Reference governors: Theoretical Extensions and Practical Applications.

As systems become downsized and operate at the limits of performance, control systems must be designed to ensure that system state and control constraints are satisfied; however, conventional control schemes are often designed without taking constraints into account. Reference governors and the related, more flexible, extended command governors are add-on, constraint enforcement schemes that modify reference signals to conventionally designed, closed-loop systems for the purpose of enforcing output constraints. The focus of this dissertation is on theoretical and methodological extensions of reference and extended command governors, and on their practical applications. Various theoretical results are presented. The first is the development of reduced-order reference and extended command governors, which enables constraint enforcement schemes using simplified models. The second, related development is that of reference governors for decentralized systems that may or may not communicate over a network. The third considers command governors with penalty functions that are used to enforce prioritized sets of constraints, as well as reference governors that are applied to a sequence of prioritized references. The fourth considers the often overlooked case of applying reference governors to linear systems subject to nonlinear constraints; various formulations of constraints are considered, including quadratic constraints and mixed logical-dynamic constraints. The final theoretical development considers using contractive sets to design reference governors for systems with time-varying reference inputs or subject to time-dependent constraints. Numerical simulations are used throughout to illustrate the theoretical advances. The design of reference governor schemes for three systems arising in practical applications is also presented. The first scheme enforces compressor surge constraints for turbocharged gasoline engines, ensuring that the compressor does not surge. The second scheme is designed for an airborne wind energy system that is subject to various flight constraints including constraints on altitude and angle of attack. The third and final scheme is designed for the constrained control of spacecraft attitude, whose discrete-time dynamics evolve on the configuration space SO(3). In the case of the first application, experimental vehicle results are reported that show successful avoidance of surge. For the other two applications, nonlinear model simulation results are reported that show enforcement of system constraints.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113518/1/kalabic_1.pd

Fixed-Point Constrained Model Predictive Control of Spacecraft Attitude

The paper develops a Model Predictive Controller for constrained control of spacecraft attitude with reaction wheel actuators. The controller exploits a special formulation of the cost with the reference governor like term, a low complexity addition of integral action to guarantee offset-free tracking of attitude set points, and an online optimization algorithm for the solution of the Quadratic Programming problem which is tailored to run in fixed-point arithmetic. Simulations on a nonlinear spacecraft model demonstrate that the MPC controller achieves good tracking performance while satisfying reaction wheel torque constraints. The controller also has low computational complexity and is suitable for implementation in spacecrafts with fixed-point processors

Advances in Constrained Spacecraft Relative Motion Planning

This dissertation considers Spacecraft Relative Motion Planning (SRMP), where maneuvers are planned for one or more spacecraft to execute in close proximity to obstacles or to each other. The need for this type of maneuver planning has grown in recent years as the space environment becomes more cluttered, and the focus on space situational awareness increases. In SRMP, maneuvers must accommodate non-linear and non-convex constraints, be robust to disturbances, and be implementable on-board spacecraft with limited computational capabilities. Consequently, many standard optimization or path planning techniques cannot be directly applied to SRMP. In this dissertation, three novel SRMP techniques are developed and simulations are presented to illustrate the implementation of each method. Firstly, an invariance-based SRMP technique is proposed. Maneuvers are planned to transition a spacecraft between specified natural motion trajectories, which require no control to follow, while avoiding obstacles and accommodating minimum and maximum actuation limits. The method is based on a graph search applied to a ``virtual net'' with nodes corresponding to natural motion trajectories. Adjacency rules in the virtual net are based on safe positively invariant tubes built around each natural motion trajectory. These rules guarantee safe transitions between adjacent natural motion trajectories, even when set-bounded disturbances are present. Procedures to construct the safe positively invariant tubes and the virtual net are developed. Methods to reduce calculations are proposed and shown to significantly reduce computation time, with tradeoffs related to maneuver planning flexibility. Secondly, a SRMP technique is developed for the specific problem of satellite inspection. In this setting, an inspector spacecraft maneuvers to gather information about a target spacecraft. An information collection model is developed and used to construct a rapidly computable analytical control law based on the local gradient of the information rate. This control law drives the inspector spacecraft on a path along which the rate of information collection is strictly increasing. To ensure constraint satisfaction, the local gradient control law is combined with a state feedback control law, and rules are developed to govern switches between the two controllers. The method is shown to be effective in generating trajectories to gather information about a specified target point while accommodating disturbances. Finally, a control strategy is proposed to generate a formation containing an arbitrary number of vehicles. This strategy is based on an add-on predictive control mechanism known as a parameter governor. Parameter governors work by modifying parameters, such as gains or offsets, in a nominal closed-loop system to enforce constraints and improve performance. The parameter governor is first developed in a general setting, using generic non-linear system dynamics and an arbitrary formation design. Required calculations are minimized, and non-convex constraints are accommodated through use of a parameter update strategy based on graph colorability theory, and by limiting parameter values to a discrete set. A convergence analysis is presented, proving that under reasonable assumptions, the parameter governor is guaranteed to generate the desired formation. Two specific parameter governors, referred to as the Scale Shift Governor and Time Shift Governor, are proposed and applied to generate formations of spacecraft. These parameter governors enforce constraints by modifying either scale- or time-shifts applied to the target trajectory provided to each spacecraft in formation. Simulation case studies show the effectiveness of each method and demonstrate robustness to disturbances.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145795/1/gfrey_1.pd

