Robert F. Stengel

Flight control design using non-linear inverse dynamics

Aircraft in extreme flight conditions such as stalls and spins experience nonlinear forces and moments generated from high angles of attack and high angular rates. Flight control systems based upon nonlinear inverse dynamics offer the potential for providing improved levels of safety and performance in these flight conditions over the competing designs developed using linearizing assumptions. Inverse dynamics are generated for specific command variable sets of a 12-state nonlinear aircraft model to develop a control system that provides satisfactory response over the entire flight envelope. Detailed descriptions of the inertial dynamic and aerodynamic models are given, and it is shown how the command variable sets are altered as functions of the system state to add stall prevention features to the system. Simulation results are presented for various mission objectives over a range of flight conditions to confirm the effectiveness of the design.

Robust Nonlinear Control of a Hypersonic Aircraft

For the longitudinal motion of a hypersonic aircraft containing twenty-eight inertial and aerodynamic uncertain parameters, robust flight control systems with nonlinear dynamic inversion structure are synthesized. The system robustness is characterized by the probability of instability and probabilities of violations of thirty-eight performance criteria, subjected to the variations of the uncertain system parameters. The design cost function is defined as a weighted quadratic sum of these probabilities. The control system is designed using a genetic algorithm to search a design parameter space of the nonlinear dynamic inversion structure. During the search iteration, Monte Carlo evaluation is used to estimate the system robustness and cost function. This approach explicitly takes into account the design requirements and makes full use of engineering knowledge in the design process to produce practical and efficient control systems. A4 MY, m 4 Nomenclatm-e speed of sound, ftls drag coefficient lift coefficient moment coefficient due to pitch rate moment coefficient due to angle of attack moment coefficient due to elevator deflection thrust coefficient reference length, 80 ft drag, lbf altitude, ft moment of inertia, 7 X lo6 slug-ft2 lift, lbf Mach number pitching moment, lbf-ft mass, 9375 slugs pitch rate, radis radius of the Earth, 20,903,500 ft radial distance from Earth’s center, ft reference area, 3603 ft2 thrust, lbf velocity, ft/S angle of attack, rad throttle setting flight-path angle, rad elevator deflection, rad gravitational constant, 1.39 X 1Or6 ft3/s2~ density of air, slugsIft

Stochastic robustness of linear time-invariant control systems

A simple numerical procedure for estimating the stochastic robustness of a linear time-invariant system is described. Monte Carlo evaluations of the systems eigenvalues allows the probability of instability and the related stochastic root locus to be estimated. This analysis approach treats not only Gaussian parameter uncertainties but non-Gaussian cases, including uncertain-but-bounded variation. Confidence intervals for the scalar probability of instability address computational issues inherent in Monte Carlo simulation. Trivial extensions of the procedure admit consideration of alternate discriminants; thus, the probabilities that stipulated degrees of instability will be exceeded or that closed-loop roots will leave desirable regions can also be estimated. Results are particularly amenable to graphical presentation.

Relationship of Gene Expression and Chromosomal Abnormalities in Colorectal Cancer

Several studies have verified the existence of multiple chromosomal abnormalities in colon cancer. However, the relationships between DNA copy number and gene expression have not been adequately explored nor globally monitored during the progression of the disease. In this work, three types of array-generated data (expression, single nucleotide polymorphism, and comparative genomic hybridization) were collected from a large set of colon cancer patients at various stages of the disease. Probes were annotated to specific chromosomal locations and coordinated alterations in DNA copy number and transcription levels were revealed at specific positions. We show that across many large regions of the genome, changes in expression level are correlated with alterations in DNA content. Often, large chromosomal segments, containing multiple genes, are transcriptionally affected in a coordinated way, and we show that the underlying mechanism is a corresponding change in DNA content. This implies that whereas specific chromosomal abnormalities may arise stochastically, the associated changes in expression of some or all of the affected genes are responsible for selecting cells bearing these abnormalities for clonal expansion. Indeed, particular chromosomal regions are frequently gained and overexpressed (e.g., 7p, 8q, 13q, and 20q) or lost and underexpressed (e.g., 1p, 4, 5q, 8p, 14q, 15q, and 18) in primary colon tumors, making it likely that these changes favor tumorigenicity. Furthermore, we show that these aberrations are absent in normal colon mucosa, appear in benign adenomas (albeit only in a small fraction of the samples), become more frequent as disease advances, and are found in the majority of metastatic samples.

