In this dissertation, we discuss the Distributed Spacecraft Attitude Control System Simulator (DSACSS) testbed developed at Virginia Polytechnic Institute and State University for the purpose of investigating various control techniques for single and multiple spacecraft. DSACSS is comprised of two independent hardware-in-the-loop simulators and one software spacecraft simulator. The two hardware-in-the-loop spacecraft simulators have similar subsystems as flight-ready spacecraft (e.g. command and data handling; communications; attitude determination and control; power; payload; and guidance and navigation). The DSACSS framework is a flexible testbed for investigating a variety of spacecraft control techniques, especially control scenarios involving coupled attitude and orbital motion. The attitude hardware simulators along with numerical simulations assist in the development and evaluation of Lyapunov based asymptotically stable, nonlinear attitude controllers with three reaction wheels as the control device. The angular rate controller successfully tracks a time varying attitude trajectory. The Modified Rodrigues Parmater (MRP) attitude controller results in successfully tracking the angular rates and MRP attitude vector for a time-varying attitude trajectory. The attitude controllers successfully track the reference attitude in real-time with hardware similar to flight-ready spacecraft. Numerical simulations and the attitude hardware simulators assist in the development and evaluation of a robust, asymptotically stable, nonlinear attitude controller with three reaction wheels as the actuator for attitude control. The MRPs are chosen to represent the attitude in the development of the controller. The robust spacecraft attitude controller successfully tracks a time-varying reference attitude trajectory while bounding system uncertainties. The results of a Global Positioning System (GPS) hardware-in-the-loop simulation of two spacecraft flying in formation are presented. The simulations involve a chief spacecraft in a low Earth orbit (LEO), while a deputy spacecraft maintains an orbit position relative to the chief spacecraft. In order to maintain the formation an orbit correction maneuver (OCM) for the deputy spacecraft is required. The control of the OCM is accomplished using a classical orbital element (COE) feedback controller and simulating continual impulsive thrusting for the deputy spacecraft. The COE controller requires the relative position of the six orbital elements. The deputy communicates with the chief spacecraft to obtain the current orbit position of the chief spacecraft, which is determined by a numerical orbit propagator. The position of the deputy spacecraft is determined from a GPS receiver that is connected to a GPS hardware-in-the-loop simulator. The GPS simulator creates a radio frequency (RF) signal based on a simulated trajectory, which results in the GPS receiver calculating the navigation solution for the simulated trajectory. From the relative positions of the spacecraft the COE controller calculates the OCM for the deputy spacecraft. The formation flying simulation successfully demonstrates the closed-loop hardware-in-the-loop GPS simulator. This dissertation focuses on the development of the DSACSS facility including the development and implementation of a closed-loop GPS simulator and evaluation of nonlinear feedback attitude and orbit control laws using real-time hardware-in-the-loop simulators. / Ph. D.

This thesis is concerned with input-output stability theory. Within this framework, it is of interest how inputs map to outputs through an operator that represents a system to be controlled or the controller itself. The Small Gain, Passivity, and Conic Sector Stability Theorems can be used to assess the stability of a negative feedback interconnection involving two systems that each have specific input-output properties. Our first contribution concerns characterization of the input-output properties of linear time-varying (LTV) systems. We present various theorems that ensure that a LTV system has finite gain, is passive, or is conic. We also consider the stability of various negative feedback interconnections. Motivated by the robust nature of passivity-based control, we consider how to overcome passivity violations. This investigation leads to the hybrid conic systems framework whereby systems are described in terms of multiple conic bounds over different operating ranges. A special case relevant to systems that experience a passivity violation is the hybrid passive/finite gain framework. Sufficient conditions are derived that ensure the negative feedback interconnection of two hybrid conic systems is stable. The input-output properties of gain-scheduled systems are also investigated. We show that a gain-scheduled system composed of conic subsystems has conic bounds as well. Using the conic bounds of the subsystems along with the scheduling signal properties, the overall conic bounds of the gain-scheduled system can be calculated. We also show that when hybrid very strictly passive/finite gain (VSP/finite gain) subsystems are gain-scheduled, the overall map is also hybrid VSP/finite gain. Being concerned with the control of aerospace systems, we use the theory developed in this thesis to control two interesting plants. We consider passivity-based control of a spacecraft endowed with magnetic torque rods and reaction wheels. In particular, we synthesize a LTV input strictly passive controller. Using hybrid theory we control single- and two-link flexible manipulators. We present two controller synthesis schemes, each of which employs numerical optimization techniques and attempts to have the hybrid VSP/finite gain controllers mimic a H2 controller. One of our synthesis methods uses the Generalized Kalman-Yakubovich-Popov Lemma, thus realizing a convex optimization problem.

