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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Active control of fan noise from a turbofan engine

A three channel active control system is applied to an operational turbofan engine in order to reduce tonal noise produced by both the fan and high pressure compressor. The control approach is the feedforward filtered-x least-mean-square algorithm implemented on a digital signal processing board. Reference transducers mounted on the engine case provides blade passing and harmonics frequency information to the controller. Error information is provided by large area microphones placed in the acoustic far field. In order to minimize the error signal, the controller actuates loudspeakers mounted on the inlet to produce destructive interference. The sound pressure level of the fundamental tone of the fan was reduced using the three channel controller by up to 16 dB over a 60 deg angle about the engine axis. A single channel controller could produce reduction over a 30 deg angle. The experimental results show the control to be robust. Simultaneous control of two tones is done with parallel controllers. The fundamental and the first harmonic tones of the fan were controlled simultaneously with reductions of 12 dBA and 5 dBA, respectively, measured on the engine axis. Simultaneous control was also demonstrated for the fan fundamental and the high pressure compressor fundamental tones.

Thomas, Russell H.↗
NASA NTRS1993

A layered approach to structural control system design for the JPL phase B testbed

This paper describes our efforts in structural control experiments for a flexible precision structure using both passive and active control. Specifically, a layered structural control approach utilizing passive viscous dampers, colocated and noncolocated active control is used. The passive dampers and active colocated control loops are used to enhance stability and robustness and the noncolocated multivariable controller is designed with respect to a partially controlled structure to further improve the performance. Our approach to the multivariable design problem requires not only a state space model description of the plant, but also an accompanying uncertainty model. To support the multivariable robust control design development, a significant effort in system identification was undertaken. The process of identification and identified results are discussed. Noncolocated controllers are designed using the H(infinity)/mu-synthesis methodology. The order of the controller is typically large, hence, model reduction is performed for practical digital implementation on a real-time control system developed at JPL. Finally, experimental results are presented and some of lessons are discussed.

Chu, Cheng-Chih↗
NASA NTRS1994

Design and evaluation of a Stochastic Optimal Feed-forward and Feedback Technology (SOFFT) flight control architecture

This paper describes the design and evaluation of a stochastic optimal feed-forward and feedback technology (SOFFT) control architecture with emphasis on the feed-forward controller design. The SOFFT approach allows the designer to independently design the feed-forward and feedback controllers to meet separate objectives and then integrate the two controllers. The feed-forward controller has been integrated with an existing high-angle-of-attack (high-alpha) feedback controller. The feed-forward controller includes a variable command model with parameters selected to satisfy level 1 flying qualities with a high-alpha adjustment to achieve desired agility guidelines, a nonlinear interpolation approach that scales entire matrices for approximation of the plant model, and equations for calculating feed-forward gains developed for perfect plant-model tracking. The SOFFT design was applied to a nonlinear batch simulation model of an F/A-18 aircraft modified for thrust vectoring. Simulation results show that agility guidelines are met and that the SOFFT controller filters undesired pilot-induced frequencies more effectively during a tracking task than a flight controller that has the same feedback control law but does not have the SOFFT feed-forward control.

Ostroff, Aaron J.↗
NASA NTRS1995

Control system design for the MOD-5A 7.3 mW wind turbine generator

This paper provides descriptions of the requirements analysis, hardware development and software development phases of the Control System design for the MOD-5A 7.3 mW Wind Turbine Generator. The system, designed by General Electric Company, Advanced Energy Programs Department, under contract DEN 3-153 with NASA Lewis Research Center and DOE, provides real time regulation of rotor speed by control of both generator torque and rotor torque. A variable speed generator system is used to provide both airgap torque control and reactive power control. The wind rotor is designed with segmented ailerons which are positioned to control blade torque. The central component of the control system, selected early in the design process, is a programmable controller used for sequencing, alarm monitoring, communication, and real time control. Development of requirements for use of aileron controlled blades and a variable speed generator required an analytical simulation that combined drivetrain, tower and blade elastic modes with wind disturbances and control behavior. An orderly two phase plan was used for controller software development. A microcomputer based turbine simulator was used to facilitate hardware and software integration and test.

