Abstrakt: This report examines different control design methods, linear as well as nonlinear, for a suborbital reusable launch vehicle. An investigation of the natural vehicle behavior is made, after which a baseline linear controller is constructed to fulfill certain handling quality criteria. Thereafter the nonlinear cascade control methods block backstepping and nonlinear dynamic inversion via time scale separation are examined and used to construct two nonlinear controllers for the vehicle. Optimal controllers, in terms of three different criteria, are found using the genetic optimization algorithm differential evolution. The optimal controllers are compared, and it is found that nonlinear dynamic inversion via time scale separation performs better than block backstepping with respect to the cases investigated. The results suggest control design by global optimization is a viable and promising complement to classical methods.

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High aspect-ratio flying wing configurations designed for high altitude, long endurance missions are characterized by high flexibility, leading to significant static aeroelastic deformation in flight, and coupling between aeroelasticity and flight dynamics. As a result of this coupling, an integrated model of the aeroelasticity and flight dynamics has to be used to accurately model the dynamics of the flexible flying wing. Such an integrated model of the flight dynamics and the aeroelasticity developed by Patil and Hodges is reviewed in this dissertation and is used for studying the unique flight dynamics of high aspect-ratio flexible flying wings. It was found that a rigid body configuration that accounted for the static aeroelastic deformation at trim captured the predominant flight dynamic characteristics shown by the flexible flying wing. Moreover, this rigid body configuration was found to predict the onset of dynamic instability in the flight dynamics seen in the integrated model. Using the concept of the mean axis, a six degree-of-freedom reduced order model of the flight dynamics is constructed that minimizes the coupling between rigid body modes and structural dynamics while accounting for the nonlinear static aeroelastic deformation of the flying wing. Multi-step nonlinear dynamic inversion applied to this reduced order model is coupled with a nonlinear guidance law to design a flight controller for path following. The controls computed by this flight controller are used as inputs to a time-marching simulation of the integrated model of aeroelasticity and flight dynamics. Simulation results presented in this dissertation show that the controller is able to successfully follow both straight line and curved ground paths while maintaining the desired altitude. The controller is also shown to be able to handle an abrupt change in payload mass while path-following. Finally, the equations of motion of the integrated model were non-dimensionalized to identify aeroelastic parameters for optimization and design of high aspect-ratio flying wings. / Ph. D.

This dissertation addresses fundamental theoretical problems relevant to flight control for aerial vehicles and weapons in highly uncertain dynamical environment. The approach taken in this dissertation is the L1 adaptive control, which is elaborated from its design perspective for output feedback solution and is extended to time-varying reference systems to support augmentation of gain-scheduled baseline controllers. Compared to conventional adaptive controllers, L1 control has the following advantages: i) it has guaranteed uniformly bounded transient response for system's both signals, input and output; ii) it enables fast adaptation while maintains a bounded away from zero time-delay margin. The proposed adaptive control approach can recover the nominal performance of the flight control systems in the presence of rapid variation of uncertainties. Furthermore, the benefit of L1 adaptive control is its promise for development of theoretically justified tools for Verification and Validation (V&V) of adaptive systems. Adaptive control for uncertain systems usually needs to handle two types of uncertainties: matched and unmatched uncertainties. Both of these two uncertainties will appear in practical flight control problems. In this dissertation, adaptive approaches which can compensate for these two types of uncertainties will be discussed respectively. Two architectures of L1 adaptive control, namely L1 state feedback adaptive control and L1 output feedback adaptive control, are studied. The state feedback adaptive control is applied for compensation of matched uncertainties. Although the state feedback scheme is capable of handling certain type of unmatched uncertainties, such approach is not explored in this dissertation. On the other hand, the output feedback approach is mainly aimed to solve problems in the presence of unmatched uncertainties. The dissertation first discusses the state feedback L1 adaptive control for time-invariant reference systems. The adaptive controller is designed to augment an existing baseline controller. The closed loop system of the plant and the baseline controller is time-invariant. This closed loop system, which is a Linear Time Invariant (LTI) system, determines the dynamics of the reference system. The adaptive feedback can compensate for nonlinear state- and time-dependent uncertainty with uniformly bounded transient response. In this dissertation we discuss the Multi-Input Multi-Output (MIMO) extension of the method. Two flight control examples,Unmanned Combat Aerial Vehicle (UCAV) and Aerial Refueling Autopilot, are considered in the presence of nonlinear uncertainties and control surface failures. The L1 adaptive controller without any redesign leads to scaled response for system's both signals, input and output, dependent upon changes in the initial conditions, system parameters and uncertainties. The time-delay margin analysis for these two examples verifies the theoretical claims. Next, the output feedback approach is studied. The adaptive output feedback controller can be applied to reference systems that do not verify the Strict Positive Real (SPR) condition for their input-output transfer function. In this dissertation, specific design guidelines are presented that render the approach suitable for practical applications. A missile autopilot design example is given to demonstrate the benefits of the design approach. Finally, the L1 state feedback adaptive controller is extended to time-varying reference systems. The adaptive controller intends to augment a gain-scheduled baseline controller. The reference system, which is determined by the closed loop system of the plant and the baseline gain-scheduled controller, is time-varying. The adaptive controller with time-varying reference system is proved to have guaranteed performance bounds similar to those obtained for the case of linear time-invariant reference systems. With this result, the aerial refueling application can be extended to a complete scenario, which includes a racetrack maneuver for an aircraft. The concluding chapter discusses the challenging issues for future research. / Ph. D.