This thesis is concerned with input-output stability theory. Within this framework, it is of interest how inputs map to outputs through an operator that represents a system to be controlled or the controller itself. The Small Gain, Passivity, and Conic Sector Stability Theorems can be used to assess the stability of a negative feedback interconnection involving two systems that each have specific input-output properties. Our first contribution concerns characterization of the input-output properties of linear time-varying (LTV) systems. We present various theorems that ensure that a LTV system has finite gain, is passive, or is conic. We also consider the stability of various negative feedback interconnections. Motivated by the robust nature of passivity-based control, we consider how to overcome passivity violations. This investigation leads to the hybrid conic systems framework whereby systems are described in terms of multiple conic bounds over different operating ranges. A special case relevant to systems that experience a passivity violation is the hybrid passive/finite gain framework. Sufficient conditions are derived that ensure the negative feedback interconnection of two hybrid conic systems is stable. The input-output properties of gain-scheduled systems are also investigated. We show that a gain-scheduled system composed of conic subsystems has conic bounds as well. Using the conic bounds of the subsystems along with the scheduling signal properties, the overall conic bounds of the gain-scheduled system can be calculated. We also show that when hybrid very strictly passive/finite gain (VSP/finite gain) subsystems are gain-scheduled, the overall map is also hybrid VSP/finite gain. Being concerned with the control of aerospace systems, we use the theory developed in this thesis to control two interesting plants. We consider passivity-based control of a spacecraft endowed with magnetic torque rods and reaction wheels. In particular, we synthesize a LTV input strictly passive controller. Using hybrid theory we control single- and two-link flexible manipulators. We present two controller synthesis schemes, each of which employs numerical optimization techniques and attempts to have the hybrid VSP/finite gain controllers mimic a H2 controller. One of our synthesis methods uses the Generalized Kalman-Yakubovich-Popov Lemma, thus realizing a convex optimization problem.

The design of controllers subject to the nonlinear H-infinity criterion is explored. The plants to be controlled are the attitude motion of spacecraft, subject to some disturbance torque. Two cases are considered: the regulation about an inertially-fixed direction, and an Earth-pointing spacecraft in a circular orbit, subject to the gravity-gradient torque. The spacecraft attitude is described using the modified Rodrigues parameters. A series of controllers are designed using the nonlinear H-infinity control criterion, and are subsequently generated using a Taylor series expansion to approximate solutions of the relevant Hamilton-Jacobi equations. The controllers are compared, using both input-output and initial condition simulations. A proof is used to demonstrate that the linearized controller solves the H-infinity control problem for the inertial pointing problem when describing the plant using the modified Rodrigues parameters.

The design of controllers subject to the nonlinear H-infinity criterion is explored. The plants to be controlled are the attitude motion of spacecraft, subject to some disturbance torque. Two cases are considered: the regulation about an inertially-fixed direction, and an Earth-pointing spacecraft in a circular orbit, subject to the gravity-gradient torque. The spacecraft attitude is described using the modified Rodrigues parameters. A series of controllers are designed using the nonlinear H-infinity control criterion, and are subsequently generated using a Taylor series expansion to approximate solutions of the relevant Hamilton-Jacobi equations. The controllers are compared, using both input-output and initial condition simulations. A proof is used to demonstrate that the linearized controller solves the H-infinity control problem for the inertial pointing problem when describing the plant using the modified Rodrigues parameters.