Barton, Robert S.↗
NASA NTRS1990

An object oriented generic controller using CLIPS

In today's applications, the need for the division of code and data has focused on the growth of object oriented programming. This philosophy gives software engineers greater control over the environment of an application. Yet the use of object oriented design does not exclude the need for greater understanding by the application of what the controller is doing. Such understanding is only possible by using expert systems. Providing a controller that is capable of controlling an object by using rule-based expertise would expedite the use of both object oriented design and expert knowledge of the dynamic of an environment in modern controllers. This project presents a model of a controller that uses the CLIPS expert system and objects in C++ to create a generic controller. The polymorphic abilities of C++ allow for the design of a generic component stored in individual data files. Accompanying the component is a set of rules written in CLIPS which provide the following: the control of individual components, the input of sensory data from components and the ability to find the status of a given component. Along with the data describing the application, a set of inference rules written in CLIPS allows the application to make use of sensory facts and status and control abilities. As a demonstration of this ability, the control of the environment of a house is provided. This demonstration includes the data files describing the rooms and their contents as far as devices, windows and doors. The rules used for the home consist of the flow of people in the house and the control of devices by the home owner.

Nivens, Cody R.↗
NASA NTRS1997

Control Synthesis for a Class of Hybrid Systems Subject to Configuration-Based Safety Constraints

We examine a class of hybrid systems which we call Composite Hybrid Machines (CHM's) that consists of the concurrent (and partially synchronized) operation of Elementary Hybrid Machines (EHM's). Legal behavior, specified by a set of illegal configurations that the CHM may not enter, is to be achieved by the concurrent operation of the CHM with a suitably designed legal controller. In the present paper we focus on the problem of synthesizing a legal controller, whenever such a controller exists. More specifically, we address the problem of synthesizing the minimally restrictive legal controller. A controller is minimally restrictive if, when composed to operate concurrently with another legal controller, it will never interfere with the operation of the other controller and, therefore, can be composed to operate concurrently with any other controller that may be designed to achieve liveness specifications or optimality requirements without the need to reinvestigate or reverify legality of the composite controller. We confine our attention to a special class of CHM's where system dynamics is rate-limited and legal guards are conjunctions or disjunctions of atomic formulas in the dynamic variables (of the type x less than or equal to x(sub 0), or x greater than or equal to x(sub 0)). We present an algorithm for synthesis of the minimally restrictive legal controller. We demonstrate our approach by synthesizing a minimally restrictive controller for a steam boiler (the verification of which recently received a great deal of attention).

Heymann, Michael↗
NASA NTRS1997

Experiments in Aircraft Roll-Yaw Control using Forebody Tangential Blowing

Advantages of flight at high angles of attack include increased maneuverability and lift capabilities. These are beneficial not only for fighter aircraft, but also for future supersonic and hypersonic transport aircraft during take-off and landing. At high angles of attack the aerodynamics of the vehicle are dominated by separation, vortex shedding and possibly vortex breakdown. These phenomena severely compromise the effectiveness of conventional control surfaces. As a result, controlled flight at high angles of attack is not feasible for current aircraft configurations. Alternate means to augment the control of the vehicle at these flight regimes are therefore necessary. The present work investigates the augmentation of an aircraft flight control system by the injection of a thin sheet of air tangentially to the forebody of the vehicle. This method, known as Forebody Tangential Blowing (FTB), has been proposed as an effective means of increasing the controllability of aircraft at high angles of attack. The idea is based on the fact that a small amount of air is sufficient to change the separation lines on the forebody. As a consequence, the strength and position of the vortices are altered causing a change on the aerodynamic loads. Although a very effective actuator, forebody tangential blowing is also highly non-linear which makes its use for aircraft control very difficult. In this work, the feasibility of using FTB to control the roll-yaw motion of a wind tunnel model was demonstrated both through simulations and experimentally. The wind tunnel model used in the experiments consists of a wing-body configuration incorporating a delta wing with 70-degree sweep angle and a cone-cylinder fuselage. The model is equipped with forebody slots through which blowing is applied. There are no movable control surfaces, therefore blowing is the only form of actuation. Experiments were conducted at a nominal angle of attack of 45 degrees. A unique apparatus that constrains the model to two degrees-of-freedom, roll and yaw, was designed and built. The apparatus was used to conduct dynamic experiments which showed that the system was unstable, its natural motion divergent. A model for the unsteady aerodynamic loads was developed based on the basic physics of the flow and results from flow visualization experiments. Parameters of the aerodynamic model were identified from experimental data. The model was validated using data from dynamic experiments. The aerodynamic model completes the equations of motion of the system which were used in the design of control laws using blowing as the only actuator. The unsteady aerodynamic model was implemented as part of the real-time vehicle control system. A control strategy using asymmetric blowing was demonstrated experimentally. A discrete vortex method was developed to help understand the main physics of the flow. The method correctly captures the interactions between forebody and wing vortices. Moreover, the trends in static loads and flow structure are correctly represented. Flow visualization results revealed the vortical structure of the flow to be asymmetric even for symmetric flight conditions. The effects of blowing, and roll and yaw angles on the flow structure were determined. It is shown that superimposing symmetric and asymmetric blowing has a linearizing effect on the actuator characteristics. Transient responses of roll and yaw moments to step input blowing were characterized, and their differences were explained based on the physical mechanisms through which these loads are generated.