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 digital model reference scheme is presented for the control of the longitudinal modes of an EBF-STOL aircraft. The method used is based on Liapunov's direct method and is used to update feedback and feedthrough matrices. An equilibrium point of the EBF-STOL is chosen about which to constrain performance to follow that of a linearized decoupled DC-9 model. The change of control matrix elements is controlled by (1) an error vector equal to the difference between state variables of the model and those of the STOL, (2) the present values of the pilot inputs and STOL state variables, (3) a P matrix obtained from the equation A_mᵀPA_m - P = - I where z(k + 1) = A_m z(k) + B_m u_p is the equation of motion for the model, (4) selected gains, and (5) a matrix B₋ᵤʳ⁻¹ whose elements are determined by the inverse of an n x n partition of the linearized input matrix B₋ᵤ of the STOL. A method for smoothing control action is discussed. / Master of Science

We consider the problem of optimal evasion when the pursuer is known to employ fixed gain proportional navigation. The performance index is a measure of closest approach. The analysis is done for planar motions at constant speed. The kinematics are first linearized around a nominal collision course. The dynamics of the opponents are modeled by first order systems and their accelerations may be bounded. Three cases are studied: unconstrained optimal evasion (where the evader is not subjected to any path constraint) against a single pursuer, optimal evasion with a terminal path angle constraint for the evader and optimal evasion against more than one pursuer. The optimal controls are shown to be 'bang - bang' with the number of switches depending on the pursuer’s navigation gain and on the particular constraints of each case. / Master of Science

The problem of determining cruise-dash trajectories is examined for the case of time-fuel optimization using a linear combination of time and fuel as the performance index. These trajectories consist of a transient arc followed by a steady-state arc. For cases where the steady-state arc is flown with full throttle the associated skeletal transient trajectories are also flown with full throttle, and approach the cruise-dash points monotonically in an asymptotic fashion. When the steady-state arc is flown at an intermediate throttle setting, the transient trajectories follow a singular control law and exhibit a complex structure that is different from the full-throttle transients. Singular transients in the vicinity of singular cruise-dash points are confined to a bounded singular surface. In state-space these trajectories trace out asymptotic spirals on the singular surface as they approach the steady-state arc. If the initial operating point lies outside the singular surface, then the transient trajectories are composites consisting of a full-throttle or zero-throttle segment flown until the singular surface is met, followed by a singular segment that fairs into the cruise-dash point. Addressing the question of optimality of the steady-state arc, it was found that although steady-state cruise fails a Jacobi-type condition, steady-state cruise-dash can satisfy this condition if the emphasis on time is sufficiently large. The outcome of the Jacobi-type test appears to be connected with the eigenstructure of the linearized state-adjoint system. / PH. D.

