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Showing papers in "Journal of Guidance Control and Dynamics in 1990"


Journal ArticleDOI
TL;DR: The design, development, analysis, and simulation testing of a Kalman filter arid reports its expected peformance and significant extensions contributed by this paper.
Abstract: A three-axis, magnetometer/Kalman filter, attitude-determination system for a spacecraft in low-altitude Earth orbit is developed, analyzed, and simulation tested. The motivation for developing this system is to achieve three-axis knowledge using magnetic field measurements only. The extended Kalman filter estimates the attitude, attitude rates, and constant disturbance torques. Covariance computation and simulation testing are used to evaluate performance. One test case, a gravity-gradient stabilized spacecraft with a pitch momentum wheel and a magnetically anchored damper, is a real satellite on which this attitude determination system will be used. The application to a nadir-pointing satellite and the estimation of disturbance torques represent the significant extensions contributed by this paper. Beyond its usefulness purely for attitude determination, this system could be used as a part of a low-cost, three-axis attitude stabilization system. I. Introduction T HE objective of this work has been to develop a low-cost system for estimation of three-axis, spacecraft-attitude information based solely on three-axis magnetometer measurements from one satellite orbit. Such a system will be useful for missions that operate in an inclined, low-Earth orbit and require only coarse attitude information. It can also serve as the sensor part of a low-cost, three-axis, closed-loop attitude control system or as a backup attitude estimator. A single three-axis magnetometer measurement can give only two-axes worth of attitude information and no attitude rate or disturbance torque information. Therefore, this attitude determination system must use a sequence of magnetometer measurements. It processes these measurements recursively in a Kalman filter. This paper describes the design, development, analysis, and simulation testing of a Kalman filter arid reports its expected peformance. A follow-on, postlaunch paper is planned to report actual performance.

235 citations


Journal ArticleDOI
TL;DR: It is contended that, with enough effort, most algorithms can be massaged to perform reasonably well, and that a more important consideration is the ease with which a given algorithm can be brought to high performance levels.
Abstract: Changes in the design of software algorithms for generating physical motion in flight simulators have typically been put forward on the grounds of improved motion cueing. Little attention has been paid to more practical criteria such as computational cost, ease of adjustment, or evaluation by experienced pilots in a realistic simulation environment. A comparison of three of the algorithms most commonly found in the literature has been performed: classical washout, optimal control, and coordinated adaptive. This consisted of pilot evaluations of these algorithms implemented on a six-degree-of-freedom flight simulator simulating a large transport aircraft during low-altitude flight and ground maneuvering. This paper presents the results of that study from the designer's viewpoint. In it, we contend that, with enough effort, most algorithms can be massaged to perform reasonably well, and that a more important consideration is the ease with which a given algorithm can be brought to high performance levels. If this criterion is used, it appears that the classical algorithm is a good starting point, and that the benefits of an adaptive algorithm can be added gradually to obtain the advantages conferred by nonlinear filtering and "intelligent" cost functions.

227 citations


Journal ArticleDOI
TL;DR: In this paper, a proportional-integral implicit model-following control law is proposed to recover the performance of a failed system to its pre-failure level, and conditions for control reconfiguration are stated.
Abstract: Studies of a proportional-integral implicit modelfollowing control law are presented. The research focuses on the ability of the control law to recover the performance of a failed system to its pre-failure 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.

192 citations


Journal ArticleDOI
TL;DR: In this article, a new method of modeling frequency-dependent material damping in structural dynamics analysis is reported, motivated by results from materials science, augmenting thermodynamic fields are introduced to interact with the usual mechanical displacement field.
Abstract: A new method of modeling frequency-dependent material damping in structural dynamics analysis is reported. Motivated by results from materials science, augmenting thermodynamic fields are introduced to interact with the usual mechanical displacement field. The methods of irreversible thermodynamics are used to develop coupled material constitutive relations and partial differential equations of evolution. These equations are implemented for numerical solution within the computational framework of the finite-element method. The method is illustrated using several examples including longitudinal vibration of a rod, transverse vibration of a beam, and vibration of a large space truss structure.

