Showing papers in "Journal of Guidance Control and Dynamics in 1979"

Direct Velocity Feedback Control of Large Space Structures

Abstract: which relates the displacements u(x,t) of the equilibrium position of a flexible structure ft (a bounded open connected set with smooth boundary dfi in /7-dimensiona l space R") to the applied force distribution F(x,t). The mass density m(x) is a positive function of the location x on the structure. The change of variables u(x,t) ^u(x,t)/m(x) l/2 eliminates m(x) without changing the properties of Eq. (1) and, henceforth, assume m(x) = \. The non-negative real number £ is the damping coefficient of the structure; it is quite small for LSS. The operator A is a symmetric, non-negative, time-invariant differential operator with compact resolvent and a square root A'/2. The domain D(A) of A contains all sufficiently differentiable functions which satisfy the appropriate boundary conditions for the LSS. D(A) is dense in the Hilbert space //=L 2 (Q) with the usual inner product (.,.)

On Optimal Guidance for Homing Missiles

Abstract: A simple class of differential games with terminal cost is treated. The results are applied to the problem of optimal guidance in the neighborhood of collision course. The evader responds ideally, while the pursuer has first-order dynamics. Both players have their bounded accelerations normal to the line of sight (LOS) as control variables. The optimal guidance law is simple and can be implemented in a closed form.

Generalized Likelihood Test for FDI in Redundant Sensor Configurations

Abstract: The Generalized Likelihood Test (GLT) approach to failure detection and isolation (FDI) in redundant sets of inertial sensors is described and its relationship to the overall FDI structure is explored. Specific formulations of both the detection and the isolation problems are presented. The performance of the resulting FDI system is analyzed by means of the second-order statistics of the detection and isolation decision functions. The equivalence of the GLT approach to several previously reported approaches for both single-degree-of-freedom (SDOF) and two-degree-of-freedom (TDOF) sensors is described. To illustrate its application, the GLT approach is used to compare the FDI performance of three different redundant sensor configurations; a conical configuration of five SDOF sensors, a dodecahedron configuration of six SDOF sensors, and an octahedron configuration of four TDOF sensors.

Optimal Open-Loop Maneuver Profiles for Flexible Spacecraft

Abstract: Using the Calculus of Variations, optimal slewing profiles minimizing a structural e xcitation criterion are e stablished for a dynamically s imple spacecraft maneuvering between two quiescent states. Two problem types are considered. In the free end point problem, the structural deformation and its time derivative are unconstrained at maneuver's end. For the constrained end point problem, these variables a re r equired to vanish, which necessarily degrades the excitation criterion. Several figures are presented that illustrate both the n ature and the limitations inherent in maneuvering the spacecraft from one attitude state to another. For a given maneuver amplitude, en, the key parameter influencing structural e xcitation is the product of the maneuver time, Ta, and the lowest significant structural frequency, w. It is shown that when wTa 10, however, this penalty is fairly minor, and some reasonable control of terminal conditions is then practical. Thus it is generally d esirable that all maneuver times meet this criterion. When this is the case, it is possible to derive a normalized suboptimal slewing profile, F(x), applicable to a1 1 maneuvers. Given 0" and Ta, the commanded maneuver rate becomes e( t) = eO F(t/Ta)/Ta. Only a minor computational and memory burden is therefore necessary to perform almost optimal re-orientations.

Representation of Realistic Evasive Maneuvers by the Use of Shaping Filters

Abstract: Shaping filters can be used in the analysis of physical systems because they allow a system with a random input to be replaced by an augmented system (the original system plus the shaping filter) excited only by the white noise. This paper shows how shaping filters can be used to represent various realistic aircraft evasive maneuver policies. The shaping filter approach leads to efficient methods of performance evaluation without resorting to Monte Carlo techniques. The effectiveness of various realistic maneuver policies are compared in a simplified example in which the pursuing missile employs proportional navigation guidance.

Complete Statistical Analysis of Nonlinear Missile Guidance Systems - SLAM

Abstract: The Statistical Linearization Adjoint Method (SLAM) is a new computerized approach for the complete statistical analysis of nonlinear missile guidance systems through the combination of the CADET method and the adjoint technique. SLAM is an excellent design and analysis tool for missile guidance systems that provides an error budget for the rms miss distance and contains information concerning system behavior.

