moving sensors in order to obtain the best estimate of a contaminant location? Many sensors or actuators, particularly those composed of smart materials, can be produced in fairly arbitrary shapes. For a given application, and mass of material, what is the best shape for achieving estimation (or a control objective)?***Results on sensor location will lead naturally to establishing a strategy for joint actuator/sensor location as part of an integrated approach to output feedback controller design.  Recent research by the principal investigator led to fundamental results on some actuator location problems and these results will be helpful in the proposed research.***Advances in theory and computation are needed. Theory that includes the effect on system dynamics of sensors and actuators will be developed. An efficient algorithm that can be used for arbitrary spatial domains is critical. Integrated DPS controller design means that hardware location is integrated with controller/estimator development.***Many processes are nonlinear. Examples include large vibrations, heating with phase change, smart-materials, charge estimation in lithium-ion batteries. Both theory for control and estimation of these systems, and methods that can be used for practical synthesis, are needed. Combined with results on actuator/sensor location this will lead to a integrated controller design strategy for DPS. *** **