176 citations


Journal ArticleDOI
TL;DR: In this article, the singularity robust inverse is introduced as an alternative to the pseudoinverse for computing torque-producing gimbal rates near singular states, which is shown by example to provide better steering law performance by allowing torque errors to be produced in the vicinity of singular states.
Abstract: Two steering laws are presented for single-gimbal control moment gyroscopes. An approach using the Moore-Penrose pseudoinverse with a nondirectional null-motion algorithm is shown by example to avoid internal singularities for unidirectional torque commands, for which existing algorithms fail. Because this is still a tangent-based approach, however, singularity avoidance cannot be guaranteed. The singularity robust inverse is introduced as an alternative to the pseudoinverse for computing torque-producing gimbal rates near singular states. This approach, coupled with the nondirectional null algorithm, is shown by example to provide better steering law performance by allowing torque errors to be produced in the vicinity of singular states.

171 citations


Journal ArticleDOI
TL;DR: In this article, a method based on back integration of the gyro torque equation from desired final conditions is used to determine a family of initial gimbal angles that avoid singularities.
Abstract: This paper deals with torque command generation using single gimbal control moment gyros. The angular momentum and torque envelopes are assumed to be known a priori. A method based on back integration of the gyro torque equation from desired final conditions is used to determine a family of initial gimbal angles that avoid singularities. Each member of this family is defined as a preferred initial gimbal angle set. The pseudoin- verse steering law is used during the numerical integrations. This procedure is demonstrated by means of numerical examples that include attitude control and momentum management of the Space Station Freedom. A feedback control scheme based on "null motion" is also developed to position the gimbals at preferred angles. ONTROL moment gyros (CMGs) are attractive space- craft attitude-control devices. They require no expendable propellant, which is a limited resource and can contaminate the spacecraft environment. Their fixed rotor speeds minimize structural dynamic excitations. They can be used for rapid slewing maneuvers and precision pointing. For low Earth or- biting spacecraft, momentum dumping can be easily achieved by gravity-gradient torques. From the steering-law viewpoint, it is widely accepted that double-gimbal CMGs (DCMGs) are preferable to single-gimbal CMGs (SCMGs). For DCMGs, steering laws proposed by Kennel 1'2 have been well accepted. The SCMGs have the advantages of possessing relative me- chanical simplicity and producing amplified torques (for low spacecraft angular velocities) on the spacecraft. However, de- velopment of gimbal steering laws for their use is made diffi- cult by the existence of internal singular states. For any system of n CMGs and any direction in space, there exist 2" sets of gimbal angles3 for which no torque can be produced in that direction, and these sets are called internal singularities. Exter- nal singular states correspond to directional angular momen- tum saturation. DCMGs have internal singularities also, but they are easier to avoid. Margulies and Aubrun3 present a geometric theory of SCMG systems. They characterize the momentum envelope of a cluster of SCMGs and identify the internal singular states. Yoshikawa4 presents a steering law for a roof-type configura- tion with four SCMGs. His steering law is based on making all of the internal singular states unstable by providing two jumps with hystereses around the singularities. Cornick5 develops singularity avoidance control laws for the pyramid configura- tion. His technique is based on the ability to calculate the instantaneous locations of all singularities. Hefner and McKenzie6 develop a technique for maximizing the minimum torque capability of a cluster of SCMGs in the pyramid con- figuration. Bauer7 concludes that it is impossible to avoid some singularities and, in general, no global singularity-avoid- ance steering law can exist. Consequently, there will be in- stances when torque demand cannot be met exactly.

156 citations


Journal ArticleDOI
TL;DR: A model following reconfigurable flight control system designed for the AFTI/F-16 is discussed, which utilizes an adaptive proportional plus integral controller with gain adjustment based on errors between desired performance and actual performance.
Abstract: In the event of a control surface failure, the purpose of a reconfigurable flight control system is to redistribute and coordinate the control effort among the aircraft's remaining effective surfaces such that satisfactory flight performance is retained. In this paper, a model following reconfigurable flight control system designed for the AFTI/F-16 is discussed. The system utilizes an adaptive proportional plus integral controller with gain adjustment based on errors between desired performance and actual performance. Stability analysis and simulation results are presented.

