Robust nonlinear observer for a non-collocated flexible motion system
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Robustness of the closed-loop system has repercussions on both stability and performance, making the study of robustness very important. Fundamentally, the performance and stability of closed-loop systems utilizing state-feedback are tied to that of the observers. The primary goal of this thesis is to develop a robust nonlinear observer and closely examine the usefulness of the observer in the presence of non-collocation and parametric uncertainty and as an integral component in closed-loop control. The usefulness of the observer being investigated depends on robustness, accuracy, computational burden, tunability, ease of design, and ease of implementation on an actual flexible motion system. The design and subsequent integration of the Kalman filter, an optimal observer, into a closed-loop system is well known and systematic. However, there are shortcomings of the Kalman filter in the presence of model uncertainty which are highlighted in this work. Simulation studies are conducted using the Simulation Module in National Instruments LabVIEW 8.5 and experiments are conducted on a physical system consisting of a single flexible link with non-collocation of actuators and sensors using LabVIEW Real Time 8.5. Simulations serve as a means to analyze the performance of the optimal observer and the robust observer by analyzing their dynamic behavior as well as that of the closed-loop system with each observer in place. The focus of experiments is on investigating implementation of the robust observer, including initialization and tuning of observer design parameters off-line and on-line. Simulations verify the robustness properties of the sliding mode observer while experiments show that the robust observer can be implemented at fast control rates and that replacing the Kalman filter with a robust observer has direct ramifications on closed-loop performance.