Pedreiro, Nelson↗
NASA NTRS1961

Stability and Control Characteristics of a Small-Scale Model of an Aerial Vehicle Supported by Two Ducted Fans

An investigation has been made to determine the stability and control characteristics in hovering and in forward flight of a free-flight model representing a type of vertical-take-off-and-landing aircraft which utilizes two fixed ducted fans as its sole source of lift and propulsion. The model, having fans 28 inches in diameter, was considered to be approximately one-third the size of a full-scale aircraft. Control moments for most of the hovering tests and all the forward-flight tests were provided by remotely controlled compressed-air jets at the sides and ends of the model. For one brief phase of the hovering investigation a system of vanes in the duct slipstreams was substituted for the jets as a means of roll control. During the forward-flight tests, the model was flown with both the tandem and side-by-side duct arrangements. In hovering the model exhibited strongly divergent oscillations about the pitch and roll axes. The pitching oscillation of the tandem configuration was of a fairly long period and was not particularly difficult to control; the rolling oscillation, however, was of a relatively short period and was extremely difficult to control. Both oscillations could be completely eliminated by the addition of a sufficient amount of artificial damping. The control moments produced by the vane-type roll control system were weak and were accompanied by a side force of appreciable magnitude and undesirable direction. In forward flight the model required an undesirably large nose-down tilt angle for equilibrium at any appreciable speed. A vane was placed transversely in the slipstream of the forward duct of the tandem configuration in an attempt to reduce this tilt angle. The vane was effective in reducing the tilt angle but apparently caused an increase in the power requirements and in the angle-of-attack instability. Without the vane, a forward speed of 30 knots (full scale) required a nose-down tilt angle of about 300. A powerful pitch control moment was required not only to maintain the trim attitude but also to 2 overcome the effects of instability with angle of attack. Less pitch control moment was required for the tandem configuration than for the side-by-side configuration at any given forward speed. The instability in roll increased with forward speed. No forward speeds in excess of about 20 knots (full scale) were achieved until the artificial damping in roll and the yaw control moment were increased appreciably above values which had proved satisfactory for hovering flight.

Parlett, Lysle P.↗
NASA NTRS1999

Simulator Evaluation of Simplified Propulsion-Only Emergency Flight Control Systems on Transport Aircraft

With the advent of digital engine control systems, considering the use of engine thrust for emergency flight control has become feasible. Many incidents have occurred in which engine thrust supplemented or replaced normal aircraft flight controls. In most of these cases, a crash has resulted, and more than 1100 lives have been lost. The NASA Dryden Flight Research Center has developed a propulsion-controlled aircraft (PCA) system in which computer-controlled engine thrust provides emergency flight control capability. Using this PCA system, an F-15 and an MD-11 airplane have been landed without using any flight controls. In simulations, C-17, B-757, and B-747 PCA systems have also been evaluated successfully. These tests used full-authority digital electronic control systems on the engines. Developing simpler PCA systems that can operate without full-authority engine control, thus allowing PCA technology to be installed on less capable airplanes or at lower cost, is also a desire. Studies have examined simplified ?PCA Ultralite? concepts in which thrust control is provided using an autothrottle system supplemented by manual differential throttle control. Some of these concepts have worked well. The PCA Ultralite study results are presented for simulation tests of MD-11, B-757, C-17, and B-747 aircraft.