153 citations


Journal ArticleDOI
TL;DR: A new, very fast algorithm for determining minimum-time trajectories for bang-bang control systems that seeks to minimize the time required to force a manipulator to travel a specified distance.
Abstract: A class of optimization problems of interest in the field of robotics is one that seeks to minimize the time required to force a manipulator to travel a specified distance. Robots employ multiple, bounded control inputs. This work describes a new, very fast algorithm for determining minimum-time trajectories for such systems. We have modified the steepest descent method of optimal programming to find time-optimal switch times for bang-bang control systems. The Switch Time Optimization (STO) program has been applied to a two-link manipulator with two control inputs. To find the minimum time for a robot end-effector to travel between two points in its workspace, one must establish the optimal position of the robot with respect to the work station. The algorithm accomplishes this by allowing optimal initial states to be determined along with the time history of the controls. Exact control switch times and optimal initial conditions have been found for minimum-time repositioning maneuvers in which the robot was required to travel a specified distance. The STO algorithm is not limited to use with manipulators; it is applicable to any bang-bang system.

151 citations


Journal ArticleDOI
TL;DR: In this article, the authors modify the original form by replacing 1(0) by a related integral 7(0), thereby removing all singularities and computational instabilities in the solution.
Abstract: are removable singularities, they may lead to computational instabilities in the solution. Especially bothersome is the fact that computational problems can occur where the true anomaly is near zero. These problems are avoided in the work of solution that does not involve 7(0), but their work is confined to elliptical orbits. The purpose of this Note is to modify the original form by replacing 1(0) by a related integral 7(0), thereby removing all singularities and computational instabilities. The resulting solution, in terms of /(0), is identical for hyperbolic, parabolic, or noncircular elliptic orbits, but the particular case determines the nature of the closed-form evaluation of 7(0). Application of this work to actual problems usually involves the solution of a two-point boundary-value problem and is not considered here. Although we emphasize the case of bounded thrust, the unbounded thrust case can also be investigated through the use of the simpler equations for unpowered flight, which we also present. If the maximum number of impulses is known for an optimal rendezvous in this case, the two-point boundary-value problem is reduced to a problem of parameter optimization on the velocity increments and their locations. We conjecture that the maximum of impulses for this problem is four. If the number of impulses is restricted to two, the problem is solved by methods similar to those of Weiss et al.11'12 For the case of bounded thrust, a method such as that used for the rendezvous problem near circular orbit16 can be applied with starting iteratives obtained from the related unbounded thrust case.

146 citations


Journal ArticleDOI
TL;DR: In this paper, a modeling method for constructing a state-space aeroservoelastic mathematical model for time-domain analysis with a low number of aerodynamic lag states is presented.
Abstract: A modeling method for constructing a state-space aeroservoelastic mathematical model for time-domain analysis with a low number of aerodynamic lag states is presented. The modeling method employs the minimumstate method for rational approximation of tabulated unsteady aerodynamic force coefficients at various reduced-frequency values. The approximation method is modified to deal with weighted aerodynamic data and with alternative constraint combinations. Two weighting types are analyzed and discussed. The first weighting is normalizing the aerodynamic data to maximum unit value of each aerodynamic coefficient. The second weighting is one in which each tabulated coefficient, at each reduced-frequency value, is weighted according to the effect of an incremental error of this coefficient on aeroelastic characteristics of the system. This weighting yields a better fit of the more important terms at the expense of less important ones. The analytical developments are presented and numerical examples, which demonstrate various features of this method, are shown to yield significant reduction in model size per given accuracy relative to other rational approximation methods.

135 citations


Journal ArticleDOI
M. B. Ignagni1
TL;DR: The paper examines various algorithms for integrating the noncommutivity rate equation arising in the implementation of the attitude reference function of a strapdown inertial navigation system, and derives a class of optimized algorithms for performing this integration.
Abstract: The paper examines various algorithms for integrating the noncommutivity rate equation arising in the implementation of the attitude reference function of a strapdown inertial navigation system, and derives a class of optimized algorithms for performing this integration. The accuracy characteristics associated with each of the algorithms, when the system is exposed to pure coning motion, as well as to a generalized vibrational environment, are defined. The class of optimized algorithms is shown to minimize the mean error in the correction provided by the algorithm in a generalized vibrational environment.