AUTONOMOUS SPACECRAFT RENDEZVOUS WITH A TUMBLING OBJECT: APPLIED REACHABILITY ANALYSIS AND GUIDANCE AND CONTROL STRATEGIES

Rendezvous and proximity operations are an essential component of both military and commercial space missions and are rising in complexity. This dissertation presents an applied reachability analysis and develops a computationally feasible autonomous guidance algorithm for the purpose of spacecraft rendezvous and proximity maneuvers around a tumbling object. Recent advancements enable the use of more sophisticated, computation-based algorithms, instead of traditional control methods. These algorithms are desirable for autonomous applications due to their ability to optimize performance and explicitly handle constraints (e.g., safety, control limits). In an autonomous setting, however, some important questions must be answered before an algorithm implementation can be realized. First, the feasibility of a maneuver is addressed by analyzing the fundamental spacecraft relative dynamics. Particularly, a set of initial relative states is computed and visualized from which the desired rendezvous state can be reached (i.e., backward reachability analysis). Second, with the knowledge that a maneuver is feasible, the Model Predictive Control (MPC) framework is utilized to design a stabilizing feedback control law that optimizes performance and incorporates constraints such as control saturation limits and collision avoidance. The MPC algorithm offers a computationally efficient guidance strategy that could potentially be implemented in real-time on-board a spacecraft.http://archive.org/details/autonomousspacec1094560364Major, United States Air ForceApproved for public release; distribution is unlimited

Extremum-Seeking Guidance and Conic-Sector-Based Control of Aerospace Systems

This dissertation studies guidance and control of aerospace systems. Guidance algorithms are used to determine desired trajectories of systems, and in particular, this dissertation examines constrained extremum-seeking guidance. This type of guidance is part of a class of algorithms that drives a system to the maximum or minimum of a performance function, where the exact relation between the function's input and output is unknown. This dissertation abstracts the problem of extremum-seeking to constrained matrix manifolds. Working with a constrained matrix manifold necessitates mathematics other than the familiar tools of linear systems. The performance function is optimized on the manifold by estimating a gradient using a Kalman filter, which can be modified to accommodate a wide variety of constraints and can filter measurement noise. A gradient-based optimization technique is then used to determine the extremum of the performance function. The developed algorithms are applied to aircraft and spacecraft. Control algorithms determine which system inputs are required to drive the systems outputs to follow the trajectory given by guidance. Aerospace systems are typically nonlinear, which makes control more challenging. One approach to control nonlinear systems is linear parameter varying (LPV) control, where well-established linear control techniques are extended to nonlinear systems. Although LPV control techniques work quite well, they require an LPV model of a system. This model is often an approximation of the real nonlinear system to be controlled, and any stability and performance guarantees that are derived using the system approximation are usually void on the real system. A solution to this problem can be found using the Passivity Theorem and the Conic Sector Theorem, two input-output stability theories, to synthesize LPV controllers. These controllers guarantee closed-loop stability even in the presence of system approximation. Several control techniques are derived and implemented in simulation and experimentation, where it is shown that these new controllers are robust to plant uncertainty.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143993/1/aexwalsh_1.pd