Experimental Feedback of Fractional Order States of a Lightly Damped Structure
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH
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The purpose of this study was to investigate the effectiveness of using fractional order time derivatives of position feedback signals in the active control of vibration. To that end, circuitry was built and evaluated that finds the half order derivative of an input signal. The magnitude responses of the fractional derivative circuits is very good, but there are large phase shifts present that may degrade the performance of the controllers. Two methods of incorporating the fractional derivative signals into the controller were examined. One method involved developing a similarity transformation that transforms an integer order state controller into an equivalent controller using fractional or mixed fractional and integer order signals. The second method was a form of traditional pole placement techniques that allowed the direct designs of a controller using fractional and integer order feedback signals. Designs were tested on an inverted cantilever beam with control provided by a shaker, and compared to theoretical predictions and to traditional integer order controllers. There is a discrepancy in the modeling that manifests itself as a large offset in magnitude, particularly at very low frequencies. However, controllers utilizing fractional order feedback provided nearly identical control authority to the traditional integer order designs.
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