Search

The linear variable stability Transfer Function Simulation Model (TFSM), inspired by the United States Air Force's NF-16D Variable stability In-flight Simulator Test Aircraft (VISTA) and created by Henrik Pettersson, can simulate any desired aircraft. The TFSM represents a non-linear aircraft model with its stability parameters - a collection of gain constants, time constants, damping ratios, and natural frequencies. Stability parameters for aircraft generally fall into two uncoupled modes: longitudinal and lateral-directional. Unfortunately, flight tests using the TFSM exhibited undesired lateral-directional coupling in the longitudinal responses. An S-turn maneuver, formation flight test, and an uncontrolled simulation with an initial bank angle of 60 degrees were the foundation for the investigation to pinpoint the TFSM's errors. The flight tests and subsequent analysis showed that although this model is highly versatile, it has three fundamental problems. First, the original creation of the TFSM incorrectly assumed that the time rate of change for the pitch angle (in the local-horizontal reference frame) is equal to the body-axis pitch-rate for all flight conditions. Second, the TFSM's dynamics do not contain gravity terms. Third, the TFSM cannot generate the angular rates needed in a turn. Integrating the aircraft's pitch, roll, and yaw angles with the equations of motion for aircraft fixed the first problem. Unfortunately, resolving this issue only intensified the second two problems. The results from this thesis show that the last two problems are part of the TFSM and cannot be fixed explicitly. Master of Science

Attitude control laws that use control moment gyros (CMGs) and momentum wheels are derived with nonlinear techniques. The control laws command the CMGs to provide rapid angular acceleration and the momentum wheels to reject tracking and initial condition errors. Numerical simulations of derived control laws are compared. A trend analysis is performed to examine the benefits of the derived controllers. We describe the design of a CMG built using commercial off-the-shelf (COTS) equipment. A mixed attitude control strategy is implemented on the spacecraft simulator at Virginia Tech. Master of Science

An Open-Source, extensible spacecraft simulation and modeling (Open-SESSAME) framework was developed with the aim of providing to researchers the ability to quickly test satellite algorithms while allowing them the ability to view and extend the underlying code. The software is distributed under the GPL (General Public License) and the package's extensibility allows users to implement their own components into the libraries, investigate new algorithms, or tie in existing software or hardware components for algorithm and flight component testing. This thesis presents the purpose behind the development of the framework, the software design architecture and implementation, and a roadmap of the future for the software package. Master of Science

Methods for allocating redundant controls for systems with four or more objectives are studied. Previous research into aircraft control allocation has focused on allocating control effectors to provide commands for three rotational degrees of freedom. Redundant control systems have the capability to allocate commands for a larger number of objectives. For aircraft, direct force commands can be applied in addition to moment commands. When controls are limited, constraints must be placed on the objectives which can be achieved. Methods for meeting commands in the entire set of of achievable objectives have been developed. The Bisecting Edge Search Algorithm has been presented as a computationally efficient method for allocating controls in the three objective problem. Linear programming techniques are also frequently presented. This research focuses on an effort to extend the Bisecting Edge Search Algorithm to handle higher numbers of objectives. A recursive algorithm for allocating controls for four or more objectives is proposed. The recursive algorithm is designed to be similar to the three objective allocator and to require computational effort which scales linearly with the controls. The control allocation problem can be formulated as a linear program. Some background on linear programming is presented. Methods based on five formulations are presented. The recursive allocator and linear programming solutions are implemented. Numerical results illustrate how the average and worst case performance scales with the problem size. The recursive allocator is found to scale linearly with the number of controls. As the number of objectives increases, the computational time grows much faster. The linear programming solutions are also seen to scale linearly in the controls for problems with many more controls than objectives. In online applications, computational resources are limited. Even if an allocator performs well in the average case, there still may not be sufficient time to find the worst case solution. If the optimal solution cannot be guaranteed within the available time, some method for early termination should be provided. Estimation of solutions from current information in the allocators is discussed. For the recursive implementation, this estimation is seen to provide nearly optimal performance. Ph. D.

Simulation, whether in-flight or ground-based, is an invaluable tool for testing and evaluating aircraft. Classically, a simulation model is specific to a single particular airframe, only able to model those flying characteristics. Vast information can be gained from a simulation that is able to model a wide range of aircraft, through a comparison of the performance of these aircraft. Such a variable stability simulation model was created based on 46 stability parameters, including natural frequencies, damping ratios, time constants, and gains. The simulation was obtained using transfer functions representing the aircraft state responses to control inputs. These transfer functions were converted into state space systems used to create the linear equations for the model. The model was first developed as a desktop simulation and then converted for use with the Virginia Tech's 2F122A flight simulator. This conversion required a simple dynamic inversion of the body axis force and moment terms. To reduce the error in these terms, a model following scheme was incorporated. A series of canned inputs and real-time pilot-in-the-loop tests were flown to evaluate the variable stability model. Results in this paper have demonstrated the successful creation of a variable stability simulation model. Master of Science

The recent addition of autonomous formation flying spacecraft to the world's satellite fleet provides new motivation to study feedback control techniques. In this thesis, we develop nonlinear orbit control laws for use in spacecraft orbital maneuvers, and spacecraft formation flying. We apply these new control laws to a number of sample maneuvers, including formation stablishment and formation keeping maneuvers for NASA-Goddard's Leonardo-BRDF formation, and coupled orbit, and attitude maneuvers for HokieSat, a spacecraft designed, and built by students at Virginia Tech to fly in the Ionospheric Observation Nanosatellite Formation (ION-F). To provide target orbit states for feedback control, we develop and apply an algorithm to calculate a formation master orbit representing the geometric center of the formation. We also define a new technique for choosing orbital element feedback gains which appropriately scales the gains for orbit maintenance, and provides an excellent starting point for gain optimization. The orbital element feedback control law, augmented by mean motion control, and applied with appropriate gains, forces asymptotic convergence to a spacecraft target orbit, for a large variety of spacecraft maneuvers. Master of Science

A comparison of two methods to deal with allocating controls for unattainable moments in an aircraft was performed using a testbed airframe that resembled an F/A-18 with a large control effector suite. The method of preserving the desired moment direction to deal with unattainable moments is currently used in a specific control allocator. A new method of prioritizing the pitch axis is compared to the moment-direction preservation. Realtime piloted simulations are completed to evaluate the characteristics and performance of these methods. A direct comparison between the method of preserving the moment direction by scaling the control solution vector and prioritizing the pitching moment axis is performed for a specific case. Representative maneuvers are flown with a highly unstable airframe to evaluate the ability to achieve the specific task. Flight performance and pilot interpretation are used to evaluate the two methods. Pilot comments and performance results favored the method of pitch-axis prioritization. This method provided favorable flight characteristics compared to the alternative method of preserving the moment direction for the specific tasks detailed in this paper. NOTE: An updated copy of this ETD was added on 09/28/2010. Master of Science

