Persistence filters for controller and observer design in singular gain systems
MetadataShow full item record
This dissertation develops a general framework for designing stabilizing feedback controllers and observers for dynamics with state/time dependent gains on the control signals and measured outputs. These gains have potential singularity periods but satisfy a technically non-trivial condition referred to as persistence of excitation. A persistence filter design constitutes the primary theoretical innovation of this work around which the controller and observer development is centered. Application areas of singular gain systems considered in this study include robotics, biomechanics, intelligent structures and spacecrafts. Several representative problems involving singular, time-dependent gains are addressed. The specific contributions of this dissertation are outlined as follows: (i) a stabilizing feedback for linear, single-input systems with time-varying, singular control scaling is designed that allows arbitrary exponential convergence rate for the closed-loop dynamics. An adaptive control generalization of this result allows asymptotic convergence in presence of unknown plant parameters. An extension to a special, single-input nonlinear system in the controller canonical form is also proposed. It is proven that this control design results in bounded tracking error signals for a trajectory tracking objective; (ii) observer design for linear, single-output systems with time-varying, singular measurement gains is considered. A persistence filter similar in structure to the control counterpart aids an observer design that guarantees exponential state reconstruction with arbitrary convergence rates; (iii) the observer and controller designs are combined to obtain an exponentially stabilizing output feedback controller for linear, single-input, single-output dynamics with singular gains on both the control and measurements. A novel separation property is established as a consequence. The construction motivates applications to stabilization with reversible transducers which can switch between sensor and actuator modes. The results are verified on two illustrative applications, vibration control using piezoelectric devices and inverted pendulum stabilization with a DC motor. The linear result is further generalized to include state dependent gains; (iv) application of the persistence filter theory to spacecraft attitude stabilization using intermittent actuation is explored. The intermittence is characterized by a time-varying, periodically singular control gain. A nonlinear persistence filter allows construction of an exponentially stabilizing controller and simulations verify convergence with intermittent actuation where conventional proportional-derivative control fails; (v) a stabilization result for a special multi-input, linear system with time-varying matrix control gains is presented. The matrix gain is assumed to be diagonal but allows fewer controls than states subject to a controllability assumption in absence of the singular gain matrix. The single-input adaptive control results are shown to extend to the multi-input case. An application to angular velocity stabilization of an underactuated rigid spacecraft is considered.
Showing items related by title, author, creator and subject.
Wu, Ying-Jeng Engin; Beaman, J.J. (1990)Geometric contour following for scanning control in SFF application is used to refine the boundary ofthe parts for increasing the accuracy or to develop the capability to arrange various scanning directions and paths for ...
Tracker controls development and control architecture for the Hobby-Eberly Telescope Wide Field Upgrade Mock, J.R.; Beno, J; Rafferty, T.H; Cornell, M.E. (2010-07)To enable the Hobby-Eberly Telescope Wide Field Upgrade, the University of Texas Center for Electromechanics and McDonald Observatory are developing a precision tracker system – a 15,000 kg robot to position a 3,100 kg ...
Characterization of an alkyl diamine surfactant for gas mobility control in gas enhanced oil recovery and conformance control Liebum, Madalyn Marie; 0000-0001-7223-3143 (2016-05)The objective of this research is to characterize the properties and performance of an amine-based “switchable” surfactant, Duomeen TTM, at various environmental conditions. In particular, bulk characterization measurements ...