Active vibration mitigation of distributed parameter, smart-type structures using Pseudo-Feedback Optimal Control (PFOC)

A new, near-optimal feedback control technique is introduced that is shown to provide excellcnt vibration attenuation for those distributed parameter _ystems that are often encountered in the areas of aeroservoelasticity and large space systems. The technique relies on a novel solution methodology for the classical optimal control problem. Specifically, the quadratic regulator control problem/'or a flexible vibrating structure is first cast in a weak functional form that admits an approxima :e solution. The necessary conditions (first-order} are then solved via a time finite-element method. The procedure produces a low dimensional, algebraic parameterizatbn of the optimal control problem that provides a rigorous basis for a discrete controller with a firstorder "l/ke" hold output. Simulation has shown that the algorithm can successfully control a wide variety of plant forms including multi-input/multi-output systems and sy:_tems exhibiting significant nonlinearities. In order to firmly establish the effica."y of the algorithm, a laboratory control experiment was implemented to provide planar (bending) vibration attenuation of a highly flexible beam (with a first clamped-free raode of approximately 0.5 Hz}. Base actuation for the cantilever was accomplished usir_[ a three degree-offreedom act/re bay (variable geometry truss} actuator. On-line pl ocessing was accomplished with a 14 rnhz "AT' type microcomputer with dat_ acquisition capability. The results of the tests corroborate the utility of the method.