The problem of magnetic control for three-axis stability of a spacecraft is examined. Two controllers, a proportional-derivative controller and a constant coefficient linear quadratic regulator, are applied to the system of equations describing the motion of the spacecraft. The stability of each is checked for different spacecraft configurations through simulations, and the results for gravity-gradient stable and non gravity-gradient stable spacecraft are compared. An optimization technique is implemented in an attempt to obtain the best performance from the controller. For every spacecraft configuration, a set of gains can be chosen for implementation in the controller that stabilizes the linear and nonlinear equations of motion for the spacecraft. Master of Science

This thesis presents an approximate solution of second order relative motion equations. The equations of motion for a Keplerian orbit in spherical coordinates are expanded in Taylor series form using reference conditions consistent with that of a circular orbit. Only terms that are linear or quadratic in state variables are kept in the expansion. A perturbation method is employed to obtain an approximate solution of the resulting nonlinear differential equations. This new solution is compared with the previously known solution of the linear case to show improvement, and with numerical integration of the quadratic differential equation to understand the error incurred by the approximation. In all cases, the comparison is made by computing the difference of the approximate state (analytical or numerical) from numerical integration of the full nonlinear Keplerian equations of motion. Master of Science

We investigate the relative equilibria of a gyrostat with a spring-mass-dashpot damper to gain new insights into the dynamics of spin-stabilized satellites. The equations of motion are developed using a Newton-Euler approach, resulting in equations in terms of system momenta and damper variables. Linear and nonlinear stability methods produce stability conditions for simple spins about the nominal principal axes. We use analytical and numerical methods to explore system equilibria, including the bifurcations that occur for varying system parameters for varying rotor momentum and damper parameters. The equations and bifurcations for zero rotor absolute angular momentum are identical to those for a rigid body with an identical damper. For the more general case of non-zero rotor momentum, the bifurcations are complex structures that are perturbations of the zero rotor momentum case. We examine the effects of spring stiffness, damper position, and inertia properties on the global equilibria. Stable equilibria exist for many different spin axes, including some that do not lie in the nominally principal planes. Some bifurcations identify regions where a jump phenomenon is possible. We use Liapunov-Schmidt reduction to determine an analytic relationship between parameters to determine if the jump phenomenon occurs. Bifurcations of the nominal gyrostat spin are characterized in parameter space using two-parameter continuation and the Liapunov-Schmidt reduction technique. We quantify the effects of rotor or damper alignment errors by adding small displacements to the alignment vectors, resulting in perturbations of the bifurcations for the standard model. We apply the global bifurcation results to several practical applications. We relate the general set of all possible equilibria to specific equilibria for dual-spin satellites with typical parameters. For systems with tuned dampers, where the natural frequency of the spring-mass-damper matches the gyrostat precession frequency, we show numerically and analytically that the existence of certain equilibria are related to the damper tuning condition. Finally, the global equilibria and bifurcations for varying rotor momentum provide a unique perspective on the dynamics of simple rotor spin-up maneuvers. Ph. D.

A new laser based flow interrogation system, capable of simultaneous measurement of planar three-component velocity data, was constructed and tested. The Virginia Tech Doppler Global Velocimeter (DGV) system was designed for use in the Virginia Tech Stability Wind Tunnel as a tool for investigating complex three-dimensional separated flow regions. The systems was designed for robustness, ease of use, and for acquisition of low uncertainty velocity data. A series of tests in the Stability Tunnel were conducted to determine the how well the new DGV system met these goals. Extensive calibration tests proved the system is capable of measuring the frequency shifts of scattered laser light, and therefore velocity. However, equipment failures and inadequate flow seed density prevented accurate velocity measurements in the separated wake region behind a 6:1 prolate spheroid. Detailed uncertainty analysis techniques demonstrated that, under the proper conditions, the system is capable of making velocity measurements with approximately +/- 2m/s uncertainty. Master of Science

Human operators often employ discontinuous or "bang-bang" control strategies when performing large-amplitude acquisition tasks. The current study applies Variable Structure Control (VSC) techniques to model human operator behavior during acquisition tasks. The result is a coupled, multi-input model replicating the discontinuous control strategy. In the VSC formulation, a switching surface is the mathematical representation of the operator's control strategy. The performance of the Variable Strategy Model (VSM) is evaluated by considering several examples, including the longitudinal control of an aircraft during the visual landing task. The aircraft landing task becomes an acquisition maneuver whenever large initial offsets occur. Several different strategies are explored in the VSM formulation for the aircraft landing task. First, a switching surface is constructed from literal interpretations of pilot training literature. This approach yields a mathematical representation of how a pilot is trained to fly a generic aircraft. This switching surface is shown to bound the trajectory response of a group of pilots performing an offset landing task in an aircraft simulator study. Next, front-side and back-side landing strategies are compared. A back-side landing strategy is found to be capable of landing an aircraft flying on either the front side or back side of the power curve. However, the front-side landing strategy is found to be insufficient for landing an aircraft flying on the back side. Finally, a more refined landing strategy is developed that takes into the account the specific aircraft's dynamic characteristics. The refined strategy is translated back into terminology similar to the existing pilot training literature. Ph. D.

Modern aircraft are capable of recording hundreds of parameters during flight. This fact not only facilitates the investigation of an accident or a serious incident, but also provides the opportunity to use the recorded data to predict future aircraft behavior. It is believed that, by analyzing the recorded data, one can identify precursors to hazardous behavior and develop procedures to mitigate the problems before they actually occur. Because of the enormous amount of data collected during each flight, it becomes necessary to identify the segments of data that contain useful information. The objective is to distinguish between typical data points, that are present in the majority of flights, and unusual data points that can be only found in a few flights. The distinction between typical and unusual data points is achieved by using classification procedures. In this dissertation, the application of classification procedures to flight data is investigated. It is proposed to use a Bayesian classifier that tries to identify the flight from which a particular data point came. If the flight from which the data point came is identified with a high level of confidence, then the conclusion that the data point is unusual within the investigated flights can be made. The Bayesian classifier uses the overall and conditional probability density functions together with a priori probabilities to make a decision. Estimating probability density functions is a difficult task in multiple dimensions. Because many of the recorded signals (features) are redundant or highly correlated or are very similar in every flight, feature selection techniques are applied to identify those signals that contain the most discriminatory power. In the limited amount of data available to this research, twenty five features were identified as the set exhibiting the best discriminatory power. Additionally, the number of signals is reduced by applying feature generation techniques to similar signals. To make the approach applicable in practice, when many flights are considered, a very efficient and fast sequential data clustering algorithm is proposed. The order in which the samples are presented to the algorithm is fixed according to the probability density function value. Accuracy and reduction level are controlled using two scalar parameters: a distance threshold value and a maximum compactness factor. Ph. D.

