Flexible Vehicle Research Articles

Hybrid control of flexible multi-body systems

In constrained systems of rigid and flexible bodies, the gross rigid body motion and elastic deformation cannot be controlled independently because of the coupling between these two motions. A hybrid control method for suppressing the vibration of a geometrically nonlinear flexible multi-body system is proposed in this paper. This method utilizes both the passive and active control concepts. In the passive control strategy, flexible components in the system are manufactured from fiber-reinforced composite laminates which have high strength-to-weight and stiffness-to-weight ratios. On the other hand, the active control scheme used in this paper utilizes measurable velocity and acceleration signals to produce the command signals required to activate the actuator forces. A small number of sensors and controllers with constant gain factors are used in order to obtain a low-cost and simple control system. The generalized active control forces associated with the system generalized coordinates are developed using the virtual work and are written in terms of the coupled set of reference and elastic coordinates. The system differential equations of motion are developed using Lagrange's equation and the Jacobian matrix of the nonlinear algebraic constraint equations describing mechanical joints in the system is used to identify a set of independent generalized coordinates. The associated independent differential equations are identified and are written in the state space formulation. The characteristics of the proposed hybrid control are evaluated through computer simulations of a seven-body flexible vehicle. The performance characteristics of the hybrid control are also compared to the performance characteristics of the passive and active controls.

BODY STRUCTURE AND VEHICLE DYNAMICS

SUMMARY This paper is a presentation of aspects on car body design for mass transit vehicles and methods which has been evolved for the analysis of non-linear flexible railway vehicles by use of normal modes. In the end of the paper results from an experimental modal analysis are shown.

The Medieval Mystical Tradition in England: Papers Read at Dartington Hall, July, 1984 ed. by Marion Glasscoe

REVIEWS the glosses and rubrics. To Gillmeister, the final disposition of CTis that of a pilgrims' anthology of allegorical stories promoting the heavenlyJerusa­ lem (p. 142), with The Parson's Tale its apotheosis. Some readers may favor, on the other hand, such a position as Charles Owen's, that the theological thrust of CT, originally framed by Melibee andParsT, waned as Chaucer grew more and more involved in the personalities of the pilgrims and the interactions of their tales. Perhaps it is time to reopen Manly and Rickert's belief (2.472) and argue that bothParsTand theRetraction"have no legitimate claim to a place in the CT." Chaucer's Conversion, reproduced from typescript, is a masterpiece of accuracy;I have not found a single misprint.IfI personally find it too filled with newefangelness, neverthelessI can admire its style and erudition and its mine of valuable references. ROSSELL HOPE ROBBINS Research Center for Medieval Studies, Saugerties, New York MARION GLASSCOE, ed. The Medieval Mystical Tradition in England: Papers Read at Dartington Hall, July, 1984. Woodbridge, Suffolk: Boydell & Brewer, 1984. Pp. 191. £15. The nine essays in this volume derive from the proceedings of theInterna­ tional Exeter Symposium, whose aim is to cultivate an interdisciplinary body of scholarship through open exchange among students of the medi­ eval mystics. Like its predecessors (published in 1980 and 1982) the collection reflects an intellectual vitality that characterizes the eclectic approach distinguishing mystic studies in recent years. Although a few of the essays are broad enough in scope to be of interest to readers with a cursory knowledge of English devotional and mystical texts, The Medieval Mystical Tradition in England will appeal primarily to specialists who can shift comfortably between textual and literary studies. For these, this volume presents provocative discussions, such as Franz Wohrer's "Ap­ proach to the Mystographical Treatises of the Cloud-Author Through Carl Albrecht's Psychology of Mystical Consciousness." The authors offer a wide variety of means to probe fruitfully mystical experience, and their scholarship collectively emphasizes the importance of locating mystical texts in cultural, historical, psychological, and literary 191 STUDIES IN THE AGE OF CHAUCER contexts. The traditional perspective of the mystic as an isolated religious phenomenon has compelled past readers to survey these highly evocative writings cautiously from either a skeptical or a respectful distance. In contrast, this series of essays successfully expounds the medieval con­ templative and devotional traditions from which the Englishmystics drew and adapted their personal and didactic forms of religious expression. In her briefforeword, editor Marion Glasscoe states that the papers form "significant groupings" and generate "coherent patterns" as an organizing principle (p. 7). She neatly juxtaposes Susan Dickman's discussion of Margery Kempe's innovative role in a Continental tradition ofpious wives with David Wallace's intriguing study ofthe cultural and political milieus that fostered similarities in the piety of Kempe and Catherine of Sienna. Dickman explores the emergence of The Book ofMargery Kempe from a "general breakdown ofold institutional forms...and the establishment of personal experience in their place," focusing on Margery's isolation from pious women as the key factor contributing to the singularity of her religious vocation (p. 157). Wallace presents both women's spiritual ex­ pression as stemming from popular literary traditions ofaffective devotion exemplified in works like the Meditationes vitae Christi. Catherine's strong familial bonds and exposure to homely devotions encouraged her, like Kempe, to find "materials for religious observance in the forms ofdomestic life" (p. 185). Together the essays provide complementary and richly informed perspectives of late-medieval feminine spirituality. Of equal interest are essays by Ritamary Bradley and A. P. Baldwin surveying the development of two widely prevalent spiritual metaphors that offered both contemplatives and beginners in spiritual instruction a means of structuring progress toward pefection: the speculum image and the tripartite reformation of the soul. Bradley's essay emphasizes the interpretative nature of mystical language and eloquently illustrates how readers must perceive such metaphors as potent, flexible vehicles ofinterior growth rather than as static emblems. In turn, Baldwin's study of the tripartite reformation ofthe soul as a structural principle in The Pearland Piers Plowman raises familiar critical questions about the success ofrigidly pressing either...

