Showing papers in "Journal of Guidance Control and Dynamics in 1999"

Robust nonlinear control of a hypersonic aircraft

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

Synchronized Formation Rotation and Attitude Control of Multiple Free-Flying Spacecraft

Abstract: Intheobservationslewingoflongbaselineinterferometersformedbymultiplefree-e yingspacecraftinformation, it is required to rotate the entire formation about a given axis and to synchronize individual spacecraft rotation with formation rotation. Using a particle model for spacecraft formation dynamics and a rigid-body model for spacecraft attitude dynamics, control laws are derived for this mode of operation in the absence of a gravitational e eld and disturbances. A simplie ed control law suitablefor implementation isalso obtained. It is shown thatunder mild conditionstheformation alignmenterrordecaystozeroexponentiallywith time. Computersimulationstudies are made for a free-e ying spacecraft triad in a triangular formation. The results show that the developed control laws are effective in synchronized formation rotation.

Adaptive Sliding-Mode Guidance of a Homing Missile

Abstract: Sliding-mode control is applied to design robust homing missile guidance law. The sufe cient and necessary condition for the sliding-mode motion of a linear time-varying system not to be affected by disturbances and the sufe cient condition for that motion not to be affected by parameter perturbations are given. An adaptive reaching law of sliding mode for a linear time-varying system is then presented and used to derive an adaptive sliding-mode guidance law. Theoretical analysis and simulation results show that the adaptive sliding-mode guidance law is robust against disturbances and parameter perturbations. Furthermore, the presented guidance law is simple to implement in practice.

Optimal Strategies for Free-Flight Air Traffic Conflict Resolution

Abstract: Recent advances in navigation and data communication technologies make it feasible for individual aircraft to plan and fly their trajectories in the presence of other aircraft in the airspace. This way, individual aircraft can take advantage of the atmospheric and traffic conditions to optimally plan their paths. This capability is termed as the free flight concept. While the free flight concept provides new degrees of freedom to the aircraft operators, it also brings-in complexities not present in the current air traffic control system. In the free flight concept, each aircraft has the responsibility for navigating around other aircraft in the airspace. While this is not a difficult task under low speed, low traffic density conditions, the complexities of dealing with potential conflict with multiple aircraft can significantly increase the pilot’s work load. This paper presents the development of a conflict resolution algorithm based on the quasilinearization method to enable the practical implementation of the free flight concept. The algorithm development uses nonlinear point-mass aircraft models, and incorporates realistic operational constraints on individual aircraft. The analytical framework can also incorporate information about ambient atmospheric conditions. Realistic conflict resolution scenarios are illustrated. Due to their speed of execution, these conflict resolution algorithms are suitable for implementation on-board aircraft.

Real-Time Parameter Estimation in the Frequency Domain

Abstract: A method for real-time estimation of parameters in a linear dynamic state space model was developed and studied. The application is aircraft dynamic model parameter estimation from measured data in flight for indirect adaptive or reconfigurable control. Equation error in the frequency domain was used with a recursive Fourier transform for the real-time data analysis. Linear and nonlinear simulation examples and flight test data from the F-18 High Alpha Research Vehicle HARV) were used to demonstrate that the technique produces accurate model parameter estimates with appropriate error bounds. Parameter estimates converged in less than 1 cycle of the dominant dynamic mode natural frequencies, using control surface inputs measured in flight during ordinary piloted maneuvers. The real-time parameter estimation method has low computational requirements, and could be implemented aboard an aircraft in real time.

Optimal Low-Thrust Escape Trajectories Using Gravity Assist

Abstract: Electric propulsion provides a spacecraft with continuous steering capabilities, which can be used to approach a planet with hyperbolic excess velocity that enhances the gravity assist. Low-thrust trajectories to escape from the solar system are considered in the present paper, which searches for the strategy that maximizes the spacecraft energy for assigned payload and engine operating time. The optimal conditions to escape using electric propulsion and gravity assist are presented for the cases of free-height and minimum-height  ybys. Optimal trajectories that exploit Jupiter or Venus  ybys have been computed for constant exhaust power with either constant or variable speciŽ c impulse; the procedure is also able to determine the optimal power level and to suggest when it is convenient to switch the engine on and off. The beneŽ t that system performance can receive by increasing the number of controls, i.e., by adding the possibility of coast arcs and engine throttling to the thrust direction control, is also noted.