Journal ArticleDOI
TL;DR: Back propagation (BP) (of errors) is the subject of this Note and is a major role in the neural­net resurgence of the 1980s.
Abstract: Introduction ARTIFICIAL neural networks (sometimes called connec­ tionist, parallel distributed processing, or adaptive net­ works) are experiencing a dramatic renaissance this decade. The roots of this subject can be traced to research into perceptrons, led by Frank Rosenblatt, and into adaptive linear filters, spearheaded by Bernard Widrow, in the late 1950s. These early neural­network researchers and their enthusiastic followers equated intelligence with pattern discrimination and association abilities acquired through learning from experi­ ence of concrete cases. Then, suddenly, neural­net research became relatively inactive in about 1965 and remained so until the early 1980s. During this interval, research on intelligent systems focused on what has become conventional artificial intelligence, a discipline that defines intelligence as problem solving based on reasoning. The concurrence of two events probably played a major role in the neural­net resurgence of the 1980s. First, by 1980 it had become increasingly apparent that conventional infer­ ence­based artificial intelligence was unable to deal success­ fully with most practical problems. It appeared that learned pattern discrimination and association abilities, not reasoning, underlay not only common­sense understanding but also most skills. Even the choice of which rules to apply when forced to resort to reasoning, and when to break these rules, seemed to require pattern recognition. Second, a formulational and computational procedure was advanced that seemed to sur­ mount certain technical roadblocks that were recognized but not successfully dealt with by the researchers of the 1950s and 1960s. This procedure is called back propagation (BP) (of errors) and is the subject of this Note. To fully appreciate BP, we must first briefly examine some groundbreaking work done during the late 1950s. At Cornell, Frank Rosenblatt designed various neurally inspired learning devices and simulated them on a digital computer. He called these designs \"perceptrons\" to emphasize their perceptive, rather than logical, abilities. The aim of many of his devices was to learn through example to distinguish whether an input was a member of one class of inputs, called class A, or of a different class, called class B, by being presented with exam­ ples of members of each class together with the correct classi­ fication. The diss members, any finite number being allowed, were represented by (n — 1) vectors where xf denotes the /th element of the cth such vector. Given a vector, the simplest perceptron would compute

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a generalization of Kane's equations for multibody codes to simulate the behavior of elastic structures undergoing large rotation and translation with small vibrations, which does not suffer from this defect and is valid for an arbifnary structure, and illustrative examples are given to demonstrate the validity and generality of the formulation.
Abstract: Conventional theories underlying my multibody codes used for simulating the behavior of elastic structures undergoing large rotation and translation with small vibrations fail to predict dynamic stiffening of the structures. This can lead to significantly incorrect simulations in many practical situations. A theory that does not suffer from this defect and is valid for an arbifnary structure is given here. The formulation is based on Kane's equations and consists of two steps: First, generalized inertia forces are written for an arbitrary structure for which one is forced to linearize prematurely in the modal coordinates; next, this defect in linearization is compensated for by the introduction of contributions to the generalized active forces from the "motion stiffness" of the stnrctwe. The stress associated with the motion stiffness is identified as due to 12 sets of inertia forces and 9 sets of inertia couples distributed throughout the body during ihe most general motion of its flying reference frame. An algorithm is set for a reader wishing to implement the theory, and illustrative examples are given to demonstrate tbe validity and generality of the formulation.

Journal ArticleDOI
TL;DR: A game-matrix approach has been developed to generate intelligent maneuvering decisions for low-flying aircraft during one-on-one air combat over hilly terrain and generates some of the tactics employed by experienced pilots in combat flight tests.
Abstract: A game-matrix approach has been developed to generate intelligent maneuvering decisions for low-flying aircraft during one-on-one air combat over hilly terrain. The decisions are made by comparing scores based on the predicted orientation, range, velocity, and terrain clearance for various maneuver combinations of both aircraft. A computer program implements the decision process in real time and computes the state of the aircraft employing the selected maneuvers. Predicted states are obtained by numerically integrating the dynamic equations. The program has been installed and demonstrated at the NASA Ames vertical motion simulator to provide an automated adversary for manned helicopter combat simulations. A stand-alone version of the program, in which the decisions of both combatants are generated by the computer, has also been prepared for nonpiloted simulations. Sample trajectories show that this new automated maneuvering logic generates some of the tactics employed by experienced pilots in combat flight tests. Whereas the current application applies to helicopter combat, the program can be used for fixed-wing aircraft by replacing those subroutines that provide the aircraft capabilities.