Equations of motion of a quasisteady flight vehicle utilizing restrained static aeroelastic characteristics

Mean axes provide the usual reference in maneuvering and dynamic response analyses of flexible vehicles. Attached or structural axes have also been used because the flexibility characteristics of the structure are only determined for a restrained structure. If the structural axes are employed, a relationship is required for the orientations of the structural axes relative to the mean axes, since the equations of motion determine the orientations of the mean axes. If this relationship is not considered, as it has not been in a number of publications, the solution to the equations of motion of the structural axes is not invariant with the choice of support configuration used in the calculation of the structural flexibility influence coefficients and is, therefore, incorrect. This relationship and the correct equations of motion for the structural axes are presented, and the correctness of the formulation is demonstrated numerically in studies of longitudinal maneuvering of an example forward-swept-wing airplane at constant forward velocity. Although the paper assumes constant airspeed in the basic developments, it concludes with discussions of aeroelastic speed derivatives and aeroelastic effects on drag. The paper assumes quasisteady equilibrium of the structure with its applied loads throughout.

Pilot modeling and closed-loop analysis of flexible aircraft in the pitch tracking task

The issue addressed in the appropriate modeling technique for pilot vehicle analysis of large flexible aircraft, when the frequency separation between the rigid-body mode and the dynamic aeroelastic modes is reduced. This situation was shown to have significant effects on pitch-tracking performance and subjective rating of the task, obtained via fixed base simulation. Further, the dynamics in these cases are not well modeled with a rigid-body-like model obtained by including only 'static elastic' effects, for example. It is shown that pilot/vehicle analysis of this data supports the hypothesis that an appropriate pilot-model structure is an optimal-control pilot model of full order. This is in contrast to the contention that a representative model is of reduced order when the subject is controlling high-order dynamics as in a flexible vehicle. The key appears to be in the correct assessment of the pilot's objective of attempting to control 'rigid-body' vehicle response, a response that must be estimated by the pilot from observations contaminated by aeroelastic dynamics. Finally, a model-based metric is shown to correlate well with the pilot's subjective ratings.