The need to design a controller that self-schedules itself during the flight of an aircraft has been an active area of research. New methods have been developed beyond the traditional gain-scheduling approach. One such design method leads to a linear parameter varying (LPV) controller that changes based on the real-time variation of system dynamics. Before such a controller can be designed, the system has to also be represented as an LPV system. The current effort proposes a LPV modeling technique that is inspired by an affine LPV modeling techniques found in recent research. The properties of the proposed modeling method are investigated and compared to the affine modeling technique. It is shown that the proposed modeling technique represents the actual system behavior more closely than the existing affine modeling technique. To study the effect of the two LPV modeling techniques on controller design, a linear quadratic regulator (LQR) controller using linear matrix inequality (LMI) formulation is designed. This control design method provides a measure of conservatism that is used to compare the controllers based on the different modeling techniques. An F-16 short-period model is used to implement the modeling techniques and design the controllers. It was found that the controller based on the proposed LPV modeling method is less conservative than the controller based on the existing LPV method. Interesting features of LMI formulation for multiple plant models were also discovered during the exercise. A stability robustness analysis was also conducted as an additional comparison of the performance of the controllers designed using the two modeling methods. A scalar measure, called the probability of instability, is used as a measure of robustness. It was found that the controller based on the proposed modeling technique has the necessary robustness properties even though it is less conservative than the controller designed based on the existing modeling approach. Master of Science

A mathematical model for the determination of the aerodynamic forces acting on an aircraft is presented. The mathematical model is based on the generalization of the idea of aerodynamically steady motions. One important use of these results is the determination of steady (time-invariant) aerodynamic forces and moments. Such aerodynamic forces can be determined using computer simulation by determining numerically the associated steady flows around the aircraft when it is moving along such generalized steady trajectories. The method required the extension of standard (inertial) CFD formulations to general non-inertial reference frames. Generalized Navier-Stokes and Euler equations have been derived. The formulation is valid for all ranges of Mach numbers including transonic flow. The method was implemented numerically for the planar case using the generalized Euler equations. The developed computer codes can be used to obtain numerical flow solutions for airfoils moving in general steady motions (i.e. circular motions). From these numerical solutions it is possible to determine the variation of the lift, drag and pitching moment with respect to the pitch rate at different Mach numbers and angles of attack. One of the advantages of the mathematical model developed here is that the aerodynamic forces become well-defined functions of the motion variables (including angular rates). In particular, the stability derivatives are associated with partial derivatives of these functions. These stability derivatives can be computed using finite differences or the sensitivity equation method. Ph. D.

Clusters of low-performance spacecraft flying in formation may provide enhanced performance over single high-performance spacecraft. This is especially true for remote sensing missions where interferometry or stereographic imaging may provide higher resolution data. The configurations of such formations vary during an orbit due to orbital dynamics, and over longer time scales due to perturbations. Selection of a configuration should be based on overall performance of the formation. In this thesis, performance measures are developed and evaluated based on integration over one orbit. The measures involve the angular separation of spacecraft, the distance between spacecraft, and an area-based measure of the separation of the spacecraft. Numerical techniques are employed to evaluate the performance measures to determine optimal scenarios for two formations. Simplifying assumptions are made to allow a closed-form analytic solution and the results are compared to those obtained numerically. Finally, the sensitivity of the measures to linearized propagation techniques is investigated. Master of Science

Steady and unsteady force and moment experiments were conducted in the Virginia Tech Stability wind tunnel using the Dynamic Plunge-Pitch-Roll (DyPPiR) model mount to perform rapid time-dependent,high-excursion maneuvers. The experiments were performed for a DARPA2 submarine model using three widely spaced 2-force-component loadcells and three tri-axial accelerometers to extract the aerodynamic loads. The DARPA2 model was tested with different body configurations in two different test sections. The body configurations for both the steady and unsteady experiments were the bare body hull, body with sail, body with stern appendages, and body with sail and stern appendages. Tests were done using trips on the bow and sail and with no trips. The bare hull configuration with no trips was the only body configuration tested in the six-foot-square test section with solid walls. All body configurations were tested in the six-foot-square test section with slotted walls that were used to reduce the blockage effects produced by the DyPPiR and model. The steady experiments were performed over a range of angles of attack and roll positions. Data were acquired through the series of angles the body encountered during the unsteady testing (-26° < ±

A comparison of two control allocation methods is performed utilizing the F-15 ACTIVE research vehicle. The control allocator currently implemented on the aircraft is replaced in the simulation with a control allocator that accounts for both control effector positions and rates. Validation of the performance of this Moment Rate Allocation scheme through real-time piloted simulations is desired for an aircraft with a high fidelity control law and a larger control effector suite. A more computationally efficient search algorithm that alleviates the timing concerns associated with the early work in Direct Allocation is presented. This new search algorithm, deemed the Bisecting, Edge-Search Algorithm, utilizes concepts derived from pure geometry to efficiently determine the intersection of a line with a convex faceted surface. Control restoring methods, designed to drive control effectors towards a ``desired" configuration with the control power that remains after the satisfaction of the desired moments, are discussed. Minimum-sideforce restoring is presented. In addition, the concept of variable step size restoring algorithms is introduced and shown to yield the best tradeoff between restoring convergence speed and control chatter reduction. Representative maneuvers are flown to evaluate the control allocator's ability to perform during realistic tasks. An investigation is performed into the capability of the control allocators to reconfigure the control effectors in the event of an identified control failure. More specifically, once the control allocator has been forced to reconfigure the controls, an investigation is undertaken into possible performance degradation to determine whether or not the aircraft will still demonstrate acceptable flying qualities. A direct comparison of the performance of each of the two control allocators in a reduced global position limits configuration is investigated. Due to the highly redundant control effector suite of the F-15 ACTIVE, the aircraft, utilizing Moment Rate Allocation, still exhibits satisfactory performance in this configuration. The ability of Moment Rate Allocation to utilize the full moment generating capabilities of a suite of controls is demonstrated. NOTE: (02/2011) An updated copy of this ETD was added after there were patron reports of problems with the file. Master of Science

