venkat - Distributed Model Predictive Control Theory and...

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Distributed Model Predictive Control: Theory and Applications by Aswin N. Venkat A dissertation submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY (Chemical Engineering) at the UNIVERSITY OF WISCONSIN–MADISON 2006
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c Copyright by Aswin N. Venkat 2006 All Rights Reserved
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i For my family . . .
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ii Distributed Model Predictive Control: Theory and Applications Aswin N. Venkat Under the supervision of Professor James B. Rawlings At the University of Wisconsin–Madison Most standard model predictive control (MPC) implementations partition the plant into sev- eral units and apply MPC individually to these units. It is known that such a completely de- centralized control strategy may result in unacceptable control performance, especially if the units interact strongly. Completely centralized control of large, networked systems is viewed by most practitioners as impractical and unrealistic. In this dissertation, a new framework for distributed, linear MPC with guaranteed closed-loop stability and performance properties is presented. A modeling framework that quantifies the interactions among subsystems is em- ployed. One may think that modeling the interactions between subsystems and exchanging trajectory information among MPCs (communication) is sufficient to improve controller per- formance. We show that this idea is incorrect and may not provide even closed-loop stability. A cooperative distributed MPC framework, in which the objective functions of the local MPCs are modified to achieve systemwide control objectives is proposed. This approach allows prac- titioners to tackle large, interacting systems by building on local MPC systems already in place. The iterations generated by the proposed distributed MPC algorithm are systemwide feasible, and the controller based on any intermediate termination of the algorithm is closed-loop sta-
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iii ble. These two features allow the practitioner to terminate the distributed MPC algorithm at the end of the sampling interval, even if convergence is not achieved. If iterated to conver- gence, the distributed MPC algorithm achieves optimal, centralized MPC control. Building on results obtained under state feedback, we tackle next, distributed MPC under output feedback. Two distributed estimator design strategies are proposed. Each es- timator is stable and uses only local measurements to estimate subsystem states. Feasibility and closed-loop stability for all distributed MPC algorithm iteration numbers are established for the distributed estimator-distributed regulator assembly in the case of decaying estimate error. A subsystem-based disturbance modeling framework to eliminate steady-state offset due to modeling errors and unmeasured disturbances is presented. Conditions to verify suit- ability of chosen local disturbance models are provided. A distributed target calculation al- gorithm to compute steady-state targets locally is proposed. All iterates generated by the distributed target calculation algorithm are feasible steady states.
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