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Comparative Assessment of Optimal Control Methods With Integrated Performance Constraints


 The relative performance of optimal vibration control methods is investigated within the context of integrated finite element modeling of piezothermoelastic structures. An IMSC and a LQR optimal control method are modified to include explicit performance constraints related to the transient settling time and steady-state gain of the modal response. When this approach is applied to the IMSC method, the result is a pole placement technique. But when it is applied to the LQR method operating in a modal subspace, the result is a method incorporating both optimal and pole placement features. The two methods are compared by means of a transient response analysis of an aluminum strip with piezoceramic sensing and actuating patches. For identical performance constraints and using identical modal subspaces, it is found that maximum actuator voltages and their distribution vary according to the control design method and the number of modes under control. In particular, it was found that the maximum actuator voltages are less for LQR than for IMSC. This is attributed to difficulty in controlling the second bending and first torsional modes of the strip independently. It is also found that for a given number of controlled modes, the maximum actuator voltage varies in a manner approximately inversely proportional to the settling time.