Research Initiation: A Passivity-Based Control Methodology for Distribution Parameter Systems (SGER Supplement)

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The intent of this project is to develop tools to analyze stability of a closed loop distributed parameter control system with plant uncertainties, and to apply these tools to the design of robustly stabilizing controllers. In the control of mechanical systems, distributed parameter plant models are often used because of major advantages over lumped parameter models. However, with the very large number of degrees of freedom in distributed parameter models and the practical limitation of computational resources, the control problem faces the challenging task of maintaining stability of the entire plant with a low dimensional controller based on inexact open loop plant information. This project proposes to extend the passivity approach to address the robust stability analysis and robust controller design problems related to this scenario. A passive system is defined as one having colocated sensors and actuators. The approach has the advantage of combining the time domain analysis (to infer stability), and the frequency domain analysis. The four topics investigated in this project include (1) incorporating the parameter robustness requirement in the passivity method, (2) generalizing the passivity approach to unbounded input and output operators, (3) reducing conservatism in the passivity based robustness analysis by using the optimal multiplier technique, and (4) validating the theoretical results through simulation and laboratory experiments.