Audio-visual materials and the curriculum—a key development?

Educational technology, with its highly structured use of carefully prepared learning materials, has been around now for 40 years. In that time, millions of pounds have been poured into it in a worldwide effort to improve the quality of teaching and the efficiency of learning. While the technical quality of what is now available is undeniably improved, its impact has been less than radical. Will the possession of expensive hardware, proliferative software, and reasonably well-trained support professionals have any. marked effect on schools of nursing? The answer—in the short term—is probably no. Given the small proportion of time students spend in school, it is unreasonable to expect qualitative results. But in the long term it is quite possible that an emphasis on these issues will quickly uncover more basic questions—curricular questions which could have far-reaching effects on nurse training. And as we move through the 80s, faced with the computer revolution, where a low-priced pocket computer game contains the entire primary mathematics syllabus—what price the syllabus of nurse training? The hope is that the coming decade will offer better, more flexible vehicles for training—but the suggestion is that to make the most productive use of developments, some degree of standardisation is necessary. Whether the nursing profession can move away from the NIH (‘not invented here’) syndrome to embrace the possibilities of the 80s remains to be seen.

Singular value analysis of deformable systems

Singular value analysis, balancing, and approximation of a class of deformable systems are investigated. The deformable systems considered herein include several important cases of flexible aerospace vehicles and are characterized by countably infinitely many poles and zeros on the imaginary axis. The analysis relies completely on the so-called asymptotic singular value decompositon of the Hankel operator associated with the impulse response of the system. A parametric study of a six-dimensional single-input single-output case is performed.

Actuator placement from degree of controllability criteria for regular slewing of flexible spacecraft

An important unresolved problem in the attitude and shape control of future large flexible spacecraft is the determination of appropriate locations throughout the flexible vehicle for placement of control system actuators. In a separate work a definition of the degree of controllability was generated for this purpose when the control objective was to return the spacecraft to the desired equilibrium configuration after any disturbance. In some potential space missions the objective will require angular slewing maneuvers of a flexible structure. The optimum actuator locations should be significantly different for this objective. In this paper, concepts of the degree of controllability of a control system for performing standard maneuvers are developed from basic physical considerations, and then numerical methods for generating the degree of controllability are developed. These results offer the control system designer a method of evaluating the effectiveness of candidate actuator distributions. The method is shown to take on a relatively simple form when spacecraft modal coordinates are used.

Optimal Large-Angle Single-Axis Rotational Maneuvers of Flexible Spacecraft

The necessary conditions formulated from Pontryagin's principle for optimal single-axis reorientations of a flexible vehicle having a control system capable of generating a continuous torque (on a rigid part of the structure) are discussed in this paper. The flexural deformations are modeled using the assumed modes method and only small (linear) flexural displacements are considered. A single-stage relaxation process is proposed for solution of the two-point boundary-value problem. Starting iteratives for initial costate variables are obtained by zeroing the kinematic nonlinearity in the state equation, leading to a closed-form solution algorithm. The relaxation process increases the participation of the nonlinearity in a sequence of neighboring optimal solutions, converging finally to the solution of the nonlinear problem.

Modal Identities for Elastic Bodies, With Application to Vehicle Dynamics and Control

It is a standard procedure to analyze a flexible vehicle in terms of its vibration frequencies and mode shapes. However, the entire mode shape is not needed per se, but two integrals of the mode shape, pi and hi, which correspond to the momentum and angular momentum in Mode i. Together with the natural frequencies ωi, these modal parameters satisfy several important identities, 25 of which are derived in this paper. Expansions in terms of both “constrained” and “unconstrained” modes are considered. A simple illustrative example is included. The paper concludes with some remarks on the theoretical and practical utility of these results, and several potential extensions to the theory are suggested.