Burcham, Frank W., Jr.↗
NASA NTRS1986

Integrating Computer Architectures into the Design of High-Performance Controllers

Modern control systems must typically perform real-time identification and control, as well as coordinate a host of other activities related to user interaction, on-line graphics, and file management. This paper discusses five global design considerations that are useful to integrate array processor, multimicroprocessor, and host computer system architecture into versatile, high-speed controllers. Such controllers are capable of very high control throughput, and can maintain constant interaction with the non-real-time or user environment. As an application example, the architecture of a high-speed, closed-loop controller used to actively control helicopter vibration will be briefly discussed. Although this system has been designed for use as the controller for real-time rotorcraft dynamics and control studies in a wind-tunnel environment, the control architecture can generally be applied to a wide range of automatic control applications.

Jacklin, Stephen A.↗
NASA NTRS1999

Development of An Intelligent Flight Propulsion Control System

The initial design and demonstration of an Intelligent Flight Propulsion and Control System (IFPCS) is documented. The design is based on the implementation of a nonlinear adaptive flight control architecture. This initial design of the IFPCS enhances flight safety by using propulsion sources to provide redundancy in flight control. The IFPCS enhances the conventional gain scheduled approach in significant ways: (1) The IFPCS provides a back up flight control system that results in consistent responses over a wide range of unanticipated failures. (2) The IFPCS is applicable to a variety of aircraft models without redesign and,(3) significantly reduces the laborious research and design necessary in a gain scheduled approach. The control augmentation is detailed within an approximate Input-Output Linearization setting. The availability of propulsion only provides two control inputs, symmetric and differential thrust. Earlier Propulsion Control Augmentation (PCA) work performed by NASA provided for a trajectory controller with pilot command input of glidepath and heading. This work is aimed at demonstrating the flexibility of the IFPCS in providing consistency in flying qualities under a variety of failure scenarios. This report documents the initial design phase where propulsion only is used. Results confirm that the engine dynamics and associated hard nonlineaaities result in poor handling qualities at best. However, as demonstrated in simulation, the IFPCS is capable of results similar to the gain scheduled designs of the NASA PCA work. The IFPCS design uses crude estimates of aircraft behaviour. The adaptive control architecture demonstrates robust stability and provides robust performance. In this work, robust stability means that all states, errors, and adaptive parameters remain bounded under a wide class of uncertainties and input and output disturbances. Robust performance is measured in the quality of the tracking. The results demonstrate the flexibility of the IFPCS architecture and the ability to provide robust performance under a broad range of uncertainty. Robust stability is proved using Lyapunov like analysis. Future development of the IFPCS will include integration of conventional control surfaces with the use of propulsion augmentation, and utilization of available lift and drag devices, to demonstrate adaptive control capability under a greater variety of failure scenarios. Further work will specifically address the effects of actuator saturation.

Calise, A. J.↗
NASA NTRS2000

Sliding Mode Control of the X-33 with an Engine Failure

Ascent flight control of the X-3 is performed using two XRS-2200 linear aerospike engines. in addition to aerosurfaces. The baseline control algorithms are PID with gain scheduling. Flight control using an innovative method. Sliding Mode Control. is presented for nominal and engine failed modes of flight. An easy to implement, robust controller. requiring no reconfiguration or gain scheduling is demonstrated through high fidelity flight simulations. The proposed sliding mode controller utilizes a two-loop structure and provides robust. de-coupled tracking of both orientation angle command profiles and angular rate command profiles in the presence of engine failure, bounded external disturbances (wind gusts) and uncertain matrix of inertia. Sliding mode control causes the angular rate and orientation angle tracking error dynamics to be constrained to linear, de-coupled, homogeneous, and vector valued differential equations with desired eigenvalues. Conditions that restrict engine failures to robustness domain of the sliding mode controller are derived. Overall stability of a two-loop flight control system is assessed. Simulation results show that the designed controller provides robust, accurate, de-coupled tracking of the orientation angle command profiles in the presence of external disturbances and vehicle inertia uncertainties, as well as the single engine failed case. The designed robust controller will significantly reduce the time and cost associated with flying new trajectory profiles or orbits, with new payloads, and with modified vehicles

Shtessel, Yuri B.↗
NASA NTRS2002

Application of Sliding Mode Methods to the Design of Reconfigurable Flight Control Systems

