Robust adaptive control using a filtering action
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This dissertation describes the design of an adaptive controller for single-input single-output (SISO) systems with guaranteed bounds on the transient response, and robustness with external disturbances and unmodeled dynamics. Developed from a current approach called "L1 adaptive controller", we show that by adding two properly designed low pass filters at the input and at the estimator we can control the transient response and the sensitivity of the overall system to external disturbances and unmodeled dynamics. Global stability of the overall adaptive system is mathematically proven under the assumption that the system is minimum phase (i.e., with the zeros of the transfer function in the stable region) and bounds of the systems parameters are known to the designer. The extension of this approach to non-minimum phase systems, such as systems with flexible appendages, is also considered. We show that a non-minimum phase plant augmented with a properly designed parallel system results in a minimum phase system. The augmenting system most easily comes from the inverse of a stabilizing Proportional-Integral-Derivative (PID) controller, designed to be least sensitive to parameter uncertainties. This approach is applied to a flexible arm in a testbed at the Naval Postgraduate School, called the Flexible Spacecraft Simulator (FSS), which emulates realistic conditions in space. Experimental results prove the effectiveness of the controller presented in this dissertation.
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