# Browsing by Subject "Space vehicles"

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Item Persistence filters for controller and observer design in singular gain systems(2011-05) Srikant, Sukumar; Akella, Maruthi Ram, 1972-; Lightsey, E G.; Bennighof, Jeffrey K.; Hull, David G.; Griffin, LisaShow more 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.Show more Item Reducing spacecraft state uncertainty through indirect trajectory optimization(2005) Zimmer, Scott Jason; Ocampo, CesarShow more The exact position and velocity of a spacecraft is never known; instead, an estimate of the spacecraft location is determined based on observations of the spacecraft state. The accuracy of this state estimate depends on numerous factors including the number, quality, frequency, and types of measurements; the accuracy with which the equations of motion are modeled; and the trajectory of the spacecraft relative to the observer. Many choices of trajectories are available to transfer a spacecraft from an initial set of constraints to a final set of constraints. Most efforts to optimize these transfers involve determining the minimum propellant or minimum time transfer. This dissertation provides a technique to determine trajectories that lead to a more accurate estimate of the spacecraft state. The calculus of variations is used to develop the necessary theory and derive the optimality conditions for a spacecraft to transfer between a set of initial and final conditions while minimizing a combination of fuel consumption and a function of the estimation error covariance matrix associated with the spacecraft Cartesian position and velocity components. The theory is developed in a general manner that allows for multiple observers, moving observers, a wide variety of observation types, multiple gravity bodies, and uncertainties in the spacecraft equations of motion based on the thrust related parameters of the spacecraft. A series of example trajectories from low Earth orbit (LEO) to a near geosynchronous Earth orbit (GEO) shows that either the trace or the integral of the trace of the covariance matrix associated with the Cartesian position and velocity can be reduced significantly with a small increase in the integral of the spacecraft thrust acceleration squared. A method to minimize the uncertainty of the spacecraft state in a set of coordinates other than the one in which the spacecraft equations of motion and covariance are expressed is also introduced. The technique allows one to minimize the uncertainty in non-Cartesian components such as the spacecraft semimajor axis, flight path angle, or range without developing the equations of motion for the spacecraft or covariance in a non-Cartesian frame. Example problems with transfers from LEO to near GEO and LEO to lunar orbit demonstrate that the covariance associated with the semimajor axis can be reduced significantly with only a slight increase in fuel consumption.Show more