The design of feedback control laws for discrete models of flexible structures is addressed. Two strategies are proposed. First, a parameter optimization method is used, in which the behavior of the controller is described by a performance measure and numerically optimized. A second method, based on continuation maps, allows several performance criterion to be met. These performance measures are quite general in nature; they may be functions of eigenvalues, eigenvectors, sensitivities, and other mission specific quantities. A model of a cantilevered flexible beam is developed and used to demonstrate capabilities and problems with the design methods. / M.S.

A general aerodynamic model for two-dimensional inviscid flows is developed. This model is used to simulate wakes and blade-vortex interaction. This model is also coupled with dynamics and feedback controls to simulate flutter and flutter suppression. The flow is assumed to be attached and incompressible. The present aerodynamic model is based on a vorticity-panel method coupled with vortex dynamics. The present aerodynamic model is used to simulate some actual experiments: wakes generated by oscillating airfoils and blade-vortex interactions in which one airfoil is placed in or near the wake generated by another oscillating airfoil upstream. The present numerical model predicts wake structures, vorticity strength, and velocity profiles across the wake that compare very favorably with the experiments. The present numerical results of the blade-vortex interaction show good agreement with the experiments when separation does not occur. If separation is involved, the present model fails to accurately simulate blade-vortex interaction because separation is not considered in the present model. Flutter is studied by means of numerical simulations. In an incompressible flow, an airfoil is mounted on an elastic support. The airfoil can pitch (rotate) and plunge (translate vertically). The dynamic equations that describe this two-degree-of-freedom motion are general and nonlinear. To calculate the aerodynamic loads on the airfoil, the aerodynamic model is coupled with this dynamic model. The motions of the airfoil and flowing air are calculated interactively and simultaneously. The coupled aerodynamic/dynamic model accurately predicts the critical flutter speed of the freestream, the speed at which the motion of the airfoil grows spontaneously. The contributions of the phase difference and energy exchange to the flutter motion are discussed. The effect of the static angle of attack on the critical flutter speed is investigated. Also the effect of the nonlinearity of the elastic support (cubic term in the hardening spring) is studied. A feedback control is coupled with aerodynamics/dynamics to suppress the flutter motion of the airfoil. A flap is added at the trailing edge of the airfoil as a control surface, and its deflection (rotation) about the hinge point is commanded by a feedback-control law. The flow, airfoil, elastic support, and control device are considered as one system, and the flow, the motions of the airfoil, and the flap deflections are calculated simultaneously. With carefully designed control laws, oscillations that would be unstable (i.e., growing) without control are suppressed. The numerical results show different control variables can be used. The model of aerodynamics/dynamics/control is also used to successfully suppress the response to a wind gust with the same control laws as used for the suppression of flutter. / Ph. D.

A feedback design procedure known as extended linearization consists in replacing a mathematical model of a nonlinear dynamical system with its family of linearizations, parametrized by the operating point, and then combining feedback gains designed for representatives of the family into a single nonlinear feedback law. The principles of the procedure, applicable both to lumped-parameter and distributed-parameter systems, are discussed at the outset. The development shows limits on feedback laws that can be designed, as well as nonuniqueness of solutions, inherent in the method. / Ph. D.

The analysis, finite element approximation, and numerical simulation of some control problems associated with fluid flows are considered. First, we consider a coupled solid/fluid temperature control problem. This optimization problem is motivated by the desire to remove temperature peaks, i.e., "hot spots", along the bounding surface of containers of fluid flows. The heat equation of the solid container is coupled to the energy equation for the fluid. Control is effected by adjustments to the temperature of the fluid at the inflow boundary. We give a precise statement of the mathematical model, prove the existence and uniqueness of optimal solutions, and derive an optimality system. We study a finite element approximation and provide rigorous error estimates for the error in the approximate solution of the optimality system. We then develop and implement an iterative algorithm to compute the approximate solution. Second, a computational study of the feedback control of the magnitude of the lift in flow around a cylinder is presented. The uncontrolled flow exhibits an unsymmetric Karman vortex street and a periodic lift coefficient. The size of the oscillations in the lift is reduced through an active feedback control system. The control used is the injection and suction of fluid through orifices on the cylinder; the amount of fluid injected or sucked is determined, through a simple feedback law, from pressure measurements at stations along the surface of the cylinder. The results of some computational experiments are given; these indicate that the simple feedback law used is effective in reducing the size of the oscillations in the lift. Finally, some boundary value problems which arise from a feedback control problem are considered. We give a precise statement of the mathematical problems and then prove the existence and uniqueness of solutions to the boundary value problems for the Laplace and Stokes equations by studying the boundary integral equation method. / Ph. D.