A Dynamics Simulation for a High Speed Magnetically Levitated Guided Ground Vehicle

An analysis and digital computer program are developed to simulate vehicle and guideway dynamic response. The magnetic levitation is of the electrodynamic suspension type. The mathematical model includes effects of the following: vehicle and guideway flexible deformations, vehicle suspension and propulsion pod translation relative to the vehicle, multiple guideway spans and aerodynamic loading. The simulation is programmed in such a way that the number of sequential spans over which the vehicle travels can be increased without increasing the degrees of freedom in the simulation. Illustrative results of the simulation are presented.

Attitude Stability of a Pseudorate Jet-Controlled Flexible Spacecraft

The small-angle stability of a single-axis spacecraft attitude control system incorporating a nonlinear pseudorate controller, jet actuator, flexible vehicle dynamics, and a loop time delay is analyzed. The dynamics include a low-frequency rigid vehicle mode and a highly underdamped flexible mode that has its modal frequency outside the rigid vehicle control system bandwidth. The single input sinusoidal describing function for the pseudorate controller is derived and used to determine the effect of the controller on each mode individually. A stable limit cycle for the rigid vehicle mode response is predicted. The flexible mode response is predicted to be stable, unstable, or to exhibit a stable limit cycle, depending on the loop time delay and the flexible mode frequency and damping. Simulation results verify the integrity and interpretation of analytically predicted stability conditions.

Control System Design in the Presence of Severe Structural Dynamics Interactions

Control system design in the presence of severe structural/control loop interactions is treated by presenting the case history of the Orbiting Solar Observatory-8 despin control loop. Analytical design work, subsequent ground testing, and resulting in-orbit behavior are discussed. The analytical work, which is based upon the hybrid coordinate method of structural dynamic modeling, led to electronic compensation of some structural modes. Ground tests of the structure, conducted to verify analytical predictions, resulted in further modifications of the design. HE influence of flexible body dynamics on spacecraft attitude control is becoming increasingly significant as vehicle configurations become more unwieldy and control requirements become more demanding. Incorporation of large, flexible solar panels or steerable payloads in configurations of newer spacecraft (such as CTS, MARINER-4, DSCS III, INTELSAT V, and TDRS), and the development of precision pointing optical instruments to fly on future spacecraft have led to complex control problems involving spacecraft structural dynamics. Future requirements of the very large space structures being considered (such as the Space Station, Solar Power Station, and Solar Sail) pose even more demanding design problems. In coming to grips with these problems, several spacecraft designers have developed general purpose computer programs for simulation and/or analysis of flexible controlled spacecraft. !~3 These programs accomplish time simulation as well as control loop stability analysis and design for flexible space vehicles. This paper describes the experience gained with the first generation of such programs developed during the Orbiting Solar Observatory (OSO)-8 project and successfully applied to several other projects. The basic analysis technique, as described in Sec. Ill, utilizes modal models of flexible elements and employs frequency domain analysis to evaluate the stability of the control loop/flexible dynamics coupling. Bode plots, along with plots of open-loop system gain vs phase (Nichols graphs), are used extensively to provide both quantitative and qualitative descriptions of the coupling dynamics.

Copyright: The New Law's Major Revisions Affecting Writers

The copyright reform bill should become law in January, 1978. Among its major revisions are the extension of protection for life plus fifty years and the mitigation of penalties for either omission of notice or “innocent infringement.” For the first time the law specifically identifies “fair use” and certain other copying practices as user rights. The issues of integrity of text and the use of protected text within computer systems have not been treated. The law's text itself remains general in the hope that it will prove to be a flexible vehicle for the future. An era of informal agreements and litigation between publishers and users can be anticipated. Scientific and technical publishing must be recognized as a special area within the publishing community on the verge of change.