Journal ArticleDOI
TL;DR: In this article, the authors employed the describing function method for the nonlinear control analysis and design of a flexible spacecraft equipped with pulse modulated reaction jets, which provided a means of characterizing the pulse modulator in terms of its gain and phase for structural mode limit cycle analysis.
Abstract: The describing function method is employed for the nonlinear control analysis and design of a flexible spacecraft equipped with pulse modulated reaction jets. The method provides a means of characterizing the pulse modulator in terms of its gain and phase for structural mode limit cycle analysis. Although the describing function method is inherently inexact and is not widely used in practice, a new way of utilizing it for practical control design problems is presented. It is shown that the approximations inherent in the method can be accounted as a modeling uncertainty for the nonlinear control robustness analysis. The pulse modulated control system of the INTELSAT 5 spacecraft is used as an example to illustrate the concept and methodology developed in the gaper. The nonlinear stability margins predicted by the describing function analysis are verified from nonlinear simulations.

Journal ArticleDOI
TL;DR: In this paper, the robotic manipulator is proposed as the mechanical analog to single gimbal control moment gyroscope systems, and it is shown that both systems share similar difficulties with singular configurations.
Abstract: The robotic manipulator is proposed as the mechanical analog to single gimbal control moment gyroscope systems, and it is shown that both systems share similar difficulties with singular configurations. This analogy is used to group gimbal angles corresponding to any momentum state into different families. The singularity problem associated with these systems is examined in detail. In particular, a method is presented to test for the possibility of nontorque-producing gimbal motion at a singular configuration, as well as to determine the admissible motions in the case when this is possible. Sufficient conditions are derived for instances where the singular system can be reconfigured into a nonsingular state by these nontorque-producing motions.

Journal ArticleDOI
TL;DR: The proposed method is applied to a pitch-rate control system for a re-entry vehicle, and comparisons with the results in current literature are made.
Abstract: This paper presents a method for finding the gain margins and phase margins of control systems with adjustable parameters. The considered systems are first modified by adding an analytical gain-phase margin tester. Then, the characteristic equations are formulated. Finally, the stability equations are used to find the boundaries of constant gain margins and phase margins. The main advantage of the proposed method is to obtain complete information about the effects of adjustable parameters on gain margins and phase margins. As an example, the method is applied to a pitch-rate control system for a re-entry vehicle, and comparisons with the results in current literature are made.

Journal ArticleDOI
TL;DR: In this paper, the optimal linear quadratic regulator (LQR) control law is used to optimize the closed-loop structural system using only structural tailoring, based on the structural properties.
Abstract: Structural tailoring provides an attractive method to optimize the performance of actively controlled space structures. However, the simultaneous optimization of control gains and structural properties often becomes prohibitively expensive for large systems and physical insight is often lost in the resulting control law. This paper presents a method for optimization of the closed loop structural system using only structural tailoring. Optimal Linear Quadratic Regulator (LQR) control theory is used with weighting matrices chosen based on physical considerations. The LQR control law depends only on two scalar gains and the structural properties. Hence, the closed loop-performance can be expressed in terms of the structural parameters. Results are given for a beam and a truss-beam to show the simplicity of the method and the importance of structural tailoring to increase dynamic performance and to reduce the control effort.

Journal ArticleDOI
TL;DR: An application of the rotation vector concept is expanded to develop an efficient attitude algorithm for a strapdown system under a coning base motion that takes four samples of gyroscope data per update and outperforms the three-sample algorithm in case of high-frequency coning motion.
Abstract: In this paper, we have expanded an application of the rotation vector concept to develop an efficient attitude algorithm for a strapdown system under a coning base motion. The proposed algorithm takes four samples of gyroscope data per update. A rotation vector error analysis for a coning motion has been employed to come up with an optimum four-sample algorithm. Also presented is an efficient way to implement the algorithm in a real-time environment. The algorithm is formulated in a recursive form using two time-rate executions and using only integer arithmetic. To compare the performance of the proposed algorithm with an already existing threesample algorithm, a simulation has been performed by varying coning motion frequency and update rate. Results Show that the four-sample algorithm outperforms the three-sample algorithm in case of high-frequency coning motion. The use of the four-sample algorithm is economical since it requires less computing time for an equal accuracy.