Thesis (PhD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: A strategy for the design of an effective, practically feasible, robust, computationally efficient autopilot for three dimensional manoeuvre flight control of Unmanned Aerial Vehicles is presented. The core feature of the strategy is the design of attitude independent inner loop acceleration controllers. With these controllers implemented, the aircraft is reduced to a point mass with a steerable acceleration vector when viewed from an outer loop guidance perspective. Trajectory generation is also simplified with reference trajectories only required to be kinematically feasible. Robustness is achieved through uncertainty encapsulation and disturbance rejection at an acceleration level. The detailed design and associated analysis of the inner loop acceleration controllers is carried out for the case where the airflow incidence angles are small. For this case it is shown that under mild practically feasible conditions the inner loop dynamics decouple and become linear, thereby allowing the derivation of closed form pole placement solutions. Dimensional and normalised non-dimensional time variants of the inner loop controllers are designed and their respective advantages highlighted. Pole placement constraints that arise due to the typically weak non-minimum phase nature of aircraft dynamics are developed. A generic, aircraft independent guidance control algorithm, well suited for use with the inner loop acceleration controllers, is also presented. The guidance algorithm regulates the aircraft about a kinematically feasible reference trajectory. A number of fundamental basis trajectories are presented which are easily linkable to form complex three dimensional manoeuvres. Results from simulations with a number of different aircraft and reference trajectories illustrate the versatility and functionality of the autopilot. Key words: Aircraft control, Autonomous vehicles, UAV flight control, Acceleration control, Aircraft guidance, Trajectory tracking, Manoeuvre flight control. / AFRIKAANSE OPSOMMING: ’n Strategie vir die ontwerp van ’n effektiewe, prakties haalbaar, robuuste, rekenkundig effektiewe outoloods vir drie dimensionele maneuver vlugbeheer van onbemande vliegtuie word voorgestel. Die kerneienskap van die strategie is die ontwerp van oriëntasie-onafhanklike binnelus-versnellingbeheerders. Hierdie beheerders stel die navigasie buitelus in staat om die voertuig as ’n puntmassa met ’n stuurbare versnellingsvektor te beskou. Trajekgenerasie is ook vereenvoudig deurdat verwysingstrajekte slegs kinematies haalbaar hoef te wees. Robuustheid word verkry deur onsekerhede en versteuringsverwerping op ’n versnellingsvlak te hanteer. Die gedetaileerde ontwerp en saamhangende analise van die binnelus versnellingsbeheerders word uitgevoer vir die geval waar die invalshoeke klein is. Dit word aangetoon dat, onder praktiese omstandighede, die binnelus dinamika ontkoppel kan word en lineêr word, wat die afleiding van geslotevorm poolplasingoplossings toelaat. Dimensionele en genormaliseerde, nie-dimensionele tydvariante van die binnelusbeheerders word ontwerp en hul onderskeidelike voordele word uitgewys. Poolplasing beperkings, wat ontstaan as gevolg van die tipiese geringe nie-minimum fasegedrag van voertuigdinamika, word ontwikkel. ’n Gepaste generiese, voertuig onafhanklike navigasiebeheer algoritme vir gebruik saam met die binnelus-versnellingsbeheerders word voorgestel. Die voertuig word om ’n kinematies haalbare verwysingstrajek deur hierdie navigasie algoritme gereguleer. ’n Aantal fundamentele trajekte word voorgestel wat maklik gekombineer kan word om komplekse drie dimensionele maneuvers te vorm. Die veelsydigheid en funksionaliteit van die outoloods word deur simulasieresultate met ’n verskeidenheid voertuie en verwysingstrajekte gedemonstreer.

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