Design of Robust Control Systems for a Hypersonic Aircraft

Robuste ightcontrolsystemsaresynthesizedforthelongitudinalmotionofahypersonicaircraft.Aircraftmotion is modeled by nonlinear longitudinal dynamic equations containing 28 uncertain parameters. Each controller is designed using a genetic algorithm to search a design coefe cient space; Monte Carlo evaluation at each search point estimates stability and performance robustness. Robustness of a compensator is indicated by the probability that stability and performance of the closed-loop system will fall within allowable bounds, given likely parameter variations. A stochastic cost function containing engineering design criteria (in this case, a stability metric plus 38 step-response metrics )is minimized, producing feasible control system coefe cient sets for specie ed control system structures. This approach trades the likelihood of satisfying design goals against each other, and it identie es the plant parameter uncertainties that are most likely to compromise robustness goals. The approach makes efe cient useofcomputationaltoolsandbroadlyacceptedengineeringknowledgetoproducepracticalcontrolsystemdesigns.

Smooth function approximation using neural networks

An algebraic approach for representing multidimensional nonlinear functions by feedforward neural networks is presented. In this paper, the approach is implemented for the approximation of smooth batch data containing the functions input, output, and possibly, gradient information. The training set is associated to the network adjustable parameters by nonlinear weight equations. The cascade structure of these equations reveals that they can be treated as sets of linear systems. Hence, the training process and the network approximation properties can be investigated via linear algebra. Four algorithms are developed to achieve exact or approximate matching of input-output and/or gradient-based training sets. Their application to the design of forward and feedback neurocontrollers shows that algebraic training is characterized by faster execution speeds and better generalization properties than contemporary optimization techniques.

A Monte Carlo approach to the analysis of control system robustness

Stochastic robustness, a simple technique used to estimate the stability and performance robustness of linear, time-invariant systems, is described. The scalar probability of instability is introduced as a measure of stability robustness. Examples are given of stochastic performance robustness measures based on classical time-domain specifications. The relationship between stochastic robustness measures and control system design parameters is discussed. The technique is demonstrated by analysing an LQG/LTR system designed for a flexible robot arm. It is concluded that the analysis of stochastic robustness offers a good alternative to existing robustness metrics. It has direct bearing on engineering objectives, and it is appropriate for evaluating robust control system synthesis methods currently practised.

Restructurable control using proportional-integral implicit model following

Studies of a proportional-integral implicit model-following control law are presented. The research focuses on the ability of the control law to recover the performance of a system with failed actuators or structural damage to its prefailure level. Properties of the implicit model-following strategy are examined, and conditions for control reconfiguration are stated. The control law is applied to the lateral-directional model of a fighter aircraft, and control restructuring is shown for changes in control and system matrices. It is concluded that the implicit model-following scheme is a good candidate for control reconfiguration.

Robust nonlinear flight control of a high-performance aircraft

This paper considers probabilistic robust control of nonlinear uncertain systems. A combination of stochastic robustness and dynamic inversion is proposed for general systems that have a feedback-linearizable nominal system. In this paper, the stochastic robust nonlinear control approach is applied to a highly nonlinear complex aircraft model, the high-incidence research model (HIRM). The model addresses a high-angle-of-attack enhanced manual control problem. The aim of the flight control system is to give good handling qualities across the specified flight envelope without the use of gain scheduling and also to provide robustness to modeling uncertainties. The proposed stochastic robust nonlinear control explores the direct design of nonlinear flight control logic. Therefore, the final design accounts for all significant nonlinearities in the aircrafts high-fidelity simulation model. The controller parameters are designed to minimize the probability of violating design specifications, which provides the design with good robustness in stability and performance subject to modeling uncertainties. The present design compares favorably with earlier controllers that were generated for a benchmark design competition.

Toward intelligent flight control

Flight control systems can benefit by being designed to emulate functions of natural intelligence. Intelligent control functions fall into three categories. Declarative actions involve decision making, providing models for system monitoring, goal planning, and system/scenario identification. Procedural actions concern skilled behavior and have parallels in guidance, navigation, and adaptation. Reflexive actions are more or less spontaneous and are similar to inner-loop control and estimation. Intelligent flight control systems will contain a hierarchy of expert systems, procedural algorithms, and computational neural networks, each expanding on prior functions to improve mission capability, to increase the reliability and safety of flight, and to ease pilot workload. >