Journal ArticleDOI
TL;DR: Nonlinear inversion/sliding control techniques are applied to design a pitch axis control system for high-performance aircraft to track pilot g commands while satisfying flying quality specifications.
Abstract: Nonlinear inversion/sliding control techniques are applied to design a pitch axis control system for high-performance aircraft. The control objectives are to track pilot g commands while satisfying flying quality specifications. In the pitch axis problem, the dominant nonlinearities are the aerodynamic coefficients variation with angle of attack and saturation of the actuators position and rate response. Two design approaches are investigated; the first defines a single output to be controlled (pilot's normal acceleration) and coordinates the elevator and the flaperon as a single input. The nonminimum phase nature of the resulting input/output pair necessitates defining a modified output to avoid stability problems inherent in inversion methods. The second approach defines a two input/two output problem and directly incorporates the flying quality specifications into the output definition. These two methods are illustrated using a simulation model. The latter approach is shown to allow more freedom to avoid actuator saturation at high g commands.

Journal ArticleDOI
TL;DR: In this article, the hyperbolic tangent (tahh) function is used as a smooth approximation to the discontinuous sgn function occurring in the rigid body "bang-bang" control.
Abstract: The near-minimum time single-axis slewing of a flexible spacecraft with simultaneous suppression of vibration of elastic modes is considered. The hyperbolic tangent (tahh) function is used as a smooth approximation to the discontinuous sgn function occurring in the rigid body "bang-bang" control. Variable structure control concepts are used to identify the necessary characteristics of the control switching line. Simulations of the rest-to-rest and tracking maneuvers indicate that the elastic energy can be reduced by several orders of magnitude with only a modest increase in the maneuver time. Introduction M ANY future large space structures, due to mass con- traints, will be flexible. For the purpose of analysis these systems can be modeled with a large number of modes of vibration. For certain applications, it will be desirable that such a spacecraft be able to slew as rapidly as possible, within the operating limits of the control actuators. The problem of control design for rotational maneuver and vibration suppres- sion of flexible spacecraft has been addressed extensively.1'10 Optimal control theory can be applied to enforce quiescent terminal conditions on the flexible modes, usually by applying a quadratic cost function that weights the control rates and the states. The order of the system model grows rapidly as the number of flexible modes to be controlled is increased, mak- ing it impractical to attempt to control more than a few flexible modes. Furthermore, there is no rigorous means by which control magnitude constraints may be enforced. Al- though a feedback method such as the linear quadratic regula- tor (LQR) with terminal constraints9"11 is attractive because it can enforce quiescent conditions oh the elastic modes, its computational complexity is burdensome. The optimal control solution to the minimum time, single- axis, rotational maneuver problem for a rigid body gives a control scheme characterized by saturation of the control throughout the maneuver with at most one control switch that is instantaneous (bang-bang). Although not exactly achiev- able in physical systems, and even though the trajectories are extremely sensitive to variations in spacecraft parameters, this control law has wide application for rigid systems using on-off thrusters. When rigorously applied to flexible systems, how- ever, the result is typically multiple control switches and excessive excitation of the flexible modes of vibration. Previ- ous investigations of the near-time optimal maneuver for flexible systems7'8 are open-loop designs requiring extensive computational effort. An alternative is to compute the re- quired parameters for a number of initial conditions off-line and use table lookup and interpolation for a particular ma- neuver. This may involve excessive storage. We start with the assumption that the minimum time solution for a rigid space- craft can serve as an initial approximation to the near-mini- mum time solution for a flexible structure. In other words, we

Journal ArticleDOI
TL;DR: In this article, the minimum time attitude slewing motion of a rigid spacecraft with its controls provided by bounded torques and forces is considered, where instead of the slewing time, an integral of a quadratic function of the controls is used as the cost function.
Abstract: The minimum time attitude slewing motion of a rigid spacecraft with its controls provided by bounded torques and forces is considered. Instead of the slewing time, an integral of a quadratic function of the controls is used as the cost function. This enables us to deal with the singular and nonsingular problems in a unified way. The minimum time is determined by sequentially shortening the slewing time. The two-point boundary-value problem is derived by applying Pontryagin's maximum prinicple to the system and solved by using a quasilinearization algorithm. A set of methods based on the Euler's principal axis rotation is developed to estimate the unknown initial costates and the minimum slewing time as well as to generate the nominal solutions for starting this algorithm. It is shown that one of the four initial costates associated with the quaternions can be arbitrarily selected without affecting the optimal controls and thus simplifying the computation. Several numerical tests are presented to show the applications of these methods.