Pilot Induced Oscillations (PIO) are described as pilot-aircraft dynamic couplings which can lead to instability in an otherwise stable system. Previous and ongoing research has attempted to explain, predict, and avoid such oscillations. In contrast to other research, this effort backs away from pilot models and PIO avoidance and focuses on the characteristics of the pilot before, during, and after a PIO. Often, PIO''s can be explained by limit cycles occurring in a non-linear system where the non-linearities cause a sustained, constant amplitude oscillation. The primary instigators in such a PIO are usually a non-linear element (i.e. rate limit saturation) and a trigger event (i.e. pilot mode switching or increased pilot gain). By performing analysis in the frequency domain, determining such oscillations becomes easier. Using spectrograms and power spectral density functions, the frequency content of a signal in the pilot-aircraft system can also be investigated. An F-14 flight test was recently performed where the hydraulic system was modified to determine the feasibility of trying to recover the aircraft (land on carrier) during such an extreme hydraulic failure. During testing, a severe PIO occurred because of the tight tracking task used during aerial refueling. While performing spectrograms and power spectral analysis, an increase in power concentration at the PIO frequency was observed. With a linear approximation of the F-14 aircraft dynamics, a closed-loop system containing the aircraft, actuator, and pilot dynamics is developed so that limit cycle analysis can be performed. With stable limit cycle solutions found possible, a pilot-in-the-loop simulation is performed to verify the pilot model used in limit cycle analysis. Using the flight test data, limit cycle analysis, and pilot-in-the-loop simulation, a connection between variation in pilot behavior and PIO predicted by the increase in power concentration is investigated. The resulting connection showed that an increase in pilot gain along with a transition from observing pitch attitude to pitch rate are the possible trigger events causing the PIO. The use of spectrograms as a PIO predictor is shown to be possible, provided the necessary calculations can be completed in real-time. Master of Science

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 realm of aircraft flight dynamics analysis reaches from local static stability to global dynamic behavior. It includes aircraft performance issues as well as structural concerns. In the particular aspect of dynamic motions of an aircraft and how we understand them, an alternate coordinate system will be introduced that will lend insight and simplification into the understanding of these dynamic motions. The main contribution of this coordinate system is that one can easily visualize how the instantaneous velocity vector relates to the instantaneous rotation vector, the angular rate vector of the aircraft. The out-of-control motion known as the Falling Leaf will be considered under the light of this new coordinate system. This motion is not well understood and can lead to loss of the aircraft and crew. Design guidelines will be presented to predict amplitude and frequency of the Falling Leaf. NOTE: (12/2009) An updated copy of this ETD was added after there were patron reports of problems with the file. Master of Science

Control Allocation addresses the problem of the management of multiple, redundant control effectors. Generally speaking, control allocation is any method that is used to determine how the controls of a system should be positioned to achieve some desired effect. An infinite number of allocation methods exist, from the straight-forward direct allocation technique, to the daisy chaining approach, to the computationally simple generalized inverse method. Because different methods have advantages and disadvantages with respect to others, the determination of the "optimal" control allocation method is left to the system designer. The many tradeoffs that are addressed during control system design, of which control allocation is an integral part, dictate the need for a reliable, computer-based design tool. The Control Allocation Toolbox for MATLAB satisfies such a need by providing the designer with a means of testing/comparing the validity of certain allocation methods under prescribed conditions. The issues involved in the development and implementation of the Control Allocation Toolbox are discussed. Master of Science

Harmonic oscillatory tests for a fighter aircraft using the Dynamic Plunge--Pitch--Roll model mount at Virginia Tech Stability Wind Tunnel are described. Corresponding data reduction methods are developed on the basis of multirate digital signal processing. Since the model is sting mounted, the frequencies associated with sting vibration are included in balance readings thus a linear filter must be used to extract out the aerodynamic responses. To achieve this, a Finite Impulse Response (FIR) is designed using the Remez exchange algorithm. Based on the reduced data, a state–space model is developed to describe the unsteady aerodynamic characteristics of the aircraft during roll oscillations. For this model, we chose to separate the aircraft into panels and model the local forces and moments. Included in this technique is the introduction of a new state variable, a separation state variable which characterizes the separation for each panel. This new variable is governed by a first order differential equation. Taylor series expansions in terms of the input variables were performed to obtain the aerodynamic coefficients of the model. These derivatives, a form of the stability derivative approach, are not constant but rather quadratic functions of the new state variable. Finally, the concept of the model was expanded to allow for the addition of longitudinal motions. Thus, pitching moments will be identified at the same time as rolling moments. The results show that the goal of modeling coupled longitudinal and lateral–directional characteristics at the same time using the same inputs is feasible. Master of Science

The problem of aircraft control allocation is that of finding a combination of control positions that cause the resulting aircraft moments to most closely satisfy a given desired moment vector. The problem is easily solved for the case of an aircraft having three control surfaces, each of which primarily imparts moments in each of the three aircraft axes. In this simple case, the solution to the control allocation problem is uniquely determined. However, many current and future aircraft designs employ a larger set of control effectors, resulting in a control redundancy in the sense that more than one combination of control positions can produce the same desired moment. When taking into account both the position and rate constraints of the control effectors, the problem is significantly more complex. Constrained moment-rate control allocation guarantees a control solution that can achieve every possible moment that is physically realizable by the aircraft. Addressed here is the real-time performance of moment-rate constrained control allocation as tested on a desktop simulation. Issues that were deemed interesting or potentially problematic in earlier batch simulation, such as control chattering due to restoring and apparent control wind-up, are investigated and an evaluation is made of the overall feasibility of these algorithms. The purpose of the research is to confirm that the results obtained from batch simulation testing are also valid using maneuvers representative of real-time flight and representative simulation frame sizes, and to uncover potential problems not observed in batch simulation. NOTE: An updated copy of this ETD was added on 05/29/2013. Master of Science

Human operator models developed using optimal control theory are typically complicated and over-parameterized, even for simple controlled elements. Methods for generating less complicated operator models that preserve the most important characteristics of the full order model are developed so that the essential features of the operator dynamics are easier to determine. A new formulation of the Optimal Control Model (OCM) of the human operator is developed that allows order reduction techniques to be applied in a meaningful way. This formulation preserves the critical neuromotor dynamics and time delay characteristics of the human operator. The Optimal Projection (OP) synthesis technique is applied to a modified version of the OCM. Using OP synthesis allows one to determine operator models that minimize the quadratic performance index of the OCM with a constraint on model order. This technique allows analysts to formulate operator models of fixed order. Operator model reduction methods based on variations of balanced realization techniques are also developed since they reduce the computational complexity associated with OP synthesis yet maintain a reasonable level of accuracy. Computer algorithms are developed that insure that the reduced order models have noise to signal ratios that are consistent with OCM theory. The OP method generates operator models of fixed order that are consistent with OCM theory in all respects, i.e. optimality, neuromotor lag, time delay, and noise to signal ratios are all preserved. The other model reduction techniques preserve these features with the exception of optimality. Each technique is applied to a variety of controlled elements to illustrate how performance and frequency response fidelity degrade when the order of the operator model is reduced. Ph. D.