Analysis of Three-Dimensional Optimal Evasion with Linearized Kinematics

Abstract: : Three-dimensional optimal missile avoidance is analysed with a linearized kinematic model. The solution requires maximum load factor and the problem is reduced to optimal roll position control having two phases: (1) orientation of the lift vector into the optimal evasion plane, (2) rapid 180 roll meanuvers governed by a switch function. For circular missile vectograms the plane of optimal evasion is perpendicular to the line of sight. Evading from roll stabilized missiles of rectangular vectogram, further advantage can be taken maximizing the target-missile maneuver ratio. Bounded rollrate reduces the miss distance but does not affect the optimal evasive maneuver structure. (Author)

Dual-Sensor Failure Identification Using Analytic Redundancy

Abstract: In this paper we present a reliable technique for failure detection and identification for dual flight control sensors aboard the F-8 digital fly-by-wire aircraft, and we discuss the successful application of the technique to identifying failures injected on test flight downlink data. The technique exploits the analytic redundancy which exists as relationships among variables being measured by dissimilar instruments, and it accommodates both modeling errors and the allowable errors on unfailed instruments. With straightforward modification the technique may be extended to provide failure monitoring of a single remaining sensor after the identified failure of its companion sensor. Nomenclature = SPRT failure threshold ( 0) = DG case orientation angle

A Rationale for Human Operator Pulsive Control Behavior

Abstract: When performing tracking tasks which involve demanding controlled elements such as those with K/s-squared dynamics, the human operator often develops discrete or pulsive control outputs. A dual-loop model of the human operator is discussed, the dominant adaptive feature of which is the explicit appearance of an internal model of the manipulator-controlled element dynamics in an inner feedback loop. Using this model, a rationale for pulsive control behavior is offered which is based upon the assumption that the human attempts to reduce the computational burden associated with time integration of sensory inputs. It is shown that such time integration is a natural consequence of having an internal representation of the K/s-squared-controlled element dynamics in the dual-loop model. A digital simulation is discussed in which a modified form of the dual-loop model is shown to be capable of producing pulsive control behavior qualitively comparable to that obtained in experiment.

Multistep Guaranteed Cost Control of Linear Systems with Uncertain Parameters

Abstract: In many physical systems, an accurate knowledge of certain parameters is very difficult or very expensive to obtain. The designer of a remotely piloted vehicle (RPV) flight control system, for example, frequently has little data available regarding aerodynamic coefficients, due to a lack of wind tunnel tests. Based on the concept of guaranteed cost control, an algorithm has been developed to analyze the effect of parameter uncertainties on closed-loop system stability. A multistep extension of the guaranteed cost control method is developed for choosing constant feedback gains which result in stable closed-loop behavior for a range of parameter values. This technique has been applied to the design of a lateral autopilot for a rudderless RPV with uncertain aerodynamic coefficients.

