The feasibility of applying active control theory to control both the transient and steady state response of a two cable-stayed bridge has been investigated. The bridge has been modeled as a two degree freedom system in bending and torsion, excited by both buffeting and self-excited loads. The existing suspension cables have been used as active tendons by which the control forces are applied to the bridge deck at the points of the anchorage. The control force from each suspension cable is actuated through a hydraulic-servomechanism which is regulated by the sensed motion of the bridge deck at the anchorage of the cable. Stability and steady state response analyses have been presented for both controlled and uncontrolled motion. The power requirement for the control devices has been derived. Finally, numerical examples have been worked out to demonstrate the feasibility of the derived theory for two cable-stayed bridges. / Ph. D.

This dissertation presents a discussion of the asymptotic behavior and estimation structure of the H_∞ central controllers in terms of the well-known behavior of the LQG controller and gives some insight into the physics of the H_∞ controller that is often presented in an unclear manner in the current literature. The connections to LQ game theory that underlie this confusion are discussed. Augmented systems that are typically used in disturbance rejection problems are also analyzed. Additionally, a controlled output equation for disturbance rejection is developed based on the physics of the problem rather than the typical ad hoc approaches of the past. These controlled output equations are also appropriate for LQG compensators. In order to verify the proposed approach, an experiment in harmonic and narrowband disturbance rejection using a simply supported steel plate is presented. Discrete-time LQG, and continuous-time H_∞ and LQG controllers that have been transformed to discrete-time are used to determine the attainable performance of each approach. The results indicate that the H_∞ controller provides more damping than either LQG approach and that discrete-time design procedures are necessary for maximum disturbance rejection. / Ph. D.

Robert Agnew proposed a new version of strain theory in 1992. In this article, Agnew argued that strain is not only a result of the blocked opportunity to achieve goals as Merton had argued, but that strain also results from the removal of positively valued stimuli and the presence of negative stimuli. With such a theory, criminologist had focused on how this may explain juvenile delinquency. Yet very little attention was given to how this may affect adult criminality as well. Similarly, Hirschi (1969) presented social control theory as a means of describing the causes of juvenile delinquency. While these theories have been repeatedly tested and supported with respect to delinquency, they have rarely been used to describe adult criminality. This paper intends to compare the utility of Agnew's general strain theory and Hirschi's control theory in explaining the criminal behavior of fathers. For general strain theory, it is predicted that fathers who have either high contact and low relationship quality or who have low contact and high relationship quality will have significantly higher criminal activity than those who have high contact and relationship quality or low contact and relationship quality. Conversely, social control theory predicts that fathers who have low relationship qualities with their children are more likely to commit criminal acts. This paper aims to ascertain which of these hypotheses is more accurate. / Master of Science

In this paper we consider two separate approaches to the development of finite dimensional control systems for approximating distributed parameter models. One method uses the “standard finite element” approximations to construct the basic system matrices. The resulting system can then be balanced by any of several balancing algorithms. The second method is based on truncating infinite dimensional balanced realizations of the input-output map. Both approaches are applied to a control problem governed by the heat equation. We present a comparison of the resulting finite dimensional models. / Ph. D.

The problem of reorienting a spacecraft to acquire a moving target is investigated. The spacecraft is modeled as a rigid body with N axisymmetric wheels controlled by axial torques, and the kinematics are represented by Modified Rodriques Parameters. The trajectory, denoted the reference trajectory, is one generated by a virtual spacecraft that is identical to the actual spacecraft. The open-loop reference attitude, angular velocity, and angular acceleration tracking commands are constructed so that the solar panel vector is perpendicular to the sun vector during the tracking maneuver. We develop a nonlinear feedback tracking control law, derived from Lyapunov stability and control theory, to provide the control torques for target tracking. The controller makes the body frame asymptotically track the reference motion when there are initial errors in the attitude and angular velocity. A spacecraft model, based on the X-ray Timing Explorer spacecraft, is used to demonstrate the effectiveness of the Lyapunov controller in tracking a given target. / Master of Science

The subject of this thesis is the motion planning algorithm known as the continuation method. To solve motion planning problems, the continuation method proceeds by lifting curves in state space to curves in control space; the lifted curves are the solutions of special initial value problems called path-lifting equations. To validate this procedure, three distinct obstructions must be overcome. The first obstruction is that the endpoint maps of the control system under study must be twice continuously differentiable. By extending a result of A. Margheri, we show that this differentiability property is satisfied by an inclusive class of time-varying fully nonlinear control systems. The second obstruction is the existence of singular controls, which are simply the singular points of a fixed endpoint map. Rather than attempting to completely characterize such controls, we demonstrate how to isolate control systems for which no controls are singular. To this end, we build on the work of S. A. Vakhrameev to obtain a necessary and sufficient condition. In particular, this result accommodates time-varying fully nonlinear control systems. The final obstruction is that the solutions of path-lifting equations may not exist globally. To study this problem, we work under the standing assumption that the control system under study is control-affine. By extending a result of Y. Chitour, we show that the question of global existence can be resolved by examining Lie bracket configurations and momentum functions. Finally, we show that if the control system under study is completely unobstructed with respect to a fixed motion planning problem, then its corresponding endpoint map is a fiber bundle. In this sense, we obtain a necessary condition for unobstructed motion planning by the continuation method. / Thesis (Ph.D, Chemical Engineering) -- Queen's University, 2012-12-18 20:53:43.272

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.

Covariance assignment theory, introduced in the late 1980s, provided the only means to directly control the steady-state error properties of a linear system subject to Gaussian white noise and parameter uncertainty. This theory, however, does not extend to control of the transient uncertainties and to date there exist no practical engineering solutions to the problem of directly and optimally controlling the uncertainty in a linear system from one Gaussian distribution to another. In this thesis I design a dual-mode Receding Horizon Controller (RHC) that takes a controllable, deterministic linear system from an arbitrary initial covariance to near a desired stationary covariance in finite time. The RHC solves a sequence of free-time Optimal Control Problems (OCP) that directly controls the fundamental solution matrices of the linear system; each problem is a right-invariant OCP on the matrix Lie group GLn of invertible matrices. A terminal constraint ensures that each OCP takes the system to the desired covariance. I show that, by reducing the Hamiltonian system of each OCP from T?GLn to gln? x GLn, the transversality condition corresponding to the terminal constraint simplifies the two-point Boundary Value Problem (BVP) to a single unknown in the initial or final value of the costate in gln?. These results are applied in the design of a dual-mode RHC. The first mode repeatedly solves the OCPs until the optimal time for the system to reach the de- sired covariance is less than the RHC update time. This triggers the second mode, which applies covariance assignment theory to stabilize the system near the desired covariance. The dual-mode controller is illustrated on a planar system. The BVPs are solved using an indirect shooting method that numerically integrates the fundamental solutions on R4 using an adaptive Runge-Kutta method. I contend that extension of the results of this thesis to higher-dimensional systems using either in- direct or direct methods will require numerical integrators that account for the Lie group structure. I conclude with some remarks on the possible extension of a classic result called Lie?s method of reduction to receding horizon control.

Thesis (Ph.D.)--Aerospace Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Haddad, Wassim; Committee Member: Feron, Eric; Committee Member: JVR, Prasad; Committee Member: Taylor, David; Committee Member: Tsiotras, Panagiotis