Due to increasingly difficult threats, current air defense missile systems are pushed to the limits of their performance capabilities. In order to defend against these more stressing threats, interceptor missiles require greater maneuverability, faster response time, and increased robustness to more severe environmental conditions. One of the most critical missile system elements is the flight control system, since its time constant is typically half of the total missile system time constant. Conventional autopilot design techniques have worked well in the past, but in order to satisfy future and more stringent design specifications, new design methods are necessary. Robust control techniques (in particular, H-Infinity Control and Mu-Synthesis) and their application to the design of missile autopilots are addressed in this thesis. In addition, conventional autopilot designs are performed as comparative benchmarks. This paper reviews the missile autopilot design problem and presents descriptions of the classical and H-Infinity/Mu design methods. Missile autopilot designs considering both rigid-body dynamics and elastic-body dynamics are presented. Comparisons of the design approaches and results are also discussed. The results show that the application of robust control techniques to the design of missile autopilots can improve the performance and stability robustness characteristics of the flight control system. Master of Science

Pilot in-the-loop oscillation (PIO) is a phenomenon which occurs due to the dynamic interaction between pilot and aircraft. This detrimental aircraft handling quality appears through a variety of flight conditions and is very difficult to predict. Due to this complex behavior, PIO is not easily eliminated. This report describes a method of PIO analysis that is capable of examining multiple asymmetric nonlinearities acting simultaneously. PIO analyses are performed on a model based on the USAF NT-33A variable stability aircraft with nonlinearities including stick position limiting, elevator deflection limiting, and elevator rate limiting. These analyses involve the use of dual input describing functions which enable the prediction of frequency, amplitude, and mean point of oscillation. Master of Science

The harmonic oscillatory tests for a fighter aircraft configuration using the Dynamic Plunge-Pitch-Roll (DyPPiR) model mount at Virginia Tech Stability Wind Tunnel are described and analyzed. The corresponding data reduction methods are developed on the basis of multirate digital signal processing techniques. Since the model is sting-mounted to the support system of DyPPiR, the Discrete Fourier Transform (DFT) is first used to identify the frequencies of the elastic modes of sting. Then the sampling rate conversion systems are built up in digital domain to resample the data at a lower rate without introducing distortions to the signals of interest. Finally linear-phase Finite Impulse Response (FIR) filters are designed by Remez exchange algorithm to extract the aerodynamic characteristics responses to the programmed motions from the resampled measurements. These data reduction procedures are also illustrated through examples. The results obtained from the harmonic oscillatory tests are then illustrated and the associated flow mechanisms are discussed. Since no significant hysteresis loops are observed for the lift and the drag coefficients for the current angle of attack range and the tested reduced frequencies, the dynamic lags of separated and vortex flow effects are small in the current oscillatory tests. However, large hysteresis loops are observed for pitch moment coefficient in the current tests. This observation suggests that at current flow conditions, pitch moment has large pitch rate and alpha-dot dependencies. Then the nondimensional maximum pitch rate q_max is introduced to characterize these harmonic oscillatory motions. It is found that at current flow conditions, all the hysteresis loops of pitch moment coefficient with same nondimensional maximum pitch rate are tangential to one another at both top and bottom of the loops, implying approximately same maximum offset of these loops from static values. Several cases are also illustrated. Based on the results obtained and those from references, a state-space model is developed to describe the unsteady aerodynamic characteristics up to the high angle of attack regime. A nondimensional coordinate is introduced as the state variable describing the flow separation or vortex burst. First-order differential equation is used to govern the dynamics of flow separation or vortex bursting through this state variable. To be valid for general configurations, Taylor series expansions in terms of the input variables are used in the determination of aerodynamic characteristics, resembling the current approach of the stability derivatives. However, these derivatives are longer constant. They are dependent on the state variable of flow separation or vortex burst. In this way, the changes in stability derivatives with the angle of attack are included dynamically. The performance of the model is then validated by the wind-tunnel measurements of an NACA 0015 airfoil, a 70 degree delta wing and, finally two F-18 aircraft configurations. The results obtained show that within the framework of the proposed model, it is possible to obtain good agreement with different unsteady wind tunnel data in high angle-of-attack regime. Ph. D.

Control Allocation as it pertains to aerospace vehicles, describes the way in which control surfaces on the outside of an aircraft are deflected when the pilot moves the control stick inside the cockpit. Previously, control allocation was performed by a series of cables and push rods, which connected the 3 classical control surfaces (ailerons, elevators, and rudder), to the 3 cockpit controls (longitudinal stick, lateral stick, and rudder pedals). In modern tactical aircraft however, it is not uncommon to find as many as 10 or more control surfaces which, instead of being moved by mechanical linkages, are connected together by complex electrical and/or hydraulic circuits. Because of the large number of effectors, there can no longer be a one-to-one correspondence between surface deflections on the outside of the cockpit to pilot controls on the inside. In addition, these exterior control surfaces have limits which restrict the distance that they can move as well as the speed at at which they can move. The purpose of Constrained Control Allocation is to deflect the numerous control surfaces in response to pilot commands in the most efficient combinations, while keeping in mind that they can only move so far and so fast. The implementation issues of Constrained Control Allocation techniques are discussed, and an aerodynamic model of a highly modified F-15 aircraft is used to demonstrate the various aspects of Constrained Control Allocation. This work was conducted under NASA research grant NAG-1-1449 supervised by John Foster of the NASA Langley Research Center Master of Science

The research presented in this dissertation investigates the use of all-at-once methods applied to aerodynamic design. All-at-once schemes are usually based on the assumption of sufficient continuity in the constraints and objectives, and this assumption can be troublesome in the presence of shock discontinuities. Special treatment has to be considered for such problems and we study several approaches. Our all-at-once methods are based on the Sequential Quadratic Programming method, and are designed to exploit the structure inherent in a given problem. The first method is a Reduced Hessian formulation which projects the optimization problem to a lower dimension design space. The second method exploits the sparse structure in a given problem which can yield significant savings in terms of computational effort as well as storage requirements. An underlying theme in all our applications is that careful analysis of the given problem can often lead to an efficient implementation of these all-at-once methods. Chapter 2 describes a nozzle design problem involving one-dimensional transonic flow. An initial formulation as an optimal control problem allows us to solve the problem as as two-point boundary problem which provides useful insight into the nature of the problem. Using the Reduced Hessian formulation for this problem, we find that a conventional CFD method based on shock capturing produces poor performance. The numerical difficulties caused by the presence of the shock can be alleviated by reformulating the constraints so that the shock can be treated explicitly. This amounts to using a shock fitting technique. In Chapter 3, we study variants of a simplified temperature control problem. The control problem is solved using a sparse SQP scheme. We show that for problems where the underlying infinite-dimensional problem is well-posed, the optimizer performs well, whereas it fails to produce good results for problems where the underlying infinite-dimensional problem is ill-posed. A transonic airfoil design problem is studied in Chapter 4, using the Reduced SQP formulation. We propose a scheme for performing the optimization subtasks that is based on an Euler Implicit time integration scheme. The motivation is to preserve the solution-finding structure used in the analysis algorithm. Preliminary results obtained using this method are promising. Numerical results have been presented for all the problems described. Ph. D.