Two Decades of Spacecraft Attitude Control

Abstract: Introduction T HIS paper does not fit into the usual pigeonholes of technical works, so it is necessary to start by telling the reader what it is and what it is not. It is a very personal perspective on spacecraft attitude control since the subject was first formalized in 1957, given by one who has followed it from the beginning. Special emphasis is on the period of concept formation, mainly prior to 1965, and on topics that fall within my own areas of special interests. The paper is obviously not an exhaustive literature survey of attitude control; the archive literature alone, with several thousand items, is simply too vast. Nor has there been any attempt to make the coverage complete, in the usual scholarly sense, even within its restricted scope. Although I have tried to maintain a balanced viewpoint, the reader must recognize that problems are always possible when history is recounted by an active participant. At the end of two decades of space flight it is appropriate to take a retrospective look at some of the major functional ingredients of spacecraft.! Attitude control is one of these. In the classical literature of astronautics it was scarcely recognized as an area worth studying. In 1977 I heard it said that in extreme cases the attitude control subsystem can represent up to 30% of the cost of the spacecraft. This much change in the subject's perceived importance is reason enough to review its evolution over the past two decades. If its role could be so underestimated then, what might have changed in our viewpoint toward the structure of the discipline itself and the methods available to perform the attitude control function? We would hardly expect attitude control to have suddenly emerged as a new discipline exactly 20 years ago, at the time space flight began. On the basis of the published literature, it is not unreasonable to pick 1952 as its nominal birth year. A history of the subject prior to 1952 already has been given , in which it was pointed out that the first systematic study of spacecraft attitude control in its own right began that year. (This study was documented only in unpublished form , i.e., as a company report whose original classification was "Secret".) Some forerunners existed (described in Ref. 1), extending from the technology of spin-stabilized projectiles in the 16th century, through the gyroscopic stabilization proposals in early speculative studies of space flight done in the late 1920's, to several secret studies of spacecraft sponsored by U.S. government agencies (under the euphemism "High Altitude Test Vehicles") in the second half of the 1940's. But as regards the specific subject of attitude control, published work was sparse, neither comprehensive nor intensive, and invariably formed an incidental part of broader system studies. Not until the mid 1950's did a trickle of publications begin in which spacecraft attitude control was the explicit central theme. Gravitational torque on an artificial satellite was the motivation of one work in 1956, although its wording had to be very carefully couched to avoid hinting at such a vehicle. In 1957 another addressed the effect of the Earth's magnetic field on satellite spin. Finally, in 1957 a third described for the first time in the open literature the general problem of actively controlling an artificial satellite so that one of its axes remains pointed downward toward the Earth. In the USSR that same year, Beletskii made two contributions' to problems of "classical type" (see later) having implications to the uncontrolled behavior of artificial satellites. Thus the open, archive publication of works on artificial satellites began at almost exactly the same time as the first space flight (in October, 1957), giving us a double motivation for choosing 1957 as the initial point of the two-decade period with which we are dealing. The purpose of this paper is to give an overview of the attitude control discipline as we see it at the end of 1977, and to put this into perspective with the 1957 viewpoint. Certain subsequent developments could be foreseen fairly well at that time, and these are reviewed. Perhaps more interesting is to identify those unforseen developments which were essentially new to the period. Finally, a few words are ventured about the future. The real substance of the two decades lies, of course, in the attitude control systems themselves, those that actually have been put into space. A review of those and their observed performance would be very appropriate at this time, but this

Relative Quaternion State Transition Relation

Abstract: The attitude of a maneuvering spacecraft relative to a desired noninertial reference is compactly represented in the quaternion format by the relative quaternion. The popular technique for bootstrapping the relative quaternion relies on the state transition matrix for the quaternion strapdown equations of motion wherein the rates are estimates of spacecraft rates relative to the desired reference written in body coordinates. Even with a perfect three-axis gyro pack, whose signals are noiseless and always proportional to spacecraft inertial rates, the mere fact that the transformation from reference to body coordinates is not exact causes the relative quaternion estimate by the popular technique to diverge from the truth. It is shown that the rate of divergence from the truth is a function of the post-update attitude error, the maneuver rate, and the gyro sample frequency. An alternate form of the state transition matrix is derived which is invariant under all transformations from reference to body coordinates. With perfect gyros and for a spacecraft spinning at a constant rate, the error in the relative quaternion estimate, using the invariant state transition matrix, remains bounded to the postupdate attitude error.

Optimal Flight Control Synthesis via Pilot Modeling

Abstract: The paper includes the development of a synthesis approach usable in the absence of quantitative aircraft handling qualities specifications, and yet explicitly includes design objectives based on pilot-rating concepts by means of an optimal-control pilot model. The methodology uses the pilot's objective function (from which the pilot model evolves) to design the stability augmentation (SAS). The procedure in6olves simultaneously solving for the stability augmentation system gains and pilot model via optimal control techniques. Simultaneous solution is required in this case since the pilot model (gains, etc.) depends upon the augmented plant dynamics, and the augmentation is obviously not a priori known.

Instability of Spinning Projectiles During Terminal Guidance

Abstract: We examine the criteria for dynamic stability of a spinning projectile subjected to steady horizontal and vertical side forces applied at the nose; such forces could, for example, be generated by canards mounted on a roll-stabilized nose. The problem requires an extension of standard aeroballistic theory which yields intersting new information on stability. It is found that the precessional and nutational modes can become unstable, depending on the magnitude and direction of the applied side force. Results of numerical simulations which confirm these conclusions are given.