Multiple Timescale Flight Control Using Reconfigurable Sliding Modes

Abstract: Adual-timescaleaircrafte ight-controlproblemisaddressedviacontinuoussliding-modecontrol.Sliding-surface boundary-layer recone guration is used to account for actuator dynamics, dee ection limits, and rate limits. A recone gurable sliding-mode e ight controller is designed that achieves robust, high-accuracy tracking of outerloop command angles before and after damage to an aircraft. Angular rate commands are robustly tracked in an inner loop. The recone gurable e ight-control strategy is based on a continuous sliding-mode controller with direct boundary-layer adaptation for recone guration. On-line explicit system or damage identie cation is not required. Therecone gurablesliding-modee ight-controltechniqueisapplied to anonlineare ight-dynamicsmodelofan F-16 aircraft. Computer simulations demonstrate stability and high-accuracy tracking performance without violation of actuator limits.

Adaptive Output Feedback Control of a Nonlinear Aeroelastic Structure

Abstract: Based on a backstepping design technique, a new adaptive controller for the control of an aeroelastic system using output feedback is derived. The chosen dynamic model describes the nonlinear plunge and pitch motion of a wing. Theparameters of thesystem areassumed to becompletely unknown, and only the plunge displacement and the pitch angle measurements are used for thesynthesis of thecontroller. A canonical state variable representation of the system is derived, and e lters are designed to obtain the estimates of the derivatives of the pitch angle and the plunge displacement. Then adaptive control laws for the trajectory control of the pitch angle and the plunge displacement are derived. In the closed-loop system the state vector asymptotically converges to the origin. Simulation results are presented, which show that regulation of the state vector to the equilibrium state and trajectory following are accomplished using a single control surface in spite of the uncertainty in the aerodynamic and structural parameters. Nomenclature a = nondimensionalized distance from the midchord to the elastic axis bs = semichord of the wing ch = structural damping coefe cient in plunge caused by viscous damping ci, L, Li, = design parameters di, C ca = structural damping coefe cient in pitch caused by

Adaptive model inversion flight control for tilt-rotor aircraft

Abstract: Neural network augmented model inversion control is used to provide a civilian tiltrotor aircraft with consistent response characteristics throughout its operating envelope, including conversion flight. The implemented response type is Attitude Command Attitude Hold in the longitudinal channel. Similar strategies can be applied to provide for Rate Command Attitude Hold in the roll channel, and Heading Hold and Turn Coordination for the yaw motion. Conventional methods require extensive gain scheduling with tiltrotor nacelle angle and speed. A control architecture is developed that can alleviate this requirement and thus has the potential to reduce development time, facilitate the implementation of handling qualities, and compensate for partial failures. One of the key aspects of the controller architecture is the accommodation of modeling error. It includes an online, i.e. learningwhile-controlling, neural network with guaranteed stability. The performance of the controller is demonstrated using the nonlinear Generic Tiltrotor Simulation code developed for the Vertical Motion Simulator at the NASA Ames Research Center.

Optimization of Launch Vehicle Ascent Trajectories with Path Constraints and Coast Arcs

Abstract: This paper describes improvements made to a hybrid analytic/numerical algorithm for optimization of launch vehicle trajectories. Modifications are described which improve the accuracy of the solution. In addition, the algorithm has been extended to include path constraints for normal force and angle of attack, and the terminal constraints have been generalized to allow optimal attachment to a target orbit defined by inclination, apogee radius and perigee radius. Singularities that occur for circular orbits and for equatorial orbits are identified. Finally, necessary conditions are derived and applied for the introduction of coasting arcs that are typically required for a great variety of missions.