Control allocation is examined for linear time-invariant problems that have more controls than degrees of freedom. The controls are part of a physical system and are subject to limits on their maximum positions. A control allocation scheme commands control deflections in response to some desired output. The ability of a control allocation scheme to produce the desired output without violating the physical position constraints is used to compare allocation schemes. Methods are developed for computing the range of output for which a given scheme will allocate admissible controls. This range of output is expressed as a volume in the n-dimensional output space. The allocation schemes which are detailed include traditional allocation methods such as Generalized Inverse solutions as well as more recently developed methods such as Daisy Chaining, Cascading Generalized Inverses, Null-Space Intersection methods, and Direct Allocation. Non-linear time-varying problems are analyzed and a method of control allocation is developed that uses Direct Allocation applied to locally linear problems to allocate the controls. This method allocates controls that do not violate the position limits or the rate limits for all the desired outputs that the controls are capable of producing. The errors produced by the non-linearities are examined and compared with the errors produced by globally linear methods. The ability to use the redundancy of the controls to optimize some function of the controls is explored and detailed. Additionally, a method to reconfigure the controls in the event of a control failure is described and examined. Detailed examples are included throughout, primarily applying the control allocation methods to an F-18 fighter with seven independent moment generators controlling three independent moments and the F-18 High Angle of Attack Research Vehicle (HARV) with ten independent moment generators. Ph. D.

A new software tool was needed for flight planning of a high altitude, low speed unmanned aerial vehicle which would be flying in winds close to the actual airspeed of the vehicle. An energy modeled NLP formulation was used to obtain results for a variety of missions and wind profiles. The energy constraint derived included terms due to the wind field and the performance index was a weighted combination of the amount of fuel used and the final time. With no emphasis on time and with no winds the vehicle was found to fly at maximum lift to drag velocity, Vmd. When flying in tail winds the velocity was less than Vmd, while flying in head winds the velocity was higher than Vmd. A family of solutions was found with varying times of flight and varying fuel amounts consumed which will aid the operator in choosing a flight plan depending on a desired landing time. At certain parts of the flight, the turning terms in the energy constraint equation were found to be significant. An analysis of a simpler vertical plane cruise optimal control problem was used to explain some of the characteristics of the vertical plane NLP results. Master of Science

A procedure for incorporating a key non-linear aerodynamic characteristic into the design optimization of a high-speed civil transport has been developed. Previously, the tendency of a high-speed aircraft to become uncontrollable (pitch-up) at high angles-of-attack during landing or takeoff for some wing shapes could not be included directly in the design process. Using response surface methodology, polynomial approximations to the results obtained from a computationally expensive estimation method were developed by analyzing a set of statistically selected wing shapes. These response surface models were then used during the optimization process to approximate the effects of wing planform changes on pitch-up. In addition, response surface approximations were used to model the effect of horizontal tail size and wing flaps on the performance of the aircraft. Optimizations of the high-speed civil transport were completed with and without the response surfaces. The results of this study provide insight into the influence of nonlinear and more detailed aerodynamics on the design of a high-speed civil transport. Master of Science

A method is developed for computing the minimum fuel trajectory for a satellite that moves between two different positions and orientations using a sequence of impulsive burns. The method makes use of the linear Clohessy-Wiltshire equations to describe translational motions, Euler's equations of rigid body motion for describing the attitude motions, and a sequential quadratic programming optimization code. Initial solutions are found assuming no coupling between the translational and rotational motions and with no imposed constraint on the time of the rendezvous. Further solutions are then found by varying the vehicle center of gravity location along one axis, thereby coupling the rotational motions into two axes of translation thrusters, and by imposing time limits on the rendezvous. A discussion of the impact that these parameters have on the optimal solutions for two different models of the satellite thruster systems is then presented. Master of Science

Numerous trim, control requirements and mission generalizations have been made to our previous multidisciplinary design methodology for a high speed civil transport. We optimize the design for minimum take off gross weight, including both aerodynamics and structures to find the wing planform and thickness distribution, fuselage shape, engine placement and thrust, using 29 design variables. While adding trim and control it was found necessary to simultaneously consider landing gear integration. We include the engine-out and crosswind landing requirements, as well as engine nacelle ground strike for lateral-directional requirements. For longitudinal requirements we include nose-wheel lift-off rotation and approach trim as the critical conditions. We found that the engine-out condition and the engine nacelle ground strike avoidance were critical conditions. The addition of a horizontal tail to provide take-off rotation resulted in a signiffcant weight penalty, and that penalty proved to be sensitive to the position of the landing gear. We include engine sizing with thrust during cruise and balanced field length conditions. Both the thrust during cruise and balanced field length constraints were critical. We include a subsonic leg in our mission analysis. The addition of a subsonic mission requirement also results in a large weight penalty. Master of Science

A stability analysis and departure prediction method has been developed and coded in a MATLAB®-based software package called the Stability And Departure Analysis Tool using Eigenvalue Sensitivity (SADATES). Using eigenvalue and eigenvector analysis, SADATES is capable of performing a full-envelope stability analysis, returning both quantitative and qualitative data regarding the stability of the airplane at a static reference condition. SADATES not only supplies the analyst with information describing where and when an aircraft is likely to depart, but also information about the departure characteristics, enabling the analyst to design for better departure resistance. While the eigenvalue and eigenvector approach is straightforward, it is a broader approach than many traditional stability parameters, yielding more accurate and reliable results than traditional methods. SADATES also analyzes the aircraft dynamics from a standpoint of eigenvalue sensitivity. Using this feature, the analyst may directly study the impact of data uncertainty and non-zero angular rates on the nominal stability of the aircraft. Of particular interest are the effects of the dynamic damping derivatives, as these derivatives are particularly difficult to estimate. In addition, the effect of an unsteady reference condition may be examined by studying the sensitivity of the eigenvalues to changes in angular rates, thereby using a static approach to give answers to a dynamic problem. Given the development of eigenvalue sensitivity data, the analyst is able to determine the margin of error on nominal aircraft stability. The utility of the SADATES package is tested using aerodynamic data of the McDonnell-Douglas F / A-18C Hornet. Bare airframe, controls fixed stability is analyzed, and its sensitivity to data uncertainty and to non-zero angular rates is examined. The Hornet's bare airframe stability characteristics are then compared to those using an active feedback control system to drive an automatic leading and trailing edge flap schedule, demonstrating the accuracy and versatility of the program. Master of Science