Distributed Control of Spinning Flexible Spacecraft

Abstract: A unified treatment of modal control of spinning flexible spacecraft is presented. The equations of motion of the spacecraft are hybrid, i.e., they consist of ordinary differential equations for the rotational motion and partial differential equations for the elastic motion. Problems involving control of distributed-p arameter systems are generally discretized and the actual control is implemented on the discrete systems. An efficient method for control of linear gyroscopic systems is via model synthesis. There remains, however, the question as to how modal control of discrete systems is related to the control of the actual distributed-parameter systems. It is the object of this paper to provide the information concerning the spatial distribution of the sensors and actuators and to relate this information to the discrete modal control.

Control Law Synthesis for Active Flutter Suppression Using Optimal Control Theory

Abstract: This paper describes a study investigating the use of optimal control theory for the synthesis of an active flutter-suppression control law. For an example design application, a high-aspect-ratio cantilever wind-tunnel wing model is considered. The structural dynamics are represented by analytically computed natural frequencies and mode shapes. The three-dimensional unsteady aerodynamic forces for oscillatory motion are computed employing the doublet-lattice technique. With the aid of finite-order approximating functions for representing the aerodynamic forces in the time domain, the "flutter equations" are written in the standard state vector form. Linear optimal control theory is then applied to find particular sets of gain values which minimize a quadratic cost function of the states and controls. These control laws are shown to increase the flutter dynamic pressure by at least 50% at Mach numbers 0.7 and 0.9. The closed-loop system's control surface activity in a gust environment is also examined.

Missile Guidance for Low-Altitude Air Defense

Abstract: Practical design considerations for a low-altitude radar-guided air defense missile are presented. Low-altitude target signals return to the receiver mixed with large clutter signals from ground and large multipath signals from smooth sea. The doppler effect and the Brewster angle effect are used to separate true target returns from clutter and multipath contaminations. Sensor design factors, including clutter and multipath rejection, doppler resolution, and sensor stabilization, are discussed in the context of a complete missile guidance and control system. Basic contributors to miss distance are discussed with a quantitative miss distance example showing the role of missile lateral acceleration capability.

Fault Detection Threshold Determination Technique Using Markov Theory

Abstract: A method for determining time-varying Failure Detection and Identification (FDI) thresholds for singlesample decision functions is described in the context of a triplex system of inertial platforms. A cost function consisting of the probability of vehicle loss due to FDI decision errors is minimized. A discrete Markov model is constructed from which this cost can be determined as a function of the decision thresholds employed to detect and identify the first and second failures. Optimal thresholds are determined through the use of parameter optimization techniques. The application of this approach to threshold determination is illustrated for the Space Shuttle's inertial measurement instruments.

An Advanced Spacecraft Autopilot Concept

Abstract: An autopilot is developed for rotation and translation control of a rigid spacecraft of arbitrary design, using reaction control jets as control effectors. The autopilot incorporates a six-dimensional phase space control law, and a linear programming algorithm for jet selection. The interaction of the control law and jet selection are investigated and a recommended configuration proposed. Simulations are performed to verify the performance of the new autopilot and comparisons are made with an existing spacecraft autopilot. The new autopilot is shown to require 35.4% fewer words of core memory, 20.5% less average CPU time, up to 65% fewer firings, and consume up to 25.7% less propellant for the cases tested. However, the cycle time required to perform the jet selection computations may render the new autopilot unsuitable for existing flight computer applications, without modifications. Finally, the new autopilot is shown to be capable of performing attitude control in the presence of a large number of jet failures.