Dynamics of linear systems with semiactive force generators

A semiactive element produces control forces in a dynamic system by controlled variation of a resistive parameter. Control constraints exist making the output of a semiactive element complex and nonlinear even for linear feedback control laws. State equations are derived for a general linear system with an arbitrary number of semiactive elements. These equations are piecewise-linear and exhibit intermittent linear dependencies among elements of the state vector. Two special cases exist yielding simplified descriptions of the semiactive control and system dynamics. Semiactive vibration control is applied to a flexible vehicle on a rough guideway. Numerical results demonstrate performance superior to passive suspensions and comparable to fully-active control. PPLICATION of modern control theory and parameter optimization techniques to shock and vibration control permit the design of high-performance suspension systems for taxiing aircraft1 and ground vehicles.27 Due to their sim- plicity, low cost, and reliability, passive suspensions com- posed of spring and damper elements are used in all but the most critical applications. Although control using active force generators receives considerable attention in the literature, its superior performance over passive control is frequently offset in practical designs by increased cost, complexity, energy requirements, and weight. While passive devices are self- powered and self-contained, an active force generator requires a power source to generate control inputs along with measurement and signal-processing systems. At least the disadvantages of a power supply can be eliminated by parametric control in which the parameters of passive elements are varied in response to a control signal. When a resistive parameter is varied, large control forces in a dynamic system may be generated by controlled dissipation of system energy. This type of control, which has been called semiac- tive, 8 combines features of passive control with the capability of generating the sophisticated feedback controls usually reserved for active systems. Recently, semiactive control has been studied in shock and vibration applications.811 In linear and nonlinear systems with deterministic810 and random inputs,911 these studies have established that the performance of semiactive force generators approaches that of fully active elements. This is not too surprising because any stable vibration-control system must eventually dissipate system vibrational energy, something a resistor does quite well. Although these studies illustrate basic applications and principles of semiactive control, a general treatment of the dynamics of a system with an arbitrary number of semiactive elements is lacking. Semiactive control introduces complex, nonstationary dynamics in even simple, linear systems.8'9 Because control forces are produced by a dissipative process, an inequality constraint on control power exists causing complex behavior of the semiactive control force. In this paper, a general theory of the dynamics of systems with semiactive elements is developed. Two special cases are found that provide sim- plified representations of the semiactive control and system dynamics.

Aeroelastic Loads Predictions using Finite Element Aerodynamics

Aerodynamic and structural influence coefficients are utilized to determine the load distributions, deflections, and trim parameters for a vehicle in quasi-static aeroelastic equilibrium. A matrix formulation is used to solve the various quasi-static aeroelastic problems. Nonlinearities in the aeroelastic trim equations are accounted for by an iteration of the classical closed form solution. Aerodynamic and structural idealizations are related by a surface spline transformation. Solutions are developed for symmetric, antisymmetric, and asymmetric load conditions on symmetric vehicles of general geometric shapes which may include both lifting surfaces and lifting bodies. INTRODUCTION With the advent of large order matrix solutions for the analysis of complex structures a need has arisen for a complementary approach to the external loads problem. Finite element structural analysis techniques demand that the external loads be distributed over the structure at discrete points. Therefore, shear, moment, and torque distributions along a psuedoelastic axis are no longer sufficient to define the external load distributions required by the stress analysis. A general finite element approach to the problem of the determination of aeroelastic loads on a flexible vehicle flying in a state of quasi-static equilibrium is presented here. The vector point loads available from this solution are directly applicable to matrix structural analyses. Structural and aerodynamic influence coefficients obtained from finite element idealizations of the aircraft are utilized as a basis for the method. The technique is primarily an extension of the method first suggested by ~ e d m a n ( l ) * and later generalized by odde en.(^) This work extends the efforts of the above-mentioned authors by * Numbers in parentheses designate References at end of paper.