Most existing environmental chambers cannot simulate dynamically changing environmental conditions. Hence there is a need for a dynamically controlled artificial environment for plant studies. This project demonstrates the control of temperature, humidity and SO₂ concentration in a Continuous Stirred Tank Reactor (CSTR) system using feedback control through a computer. An IBM-PC was connected to the measuring instrumentation and control equipment through a data acquisition and control system. Temperature and humidity were controlled by an ON-OFF control scheme. Sulfur dioxide concentration was controlled by means of a modified proportional derivative control algorithm. The system is capable of achieving a wide range of temperatures (7°C to 40°C), humidities (30% to 97%), and SO₂ concentrations. Temperature is maintained within ±0.5°C of the desired value and humidity is controlled within ±4% of the desired value. Sulfur dioxide concentration is kept within ±10% of the desired concentration. It was found that as humidity increases, the supply rate of SO₂ must be increased to maintain a given concentration. Software response time is slow. This causes time lags in the modification of the controlled parameters to achieve desired values. The heating and cooling characteristics of the system can be improved by better insulation of the chamber walls. The system demonstrates that computerized feedback control is practical for application to controlling environmental parameters in a fumigation chamber. / Master of Science

The concept of using heat flux measurements to provide the input for a feedforward temperature control loop is investigated. The feedforward loop is added to proportional and integral feedback control to increase the speed of the response to a disturbance. Comparison is made between the feedback and the feedback plus feedforward control laws. The control law with the feedforward control loop is also compared to the conventional approach of adding derivative control to speed up the system response to a disturbance. The concept was tested using a simple flat plate heated on one side and exposed to a step change in the convective heat loss on the other side. A controller was constructed using an analog computer to compare the feedforward and feedback approaches. The conventional control approach was tested using a commercial temperature controller. The feedback and feedforward approaches were also simulated. The results showed that the feedforward control approach produced significant improvements in the response to the disturbance. The integral of the squared error between the setpoint and actual temperature was reduced by approximately 90 percent by the addition of feedforward control to the feedback control. The maximum temperature deviation from the setpoint was also reduced by 70 percent with the addition of feedforward control. Qualitative agreement was obtained between the experimental results and the computer simulations. The conventional approach of adding derivative control to the proportional and integral control showed an increase of 20 percent in the integral of the squared error, but offered no significant improvement in the maximum temperature deviation. The addition of derivative control also caused the stability of the system to decrease, while the addition of feedforward had no adverse effects on the system stability. The concept of using heat flux measurements for feedforward control was successfully demonstrated by both simulations and experiments. / Master of Science

The design of controllers for structural systems, particularly those associated with large space structures, has received a considerable amount of attention in the past few years. The usual approach to designing these controllers is to apply modern control theory to a reduced linear system obtained from finite element analysis or from a truncated modal analysis. In most of these designs, the sensor signal must be processed to separate out the contributions from each mode so that it may be sent to the appropriate actuators. The analysis presented here, on the other hand, obtains exact solutions for a selected set of sensor and actuator positions for simple structural elements. Sensor signals are fed back directly to the actuators with appropriate gains. The method of analysis is that of classical control theory using Laplace transforms and the associated open and closed-loop transfer functions. Single-input-single-output feedback control is applied to various flexible cable and beam configurations. Root-loci for various values of gain are constructed and the system characteristics and the global system stability are determined. Although the procedure outlined above can be carried out for basic structural elements, more complex structures and control configurations are synthesized using the dynamic stiffness matrix method. With this method, the exact relationships of the basic elements can be combined to allow analysis of multi-input-multi-output control of more complex structures. Using this approach, examples for flexible cable and beam configurations are presented. It was found that exact solutions can be obtained using a finite number of sensors and actuators. It was also determined that a single co-located sensor-actuator at the boundary of a fixed-free cable or beam can control all the vibrational modes of the cable or beam. Also, pure signals from a perfect sensor can be used without any additional signal processing. The multi-input-multi-output investigation demonstrates that, even without cross-gain feedback, there is interaction between the sets of co-located sensor-actuator pairs. It appears that this interactive effect needs to be included in any multi-input-multi-output control design. By starting with fundamental elements of beams and cables, it was shown that reasonably sophisticated systems can be modeled. Finally, considerable insight is offered by analyzing the control of flexible structures using exact transfer function relationships. / Ph. D.