Geometrical Interpretation of the Angles CY and B in Lambert's Problem

Abstract: Szebehely, V., Theory of Orbits, Academic Press, New York, 1967. Battin, R.H., Astronautical Guidance, McGraw-Hill, New York, 1964, Chap. 2. Goodyear, W.H., "A General Method for the Computation of Cartesian Coordinates and Partial Derivatives of the Two-Body Problem," NASA CR-522, Sept. 1966. Stumpff, K., Himmelsmechanik, VES Verlag, Berlin, 1959. Herrick, S., Astrodynamics, Vol. I, Van Nostrand Reinhold Co., London,1971. Pines, S., and Fang, T.C., "A Uniform Closed Solution of the Variational Equations for Optimal Trajectories during Coast," Advanced Problems and Methods for Space Flight Optimization, edited by F. de Veubeke, Pergammon Press, New York, 1969, p. 175.

Linearization of the boundary-layer equations of the minimum time-to-climb problem

Abstract: Ardema (1974) has formally linearized the two-point boundary value problem arising from a general optimal control problem, and has reviewed the known stability properties of such a linear system. In the present paper, Ardema's results are applied to the minimum time-to-climb problem. The linearized zeroth-order boundary layer equations of the problem are derived and solved.

Magnetic Attitude Control of a Momentum-Biased Satellite in Near-Equatorial Orbit

Abstract: A novel closed-loop magnetic attitude control scheme is described for momentum-biased, near-equatorial orbit satellites. Unlike the other schemes proposed so far, the controller presented here performs both the attitude correction and nutation damping, thus obviating the need for a separate nutation damping mechanism. The magnetic torquer is placed along the roll axis of the spacecraft. The roll error , obtained from the Earth sensor, is filtered out into two components; one varying at orbital frequency 0 , and the other varying at nutational frequency „. The control dipole moment .Mc of the magneto-torquer is governed by the control law, Mc = K2 n -K'l^0, where K'j and K'2 are constants. Analytical expressions for time response of the system and conditions for stability are derived, using linearized equations of motion. The roll/yaw dynamics of the satellite were simulated on an analog computer, and the simulation and analytical results matched well. Also, the simulation results indicate that enough damping is provided in the yaw channel. Design aspects such as choice of feedback gains and saturation characteristics of the magneto-torquer are discussed.

Constrained Impulsive Trajectory Optimization for Orbit-to-Orbit Transfer

Abstract: A method for rapidly generating preliminary estimates of performance for orbit-to-orbit transfer vehicles subject to complex operational constraints is presented. Given the characteristics of a particular multistage design and the position and time of the thrusting arcs, the performance index and constraints are evaluated by solving Lambert's problem. An intrinsic equality constraint is imposed on each thrusting arc to insure that the velocity increment provided by each stage is equal to the impulsive velocity increment required by the solution to Lambert's problem. A problem solution is sought by solving a nonlinear programming problem where the independent variables may be chosen from a set of vehicle design parameters and the positions and times of the various thrusting arcs. A Lambert's problem formulation is shown to be preferable to a Kepler's problem formulation for complex missions. Pitfalls in the solution to Lambert's problem are highlighted. A variation of the Method of Multipliers is used for reliably solving the nonlinear programming problem generated by the problem formulation. Finally, several highly constrained orbit-to-orbit transfer problems are presented as examples.

Annular Suspension and Pointing System

Abstract: The Annular Suspension and Pointing System (ASPS) is a general-purpose mount designed to provide orientation, mechanical isolation, and fine pointing for space experiments. The ASPS consists of two assemblies, the first being a set of two gimbals attached to a carrier spacecraft (e.g., Space Shuttle) and providing coarse pointing, and the second a magnetic vernier-pointing and isolation assembly attached to the inner gimbal of the first assembly and providing fine pointing. Discussion of the evolution of this concept, required technology, and data from analyses and simulations predicting pointing accuracies that allowed the specification of hardware design requirements is presented.

Observer Modal Control of Dual-Spin Flexible Spacecraft

Abstract: A procedure is presented for the control of a dual-spin spacecraft consisting of a spinning rigid rotor and a flexible despun section. Such a system exhibits gyroscopic effects. The system equations of motion are uncoupled by using gyroscopic modal analysis and the active control of the spacecraft is accomplished by synthesizing the control on the independent spacecraft modes. A deterministic (Luenberger-type) observer is designed by using decoupled dynamics and inserted in the control loop, where the control operates on an on-off scheme. Proportional control representing classical linear feedback approach is also discussed. Finally, the relation between spatially distributed actuators and modal control is discussed.