Relay control of undamped linear systems using Lyapunov's second method

A method is presented for the application of Lyapunov's second method to the synthesis of relay-control systems for plants that have undamped responses. A technique is presented for overcoming the problems associated with the solution of the Lyapunov matrix equation when the plant eigenvalues have zero real part. The method is applied to the attitude control of a flexible space vehicle.

A General Purpose Computer Program for the Dynamic Simulation of Vehicle-Guideway Interactions

A general purpose computer program for calculating the dynamic response of vehicles traveling over surface or evaluated guideways is described. The program has application to a broad class of transportatio n systems and hence eliminates the need for numerous specialized programs. The program is modular in design and is based on the finite element or building block method in which a complex dynamic system is made up of a number of components. The equations of motion for each of these components is known, and the program automatically combines the component equations to form equations of motion for the complete system. The equations of motion are then integrated numerically to give the response of the system to variables such as guideway roughness, span length, etc. Several output options are available and on-line printer plots or off-line CalComp plots of the response can be obtained. Addition building blocks can be easily added to.the program whenever desired. The program is written in PL/I language and has been used on the IBM 360/91 computer. The program has been used on a limited number of problems, several of which are included in this paper. GENERAL purpose computer program (APLDYN)1 has been written for the simulation of the dynamics associated with vehicles traveling over surface or elevated guideways with prescribed irregularities. The program has application to a broad class of transportation systems and hence eliminates the need for numerous specialized programs. It is based on the finite element method in which a complex system is made up of a number of discrete components. This technique is not new to the structural engineer, but it has seen limited application to dynamic problems associated with discrete moving masses. The APLDYN application of this finite element technique to moving vehicle problems is similar to, but more general than that used by Hunt 2 to determine the dynamic response of a flexible vehicle moving along a flexible supporting structure. Other simulations3 ~~ 5 although useful for studying the dynamic behavior of specific systems, have been limited in scope and versatility. Kaplan et al. 3 have developed a simulation for the vertical response of a single car or a two-car train traveling across an elevated guideway with no irregularities. The guideway flexibility provides the dynamic ex citation. McHenry and Deleys4 have written a simulation for the response of automobiles when encountering obstacles such as guard rails, railroad crossings and abutments. The simulation does not handle the more general class of vehicles, elevated guideways, and roadbed irregularities encountered in new transportation systems. Melpar has also developed a comprehensive computer program5 but this program is written specifically for a conventional railcar on a surface track. The Melpar program handles a multidegree-of -freedom system but is limited in the number of mass elements that can be simulated.

Dynamic Analysis of a Flexible Vehicle Moving along a Flexible Support

This paper presents the procedures and rationale of a numeric method for determining the dynamic response of a flexible vehicle moving along a flexible supporting structure. A discrete-element model of the structure is used in the approach which permits a concise matrix formulation of the problem based more on physical than mathematical considerations. The primary factor in this discrete-element analysis is a time-dependent stiffness matrix that is established by a coordinate transformation operation and affected by 1) vehicle movement along the supporting structure and 2) intermittent detachment of the moving vehicle. Any initial curvature of the supporting structure is also taken into account. The development and results of a numerical experiment predicted on this approach are delineated.

Attitude control of flexible space vehicles

Objectives of this paper are to enhance the concept of multiple control in attitude control systems for large flexible space vehicles and to discuss some questions of stability and structure-control system interaction. The approach to the design of a multiple control system is illustrated with a typical example for which the control system configuration includes a main loop providing control for the main portion of the structure arid auxiliary loops providing active damping for the flexible appendages. Criteria for the first cut design of each auxiliary loop are given. The performance of the multiloop control system described, vs that of the corresponding single-loop, is illustrated by the results of analog simulation. Qualitative results of analysis and stability limitations of different classes of attitude control system configurations for large flexible space vehicles are also discussed. The normal mode approach particularly suitable for the use of transfer functions is considered in modeling the structure dynamics. A criterion for mode separability in a multimode structure is presented. The simplification deriving from its application to the analysis of an attitude control system is illustrated.