The feasibility of utilizing a neural network to solve the constrained flight control allocation problem is investigated for the purposes of developing guidelines for the selection of a neural network structure as a function of the control allocation problem parameters. The control allocation problem of finding the combination of several flight controls that generate a desired body axis moment without violating any control constraint is considered. Since the number of controls, which are assumed to be individually linear and constrained to specified ranges, is in general greater than the number of moments being controlled, the problem is nontrivial. Parallel investigations in direct and generalized inverse solutions have yielded a software tool (namely CAT, for Control Allocation Toolbox) to provide neural network training, testing, and comparison data. A modified back propagation neural network architecture is utilized to train a neural network to emulate the direct allocation scheme implemented in CAT, which is optimal in terms of having the ability to attain all possible moments with respect to a given control surface configuration. Experimentally verified heuristic arguments are employed to develop guidelines for the selection of neural network configuration and parameters with respect to a general control allocation problem. The control allocation problem is shown to be well suited for a neural network solution. Specifically, a six hidden neuron neural network is shown to have the ability to train efficiently, form an effective neural network representation of the subset of attainable moments, and independently discover the internal relationships between moments and controls. The performance of the neural network control allocator, trained on the basis of the developed guidelines, is examined for the reallocation of a seven control surface configuration representative of the F/A-18 HARV in a test maneuver flown using the original control laws of an existing flight simulator. The trained neural network is found to have good overall generalization performance, although limitations arise from the ability to obtain the resolution of the direct allocation scheme at low moment requirements. Lastly, recommendations offered include: ( 1) a proposed application to other unwieldy control al1ocation algorithms, with possible accounting for control actuator rate limitations, so that the computational superiority of the neural network could be fully realized; and (2) the exploitation of the adaptive aspects of neural network computing. Master of Science

A method for determining the maximum control moments required for an aircraft to perform a velocity vector roll is investigated. The velocity vector roll is assumed to occur at constant angle of attack, constant velocity, and zero sideslip. A simplified set of equations is developed for the non dimensional control moments about the three principal body axes. These equations take on a form well suited for numerical optimization methods. The Schittkowski sap optimization code is used to provide fast, accurate solutions. The numerical method also shows the advantage of being adaptable to changing the airframe and flight performance parameters. An exercise to find the global control moment maxima was performed for a an F-18 with constant aerodynamic derivatives and a load factor of one. The optimization was run for a range of discrete steady state roll rates, roll mode time constants and velocities. The results showed trends for the maxima to occur at the highest steady state roll rate parameter, smallest roll mode time constant and lowest velocity. Each control axis maximum is specific to a particular orientation and angle of attack. For the roll axis, the maximum occurs at nearly zero angle of attack and 270 of wind axis bank angle. The yaw axis maximum occurs at the largest angle of attack (70) and 90 of wind axis bank angle. The pitch maximum occurs near 270 of wind axis bank and 55 angle of attack, but is highly sensitive to the selection of Cma . All control moment maxima occur at a flight path angle of O. The roll and yaw control moment maxima occur upon a maximum roll input starting from rest at the specified orientation and angle of attack. The pitch control maximum occurs at the steady state roll rate when the proper orientation and angle of attack is encountered. Master of Science

Steady state and transient maneuver problems for a high performance fighter aircraft with and without thrust vectoring are investigated. The steady state aspect of these studies determines control combinations with and without thrust vectoring which optimize selected level-flight point performance criteria including minimum speed, maximum instantaneous range, and maximum sustained turn rate. The transient maneuvers are initiated from straight and level flight and include a longitudinal pitch-up to a desired fuselage pointing angle and a lateral-directional transition (wind-up) to a desired steady level turn rate. For the transient maneuvers, a full six-degree-of-freedom model of the aircraft is used with three conventional aerodynamic controls, throttle control and pitch and yaw thrust vectoring control. Each of the control time histories are parameterized so as to include both the rate and range limits of the controls. A nonlinear programming algorithm is used to determine the control parameter values which yield the minimum time to execute the prescribed maneuvers. Results indicate that thrust vectoring does not significantly change the steady state behavior in the scenarios investigated. However, flight times for the transient maneuvers are found to be reduced by up to 28%. The greatest effect of thrust vectoring occurs at low Mach number. Master of Science

An approach to aerodynamic configuration optimization is presented for the high-speed civil transport (HSCT). Methods to parameterize the wing shape, fuselage shape and nacelle placement are described. Variable-complexity design strategies are used to combine conceptual and preliminary-level design approaches, both to preserve interdisciplinary design influences and to reduce computational expense. The preliminary-design-level analysis methods used to estimate aircraft performance are described. Conceptual-design-level (approximate) methods are used to estimate aircraft weight, supersonic wave drag and drag due to lift, and landing angle of attack. The methodology is applied to the minimization of the gross weight of an HSCT that flies at Mach 2.4 with a range of 5500 n.mi. Results are presented for wing plan form shape optimization and for combined wing and fuselage optimization with nacelle placement. Case studies include both all-metal wings and advanced composite wings. The results indicate the beneficial effect of simultaneous design of an entire configuration over the optimization of the wing alone and illustrate the capability of the optimization procedure. Ph. D.

All aircraft must meet controllability requirements to be certified for commercial use or adopted by the mi1itary. Aircraft maneuverability is often 1imited by control authority. Thus, it is essential for designers to evaluate a candidate concept's control authority early in the conceptual design phase. In this thesis, a methodology for rapid control power evaluation of preliminary design configurations against requirements at the key flight conditions is established. First, a collection of critical flight conditions to be considered using this methodology is identified. To examine a variety of aircraft configurations and accelerate the process of estimating stability and control derivatives, a FORTRAN program using the Vortex-Lattice Method was written to estimate subsonic, low angle-of-attack aerodynamics. Then, a spreadsheet processes the aerodynamic data to check whether the design configuration possesses adequate control power to satisfy the requirements of the critical flight conditions. Master of Science

In two-dimensional flow, the point of flow separation from the surface coincides with the point at which the skin friction vanishes. However, in three-dimensional flow, the situation is much more complex and the flow separation is rarely associated with the vanishing of the wall shear stress except in a few special cases. Though the effects of cross-plane separation are substantial and have been recognized for some time, the phenomenon of flow separation over three-dimensional bodies is still far from being completely understood. The flow is so complex that no completely satisfactory analytical tools are available at the moment. In an attempt to logically identify the various effects and parametric dependence while simultaneously minimizing configuration dependent issue, the flow over a 6 to 1 prolate spheroid, which is a generic three-dimensional body, is investigated. For the identification of the general flow pattern and better understanding of the flow field, surface-oil-flow visualization tests and force and moment tests were performed. The angle of attack effect and Reynolds number effect on the separation location are studied with natural transition. Forces and moments tests, surface pressure distribution measurements as well as the surface presure fluctuations, and mini-tuft flow visualization tests were made to document the flow characteristics on the surface of the body with an artificial boundary layer trip. It was found that there exists a critical Reynolds number at which the flow characteristics of the afterbody changes. This critical Reynolds number was also confirmed by the force and moment tests. Above this Reynolds number, as the Reynolds number increases, the separation lines do not change their circumferential location but stretch to the upstream of the body. For the low supercritical Reynolds number range, the angle of attack effect on the location of the primary separation is not as prominent as in the higher Reynolds number range where the cross-flow component effect becomes dominant. Surface pressure fluctuation data and surface pressure spectra were measured and documented for the first time for this type of three-dimensional flow. For the extension of the study to unsteady transient motion effects, a new Dynamic-Plunge-Pitch-Roll (DyPPiR) model mount was designed and developed to generate required transient motions. The measurements carried out during this study are to be used as reference data to identify the unsteady transient effect of the flow field undergoing unsteady transient maneuvers. Ph. D.