No description available.

A 6-Degree Of Freedom (DOF) numeric model and computer simulation along with the 1/10th scale physical model of the Rapidly Deployable Stable Platform (RDSP) are being developed at Florida Atlantic University in response to military needs for ocean platforms with improved sea keeping characteristics. The RDSP is a self deployable spar platform with two distinct modes of operation enabling long distance transit and superior seakeeping. The focus of this research is the development of a Dynamic Position (DP) and motion mitigation system for the RDSP. This will be accomplished though the validation of the mathematical simulation, development of a novel propulsion system, and implementation of a PID controller. The result of this research is an assessment of the response characteristics of the RDSP that quantifies the performance of the propulsion system coupled with active control providing a solid basis for further controller development and operational testing. / by Sean P. Marikle. / Thesis (M.S.C.S.)--Florida Atlantic University, 2009. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2009. Mode of access: World Wide Web.

Despite the fact that significant progress has been made on the research of these two problems for nonlinear systems for over two decades, many problems are still open. In particular, so far the output regulation problem is mainly handled by robust control approach. This approach has certain fundamental limitations and cannot handle the following three cases. (1) The control direction is unknown. (2) The boundaries of system uncertainties are unknown. (3) The exosystem is not known precisely. / Stabilization and output regulation are two fundamental control problems. The output regulation problem aims to design a feedback controller to achieve asymptotic tracking of a class of reference inputs and rejection of a class of disturbances in an uncertain system while maintaining the internal stability of the closed-loop system. Thus the output regulation problem is more demanding than the stabilization problem. Nevertheless, under some assumptions, the output regulation problem can be converted into a stabilization problem for a well defined augmented system and the solvability of the stabilization problem for this augmented system implies that of the output regulation problem for the original plant. Therefore, to a large extent, the study of the stabilization problem will also lay a foundation for that of the output regulation problem. / To handle these problems and overcome the shortcomings of the robust control approach, in this thesis, we have incorporated the adaptive control approach with the robust control approach. Both stabilization problem and output regulation problem are considered for two important classes of nonlinear systems, namely, the output feedback systems and lower triangular systems. The main contributions are summarized as follows. (1) The adaptive output regulation problem for nonlinear systems in output feedback form is addressed without knowing the control direction. The Nussbaum gain technique is incorporated with the robust control technique to handle the unknown control direction and the nonlinearly parameterized uncertainties in the system. To overcome the dilemma caused by the unknown control direction and the nonlinearly parameterized uncertainties, we have adopted a Lyapunov direct method to solve the adaptive output regulation problem. (2) The adaptive stabilization problem for nonlinear systems in lower triangular form is solved when both static and dynamic uncertainties are present and the control direction is unknown. Technically, the presence of dynamic uncertainty has made the stabilization problem more difficult than the previous work. We have managed to combine the changing supply rate technique and the Nussbaum gain technique to deal with this difficulty. The result is also applied to solve the output regulation problem for lower triangular systems with unknown control direction. (3) The adaptive output regulation problem for nonlinear systems in output feed-back form with unknown exosystem is studied. The adaptive control technique is applied to estimate the unknown parameter results from the unknown exosystem. The condition under which the parameter estimation converges to its real value is also discussed. Further, the global disturbance rejection problem for nonlinear systems in lower triangular form is solved by formulating the unknown external disturbance as a signal produced by an unknown exosystem. (4) The theoretical results have been applied to several typical control systems leading to the solution of some long standing open problems. Some exemplified applications are: (a) Global adaptive stabilization of Chua's circuit without knowing the control direction; (b) Global output synchronization of the Chua's circuit and the harmonic system; (c) Global adaptive disturbance rejection problem of the Duffing's system with all parameters unknown; (d) Global adaptive output regulation of Van der Pol oscillator with an uncertain exosystem. / Liu, Lu. / Adviser: Jie Huang. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3693. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 204-214). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.