Observer-based sliding mode control is investigated for application to aircraft reconfigurable flight control. A comprehensive overview of reconfigurable flight control is given, including, a review of the current state-of-the-art within the subdisciplines of fault detection, parameter identification, adaptive control schemes, and dynamic control allocation. Of the adaptive control methods reviewed, sliding mode control (SMC) appears very promising due its property of invariance to matched uncertainty. An overview of sliding mode control is given and its remarkable properties are demonstrated by example. Sliding mode methods, however, are difficult to implement because unmodeled parasitic dynamics cause immediate and severe instability. This presents a challenge for all practical applications with limited bandwidth actuators. One method to deal with parasitic dynamics is the use of an asymptotic observer in the feedback path. Observer-based SMC is investigated, and a method for selecting observer gains is offered. An additional method for shaping the feedback loop using a filter is also developed. It is shown that this SMC prefilter is equivalent to a form of model reference hedging. A complete design procedure is given which takes advantage of the sliding mode boundary layer to recast the SMC as a linear control law. Frequency domain loop shaping is then used to design the sliding manifold. Finally, three aircraft applications are demonstrated. An F-18/HARV is used to demonstrate a SISO pitch rate tracking controller. It is also used to demonstrate a MIMO lateral-directional roll rate tracking controller. The last application is a full linear six degree-of-freedom advanced tailless fighter model. The observer-based SMC is seen to provide excellent tracking with superior robustness to parameter changes and actuator failures.

Wells, Scott R.↗
NASA NTRS2004

Monitoring the Performance of a Neuro-Adaptive Controller

Traditional control has proven to be ineffective to deal with catastrophic changes or slow degradation of complex, highly nonlinear systems like aircraft or spacecraft, robotics, or flexible manufacturing systems. Control systems which can adapt toward changes in the plant have been proposed as they offer many advantages (e.g., better performance, controllability of aircraft despite of a damaged wing). In the last few years, use of neural networks in adaptive controllers (neuro-adaptive control) has been studied actively. Neural networks of various architectures have been used successfully for online learning adaptive controllers. In such a typical control architecture, the neural network receives as an input the current deviation between desired and actual plant behavior and, by on-line training, tries to minimize this discrepancy (e.g.; by producing a control augmentation signal). Even though neuro-adaptive controllers offer many advantages, they have not been used in mission- or safety-critical applications, because performance and safety guarantees cannot b e provided at development time-a major prerequisite for safety certification (e.g., by the FAA or NASA). Verification and Validation (V&V) of an adaptive controller requires the development of new analysis techniques which can demonstrate that the control system behaves safely under all operating conditions. Because of the requirement to adapt toward unforeseen changes during operation, i.e., in real time, design-time V&V is not sufficient.

Schumann, Johann↗
NASA NTRS2004

Pilots Rate Augmented Generalized Predictive Control for Reconfiguration

The objective of this paper is to report the results from the research being conducted in reconfigurable fight controls at NASA Ames. A study was conducted with three NASA Dryden test pilots to evaluate two approaches of reconfiguring an aircraft's control system when failures occur in the control surfaces and engine. NASA Ames is investigating both a Neural Generalized Predictive Control scheme and a Neural Network based Dynamic Inverse controller. This paper highlights the Predictive Control scheme where a simple augmentation to reduce zero steady-state error led to the neural network predictor model becoming redundant for the task. Instead of using a neural network predictor model, a nominal single point linear model was used and then augmented with an error corrector. This paper shows that the Generalized Predictive Controller and the Dynamic Inverse Neural Network controller perform equally well at reconfiguration, but with less rate requirements from the actuators. Also presented are the pilot ratings for each controller for various failure scenarios and two samples of the required control actuation during reconfiguration. Finally, the paper concludes by stepping through the Generalized Predictive Control's reconfiguration process for an elevator failure.

Soloway, Don↗
NASA NTRS2004

A Flight Control Approach for Small Reentry Vehicles

Flight control of small crew return vehicles during atmospheric reentry will be an important technology in any human space flight mission undertaken in the future. The control system presented in this paper is applicable to small crew return vehicles in which reaction control system (RCS) thrusters are the only actuators available for attitude control. The control system consists of two modules: (i) the attitude controller using the trajectory linearization control (TLC) technique, and (ii) the reaction control system (RCS) control allocation module using a dynamic table-lookup technique. This paper describes the design and implementation of the TLC attitude control and the dynamic table-lookup RCS control allocation for nonimal flight along with design verification test results.

