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18 April 2007 Utilizing spatial robustness measures for the optimization of a PZT-actuated flexible beam
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In this work, we revisit the problem of actuator placement within the context of spatial robustness. When one optimizes location-parameterized H2 or H closed loop measures, arrives at actuator locations that provide performance optimality. However, these measures assume an a priori given distribution of disturbances. When the above measures include an additional optimization stage whereby one searches for the worst distribution of disturbances, then the resulting actuator location will result in both an improved performance and enhanced spatial robustness. Using an analytical bound approach that provides an explicit expression for an upper bound on the H norm of the system transfer function, the worst distribution of disturbances can be found that maximizes the open loop H bound. Subsequently, an optimal actuator location is found that minimizes the H∞ bound of the closed loop transfer function. This method minimizes the optimization complexity and provides great computational advantages in large scale flexible systems where the solution to H∞ optimization problems using standard tools becomes computationally prohibitive.
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Michael A. Demetriou and Karolos M. Grigoriadis "Utilizing spatial robustness measures for the optimization of a PZT-actuated flexible beam", Proc. SPIE 6523, Modeling, Signal Processing, and Control for Smart Structures 2007, 65230N (18 April 2007);

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