Journal ArticleDOI
TL;DR: In this paper, the mass and center of mass of a rigid spacecraft can be determined using torque-producing actuators such as controlmoment gyros or reaction wheels, and commonly available sensors, e.g., rate gyros and accelerometers.
Abstract: Previous studies indicated that an applied force was necessary to perform in-flight identification of the mass and center of mass of a spacecraft. This paper shows that the mass and center of mass of a rigid spacecraft can be determined using only torque-producing actuators such as control-moment gyros or reaction wheels, and commonly available sensors, e.g., rate gyros and accelerometers. A space-station application is presented.

Journal ArticleDOI
TL;DR: In this paper, an analysis of the interaction between a structure, an actuator used to control the vibration of the structure, and the control law to be implemented by the actuator is presented.
Abstract: This paper presents an analysis of the interaction between a structure, an actuator used to control the vibration of the structure, and the control law to be implemented by the actuator. The control hardware used is a proof-mass actuator with experimentally verified dynamics capable of being used in a space structure configuration. A local rate-feedback control law is used. The control of two different structures is presented. The first structure is a cantilevered beam constructed of a quasi-isotropic composite material that is controlled by a single actuator forming the experimental component of the investigation. The second structure is a finite-element model of a truss system controlled by a single actuator. Models of both structures predict the presence of potential instabilities in system performance if proper consideration is not given to interactions between the control law, the structure, and the actuator.

Journal ArticleDOI
TL;DR: In this article, the authors present an algorithm that aids the control engineer in specifying a sensor and actuator configuration for regulation of large-scale, linear, stochastic systems such as a large space structure model.
Abstract: This paper presents an algorithm that aids the controls engineer in specifying a sensor and actuator configuration for regulation of large-scale, linear, stochastic systems such as a large space structure model. The algorithm uses a linear quadratic Gaussian controller, an efficient weight-selection technique based on successive approximation, and a measure of sensor and actuator effectiveness to specify a final sensor and actuator configuration. This configuration enables the closed-loop system to meet output specifications with minimal input power. The algorithm involves no complex gradient calculations and is numerically tractable for large linear models, as demonstrated by the solar optical telescope example in this paper. Additionally, the algorithm provides the controls engineer with information on the important design issues of actuator sizing, reliability, redundancy, and optimal number. HE advent of the Space Shuttle makes the large space structure (LSS) an imminent reality. These future space structures will be measured in kilometers and, of necessity, will be lightweight and highly flexible (light damping). Standard LSS missions will include power generation, surveillance, astronomy, and communications. These missions will require stringent pointing accuracy, shape control, and vibration suppression. To satisfy these demanding mission requirements, the LSS will almost certainly require an active, regulator-type controller with multiple sensors and actuators located throughout the structure.i-6 Furthermore, given the size of an LSS, there will be a large set of admissible sensor and actuator locations. The controls engineer then faces the problem of selecting a limited number of sensor and actuator locations to "best achieve" the LSS mission. The term "best achieve" in this paper means achieving the LSS output specifications with minimal actuator power. The solution to this sensor and actuator selection (SAS) problem needs at least the following ingredients: 1) A specific closed-loop control law structure; 2) a technique for systematically adjusting (tuning) control law parameters to achieve output specifications with minimal power; and 3) a technique to evaluate the effectiveness of possible sensor and actuator configurations in achieving output specifications with minimal power. This paper incorporates the preceding ingredients into an algorithm that solves the SAS problem for an LSS modeled as a linear stochastic system. Some necessary background information on linear stochastic systems and linear quadratic Gaussian (LQG) control theory are presented in Sec. II along with a formal statement of the SAS problem. Section III contains two important selection theorems, four pertinent facts, and the general flow of the SAS algorithm. Results from the SAS algorithm applied to the controller design for a large space telescope are presented in Sec. IV, and Sec. V contains concluding remarks.