Bevacqoa, Tim↗
NASA NTRS2005

Effects of Control Mode and R-Ratio on the Fatigue Behavior of a Metal Matrix Composite

Composite Because of their high specific stiffness and strength at elevated temperatures, continuously reinforced metal matrix composites (MMC's) are under consideration for a future generation of aeropropulsion systems. Since components in aeropropulsion systems experience substantial cyclic thermal and mechanical loads, the fatigue behavior of MMC's is of great interest. Almost without exception, previous investigations of the fatigue behavior of MMC's have been conducted in a tension-tension, load-controlled mode. This has been due to the fact that available material is typically less than 2.5-mm thick and, therefore, unable to withstand high compressive loads without buckling. Since one possible use of MMC's is in aircraft skins, this type of testing mode may be appropriate. However, unlike aircraft skins, most engine components are thick. In addition, the transient thermal gradients experienced in an aircraft engine will impose tension-compression loading on engine components, requiring designers to understand how the MMC will behave under fully reversed loading conditions. The increased thickness of the MMC may also affect the fatigue life. Traditionally, low-cycle fatigue (LCF) tests on MMC's have been performed in load control. For monolithic alloys, low-cycle fatigue tests are more typically performed in strain control. Two reasons justify this choice: (1) the critical volume from which cracks initiate and grow is generally small and elastically constrained by the larger surrounding volume of material, and (2) load-controlled, low-cycle fatigue tests of monolithics invariably lead to unconstrained ratcheting and localized necking--an undesired material response because the failure mechanism is far more severe than, and unrelated to, the fatigue mechanism being studied. It is unknown if this is the proper approach to composite testing. However, there is a lack of strain-controlled data on which to base any decisions. Consequently, this study addresses the isothermal, LCF behavior of a [0]_32 MMC tested under strain- and load-controlled conditions for both zero-tension and tension-compression loading conditions. These tests were run at 427 C on thick specimens of SiC-reinforced Ti-15-3. For the fully-reversed tests, no difference was observed in the lives between the load- and strain-controlled tests. However, for the zero-tension tests, the strain-controlled tests had longer lives by a factor of 3 in comparison to the load-controlled tests. This was due to the fact that under strain-control the specimens cyclically softened, reducing the cracking potential. In contrast, the load-controlled tests ratcheted toward larger tensile strains leading to an eventual overload of the fibers. Fatigue tests revealed that specimens tested under fully-reversed conditions had lives approximately an order of magnitude longer than for those specimens tested under zero tension. When examined on a strain-range basis, the fully reversed specimens had similar, but still shorter lives than those of the unreinforced matrix material. However, the composite had a strain limitation at short lives because of the limited strain capacity of the brittle ceramic fiber. The composite also suffered at very high lives because of the lack of an apparent fatigue limit in comparison to the unreinforced matrix. The value of adding fibers to the matrix is apparent when the fatigue lives are plotted as a function of stress range. Here, the composite is far superior to the unreinforced matrix because of the additional load-carrying capacity of the fibers.

Source record↗
NASA NTRS2006

Reconfigurable Control with Neural Network Augmentation for a Modified F-15 Aircraft

Description of the performance of a simplified dynamic inversion controller with neural network augmentation follows. Simulation studies focus on the results with and without neural network adaptation through the use of an F-15 aircraft simulator that has been modified to include canards. Simulated control law performance with a surface failure, in addition to an aerodynamic failure, is presented. The aircraft, with adaptation, attempts to minimize the inertial cross-coupling effect of the failure (a control derivative anomaly associated with a jammed control surface). The dynamic inversion controller calculates necessary surface commands to achieve desired rates. The dynamic inversion controller uses approximate short period and roll axis dynamics. The yaw axis controller is a sideslip rate command system. Methods are described to reduce the cross-coupling effect and maintain adequate tracking errors for control surface failures. The aerodynamic failure destabilizes the pitching moment due to angle of attack. The results show that control of the aircraft with the neural networks is easier (more damped) than without the neural networks. Simulation results show neural network augmentation of the controller improves performance with aerodynamic and control surface failures in terms of tracking error and cross-coupling reduction.

Burken, John J.↗