Model-following control design methodology is introduced for nonlinear plants and models. The plant equations are considered to be linear in the control input. Dynamic matching conditions are presented and the resulting error dynamics are given. The stability of error dynamics is ensured, using Liapunov's second theorem; by modifying the model state rates, which effectively introduces error feedback. The methodology is applied to two problems. Motion control of an n-link manipulator with torque controllers on each linkage, and control of an aircraft lacking direct control of lift and side force. The former represents the systems where all of the degrees of freedom can be controlled, and the latter represents the systems where only some of the degrees of freedom can be controlled. The aircraft control problem is analyzed in more detail. The resulting control law does not require any explicit gain scheduling, but instead, requires estimates of the stability and control derivatives. A method is proposed to compensate for actuator dynamics. The control law is then verified by simulating some maneuvers on the aircraft model provided for the AIAA Controls Design Challenge, which includes nonlinear and full-envelope aerodynamic and engine models, and rate and position limited controls. The maneuvers simulated include a level acceleration and a 3-g turn. Master of Science

The problem of optimal guidance design for the low altitude, subsonic, vertical plane approach maneuver of an air vehicle constrained to maintain view of a fixed final position is studied using a nonlinear, constrained, optimal control problem formulation. Multiple, competing optimization criteria are included separately as performance goals and in combination as state equality constraints for design tradeoff analysis. In conjunction with vehicle flight constraints, a sensor line-of -sight (LOS) angle limit is imposed as a control variable inequality constraint to provide a sensor field of regard influence on the guidance design. Numerical results are provided that illustrate the optimal guidance for different performance criteria, the sensor LOS profile along the optimal maneuvers, and the influence of the sensor limit on the guidance law design. A near-optimal, closed-loop feedback guidance law that incorporates the sensor constraint is developed based on neighboring extremals. Ph. D.

A design method for a multi-loop mixed discrete/continuous trajectory following pitch control algorithm for a generic aerospace vehicle is presented. This design methodology is facilitated by a time scale separation observed in the dynamical system. Two variations of this algorithm are considered, with features and drawbacks of both evaluated. The algorithm is then tested by simulations with two vehicles flying arbitrary trajectories. Results are presented for a thrust-vector controlled high-performance missile without atmospheric effects, and for a single-stage-to-orbit hypersonic vehicle with both elevator and thrust-vector control. It is shown that the control algorithm results in a pitch loop feedback controller that is robust and very stable, and is at least near optimal for the class of trajectories considered. No claims of optimality are made for the outer loop, but it is shown in the simulations that the outer loop tracker can do a reasonable job of following the prescribed nominal trajectory. Ph. D.

The problem of time-optimal fuselage-reorientation maneuvering of a combat aircraft, with and without thrust-vectoring capability, was analyzed. An accurate mathematical model for the reorientation maneuvers of interest was developed, to ensure practical value of the analysis. In particular, an effective method for smooth fitting of the aerodynamic data was devised. The Minimum Principle from optimal control theory was applied and the optimal control problems of interest cast into a form of numerical multipoint boundary-value problems. These are extremely difficult to solve. To alleviate their treatment, a hybrid approach was adopted. Homotopy ideas were combined with comprehensive analyses of the structure of the dynamical equations and engineering insight into the mechanics of the reorientation motions. The approach successfully yielded a number of extremal solutions for a few typical reorientation maneuvers. The nature and essential characteristics of the extremal motions were understood, as well as their domains of existence. A few parametric studies showed how aircraft design parameters should be tailored to allow for improved maneuverability. Ph. D.

This dissertation evaluates higher-order modal methods for predicting thermal and structural response. More accurate methods or ones which can significantly reduce the size of complex, transient thermal and structural problems are desirable for analysis and are required for synthesis of real structures subjected to thermal and mechanical loading. A unified method is presented for deriving successively higher-order modal solutions related to previously developed, lower-order methods such as the mode-displacement and mode-acceleration methods. A new method, called the force derivative method, is used to obtain higher-order modal solutions for both uncoupled (proportionally-damped) structural problems as well as thermal problems and coupled (non-proportionally damped) structural problems. The new method is called the force-derivative method because, analogous to the mode-acceleration method, it produces a term that depends on the forcing function and additional terms that depend on the time derivatives of the forcing function. The accuracy and convergence history of various modal methods are compared for several example problems, both structural and thermal. The example problems include the case of proportional damping for: a cantilevered beam subjected to a quintic time varying tip load and a unit step tip load and a muItispan beam subjected to both uniform and discrete quintic time-varying loads. Examples of non-proportional damping include a simple two-degree-of-freedom spring-mass system with discrete viscous dampers subjected to a sinusoidally varying load and a multispan beam with discrete viscous dampers subjected to a uniform, quintic time varying load. The last example studied is a transient thermal problem of a rod subjected to a linearly-varying, tip heat load. Ph. D.

A systems engineering approach was used to produce a preliminary design configuration for an ion-propelled orbital transfer vehicle system. The four components of the system are: ground software, ground hardware, the orbital transfer vehicle and the space shuttle. The orbital transfer vehicle uses electrostatic propulsion to transfer payload satellites from a low earth orbit, to any other desired orbit. The system maintenance concept, and a conceptual design are derived from the statement of need and the system operational requirements. The resulting design, maintainability, reliability and support requirements are discussed. A discussion of the feasibility of an ion propelled orbital transfer vehicle is included. Master of Science

The terminal stage of a minimum-time mission of a high- performance aircraft is studied using both a reduced-order "energy" model formulation and a point-mass model formulation of the aircraft. The mission is confined to vertical plane maneuvers, and is defined as consisting of three stages; a climb to the dash point,a steady-state dash at the high velocity point, and finally, a terminal transient from the dash point to the final state. This terminal maneuver evolves outside of the flight envelope, rapidly decreasing altitude while increasing the velocity to values greater than the dash velocity. The velocity then decreases from this maximum value as required in order to meet the final state specification. Some of the trajectories that are generated during this terminal transient maneuver experience dynamic pressures that will exceed the dynamic pressure limit unless a constraint is placed on the state variables. Because of the need for enforcing this state constraint, a direct adjoining method for handling state constraints in the optimal control problem is studied. A numerical example is given to demonstrate the application of this method of handling state constraints for the case of the dynamic pressure limit. Finally, trajectories are generated that lead from the dash point to a final state having lower altitude and energy values than those of the dash point, and observations are made concerning the characteristics of these maneuvers. Master of Science