Journal ArticleDOI
TL;DR: In this article, a feedback model for human use of motion cues in tracking and regulation tasks is proposed, where proprioceptive cues and an internal representation of the vehicle dynamics allow the human to create compensation characteristics that are appropriate for the dynamics of the particular vehicle being controlled.
Abstract: A feedback model for human use of motion cues in tracking and regulation tasks is offered. The motion cue model is developed as a simple extension of a structural model of the human pilot, although other equivalent dynamic representations of the pilot could be used in place of the structural model. In the structural model,it is hypothesized that proprioceptive cues and an internal representation of the vehicle dynamics allow the human to create compensation characteristics that are appropriate for the dynamics of the particular vehicle being controlled. It is shown that an additional loop closure involving motion feedback can improve the pilot/vehicle dynamics by decreasing high-frequency phase lags in the effective open-loop system transfer function. Data from a roll-attitude tracking/regulation task conducted on a moving base simulator are used to verify the modeling approach.

Journal ArticleDOI
TL;DR: Flight test results for the BO-105 show the need for including coupled body/rotor flapping and lead-lag dynamics in the identification model structure to allow the accurate prediction of control system bandwidth limitations.
Abstract: The application of system identification methods to high-bandwidth rotorcraft flight control system design is examined. Flight test and modeling requirements are illustrated using flight test data from a BO-105 hingeless rotor helicopter. The proposed approach involves the identification of nonparametric frequency-response models followed by parametric (transfer funtion and state space) model identification. Results for the BO-105 show the need for including coupled body/rotor flapping and lead-lag dynamics in the identification model structure to allow the accurate prediction of control system bandwidth limitations. Lower-order models are useful for estimating nominal control system performance only when the flight data used for the identification are band-limited to be consistent with the frequency range of applicability of the model. The flight test results presented in this paper are consistent with theoretical studies by previous researchers.

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a dual-control guidance law based on the Gramian performance index (GPI), which is a measure of the relative position and relative velocity of a vehicle.
Abstract: = gain = measurement matrix = observability Gramian = performance index = navigation ratio = time, s = components of relative velocity, ft/s = control vector = positive-definite, diagonal weighting matrix (constant) = constant weight in dual-control guidance law, s~ = positive-definite, diagonal weighting matrix (time varying) = components of relative position, ft = state vector = matrix in gain vector

Journal ArticleDOI
TL;DR: In this paper, a unified theoretical basis for a class of methods that generate the governing equations of constrained dynamical systems by eliminating the constraints is presented, and a dual basis for the orthogonal complement is derived.
Abstract: This paper presents a unified theoretical basis for a class of methods that generate the governing equations of constrained dynamical systems by eliminating the constraints. By using Maggi's equations in conjunction with a common projective theory from numerical analysis, it is shown that members of the class are precisely characterized by the basis they choose for the null-space of the variational form of the constraints. For each method considered, the specific basis chosen for the null-space of the variational constraints is derived, as well as a dual basis for the orthogonal complement. The latter basis is of particular interest since it is shown that its knowledge theoretically enables one to generalize certain methods of the class to calculate constraint forces and torques. Practical approaches based on orthogonal transformations to effect this strategy are also outlined. In addition, since the theory presented herein stresses a common, fundamental structure to the various methods, it is especially useful as a means of comparing and evaluating individual numerical algorithms. The theory presented makes clear the relationship between certain numerical instabilities that have been noted in some methods that eliminate a priori constraint contributions to the governing equations by selecting an independent subset of unknowns. It is also briefly indicated how this formalism can be extended, in principle, to the wider class of nonlinear nonholonomic constraints.

Journal ArticleDOI
TL;DR: In this article, the dynamics and control of a spacecraft consisting of a rigid platform and a given number of retargeting flexible antennas are investigated, where the mission consists of maneuvering the antennas so as to coincide with preselected lines of sight while stabilizing the platform in an inertial space and suppressing the elastic vibration of the antennas.
Abstract: This investigation is concerned with the dynamics and control of a spacecraft comprising a rigid platform and a given number Of retargeting flexible antennas. The mission consists of maneuvering the antennas so as to coincide with preselected lines of sight while stabilizing the platform in an inertial space and suppressing the elastic vibration of the antennas. The paper contains the derivation of the equations of motion by a Lagrangian approach using quasicoordinates, as well as a procedure for designing the feedback controls. A numerical example involving a spacecraft consisting of a rigid platform and a flexible antenna is presented.