In this thesis novel feedback attitude control algorithms and attitude estimation algorithms are developed for a three-axis stabilised spacecraft attitude control system. The spacecraft models considered include a rigid-body spacecraft equipped with (i) external control torque devices, and (ii) a redundant reaction wheel configuration. The attitude sensor suite comprises a three-axis magnetometer and three-axis rate gyroscope assembly. The quaternion parameters (also called Euler symmetric parameters), which globally avoid singularities but are subject to a unity-norm constraint, are selected as the primary attitude coordinates. There are four novel contributions presented in this thesis. The first novel contribution is the development of a robust control strategy for spacecraft attitude tracking maneuvers, in the presence of dynamic model uncertainty in the spacecraft inertia matrix, actuator magnitude constraints, bounded persistent external disturbances, and state estimation error. The novel component of this algorithm is the incorporation of state estimation error into the stability analysis. The proposed control law contains a parameter which is dynamically adjusted to ensure global asymptotic stability of the overall closedloop system, in the presence of these specific system non-idealities. A stability proof is presented which is based on Lyapunov's direct method, in conjunction with Barbalat's lemma. The control design approach also ensures minimum angular path maneuvers, since the attitude quaternion parameters are not unique. The second novel contribution is the development of a robust direct adaptive control strategy for spacecraft attitude tracking maneuvers, in the presence of dynamic model uncertainty in the spacecraft inertia matrix. The novel aspect of this algorithm is the incorporation of a composite parameter update strategy, which ensures global exponential convergence of the closed-loop system. A stability proof is presented which is based on Lyapunov's direct method, in conjunction with Barbalat's lemma. The exponential convergence results provided by this control strategy require persistently exciting reference trajectory commands. The control design approach also ensures minimum angular path maneuvers. The third novel contribution is the development of an optimal control strategy for spacecraft attitude maneuvers, based on a rigid body spacecraft model including a redundant reaction wheel assembly. The novel component of this strategy is the proposal of a performance index which represents the total electrical energy consumed by the reaction wheel over the maneuver interval. Pontraygin's minimum principle is applied to formulate the necessary conditions for optimality, in which the control torques are subject to timevarying magnitude constraints. The presence of singular sub-arcs in the statespace and their associated singular controls are investigated using Kelley's necessary condition. The two-point boundary-value problem (TPBVP) is formulated using Pontrayagin's minimum principle. The fourth novel contribution is an attitude estimation algorithm which estimates the spacecraft attitude parameters and sensor bias parameters from three-axis magnetometer and three-axis rate gyroscope measurement data. The novel aspect of this algorithm is the assumption that the state filtering probability density function (PDF) is Gaussian distributed. This Gaussian PDF assumption is also applied to the magnetometer measurement model. Propagation of the filtering PDF between sensor measurements is performed using the Fokker-Planck equation, and Bayes theorem incorporates measurement update information. The use of direction cosine matrix elements as the attitude coordinates avoids any singularity issues associated with the measurement update and estimation error covariance representation.

The design of an attitude control system for a flexible spacecraft using magnetic actuation is considered. The nonlinear, linear, and modal equations of motion are developed for a general flexible body. Magnetic control is shown to be instantaneously underactuated, and is only controllable in the time-varying sense. A PD-like control scheme is proposed to address the attitude control problem for the linear system. Control gain limitations are shown to exist for the purely magnetic control. A hybrid control scheme is also proposed that relaxes these restrictions by adding a minimum control effort from an alternate three-axis actuation system. Floquet and passivity theory are used to obtain gain selection criteria that ensure a stable closed-loop system, which would aid in the design of a hybrid controller for a flexible spacecraft. The ability of the linearized system to predict the stability of the corresponding nonlinear system is also investigated.

The design of an attitude control system for a flexible spacecraft using magnetic actuation is considered. The nonlinear, linear, and modal equations of motion are developed for a general flexible body. Magnetic control is shown to be instantaneously underactuated, and is only controllable in the time-varying sense. A PD-like control scheme is proposed to address the attitude control problem for the linear system. Control gain limitations are shown to exist for the purely magnetic control. A hybrid control scheme is also proposed that relaxes these restrictions by adding a minimum control effort from an alternate three-axis actuation system. Floquet and passivity theory are used to obtain gain selection criteria that ensure a stable closed-loop system, which would aid in the design of a hybrid controller for a flexible spacecraft. The ability of the linearized system to predict the stability of the corresponding nonlinear system is also investigated.