Regulation About Time-Varying Trajectories: Precision Entry Guidance Illustrated

Abstract: Anewmethodforregulating nonlineardynamicsystemsabouttime-varying referencetrajectoriesisintroduced. The control law is a closed-form approximate receding-horizon control law based on the linearized time-varying dynamics. No on-line integration or explicit gain scheduling is required for implementation. Closed-loop stability canalwaysbeachievedwithsuchacontrollaw.TheapplicationofthismethodinentryguidancefortheX-33vehicle leads to very accurately controlled e ight in all the state variables in simulations, which was dife cult to achieve previously. This application demonstrates the potential of this approach as a powerful guidance and trajectory control method in cases for which high precision is required. I. Introduction T HE trajectory control problem for dynamic systems is often addressed in two steps: off-line trajectory planning and on-line trajectory tracking. It is the case for many robot control problems. Inaerospaceengineering,entryguidanceofa spacecraftis currently performed this way. Off-line trajectory planning allows careful design of the trajectory to satisfy all the constraints, optimize performance,andbalancethecone icting requirementsarising fromdifferent aspects of the mission. In the on-line implementation, however, some judicious choices in deciding how to accomplish the control objectives may have to be made because of the limited number of controlsand nonlineardynamics.Forinstance,intheentry guidance problem, the primary means for trajectory control is through modulation of the bank angle. Current nonlinear control methodology

Time-Optimal Control of Axisymmetric Rigid Spacecraft Using Two Controls

Abstract: In this paper, we consider the minimum-time reorientation problem of an axisymmetric rigid spacecraft with two independent control torques mounted perpendicular to the spacecraft symmetry axis. The objective is to reorient the spacecraft from an initial attitude, with some angular velocity, to a e nal attitude with a certain angular velocity in minimum time. All possible control structures, including both singular and nonsingular arcs, arestudied completely byderivingthecorrespondingformulasand thenecessary optimality conditions. Itisshown that a second-order singular control can be part of the optimal trajectory. It is also shown that for an inertially symmetric and a nonspinning axisymmetric rigid body, it is possible for ine nite-order singular controls to be part of or the whole optimal trajectory. In particular, for a nonspinning axisymmetric rigid body, the second-order singular trajectory is shown to be an eigenaxis rotation. An efe cient method for numerically solving the optimal controlproblem,basedonacascadedcomputationalschemethatusesbotha directmethodand anindirectmethod, is also presented. Numerical examples demonstrate optimal reorientation maneuvers with both nonsingular and singular subarcs, and comparisons are made between eigenaxis rotations and the true time-optimal rotations.

Spacecraft Vibration Reduction Using Pulse-Width Pulse-Frequency Modulated Input Shaper*

Abstract: Minimizing vibrations of a flexible spacecraft actuated by on-off thrusters is a challenging task. This paper presents the first study of Pulse-Width PulseFrequency (PWPF) modulated thruster control using command input shaping. Input shaping is a technique which uses shaped command to ensure zero residual vibration of a flexible structure. PWPF modulation is a control method which provides pseudo-linear operation for an on-off thruster. The proposed method takes full advantage of the pseudo-linear property of a PWPF modulator and integrates it with a command shaper to minimize the vibration of a flexible spacecraft induced by on-off thruster firing. Compared to other methods, this new approach has numerous advantages: 1) effectiveness in vibration suppression, 2) dependence only on modal frequency and damping, 3) robustness to variations in modal frequency and damping, 4) easy computation and 5) simple implementation. Numerical simulations performed on an eight-mode model of the Flexible Spacecraft Simulator (FSS) in the Spacecraft Research and Design Center (SRDC) at US Naval Postgraduate School (NPS) demonstrate the efficacy and robustness of the method.

Uncertainty Modeling for Multivariable-Control Robustness Analysis of Elastic High-Speed Vehicles

Abstract: High-speed (supersonic or hypersonic ) atmospheric e ight vehicles are typically characterized by a signie cant degree of interaction between the highly elastic airframe and the propulsion system. To achieve adequate stability and performance requirements, robust, integrated multivariable control laws will be required. But to apply robust-control analysis or synthesis techniques such as structured-singular-value techniques (π) or quantitative feedbacktheory,theuncertaintyintheplantdynamicsmustbecharacterized inspecialways.Furthermore,certain assumptions regarding the uncertainties present are frequently made in the application of these techniques. The focus of this research is the development of uncertainty models for this class of e ight vehicle that are derived from the physics of the system, yet are compatible with the cited control synthesis techniques. The potential sources of uncertainty for this class of vehicle are discussed, and three forms of uncertainty models are developed: real parameter,unstructured,and structured. Weareespecially interestedinhowtheusualsourcesofuncertaintymanifest themselves in this context. It will be shown that for this class of vehicle care is required in making the usual assumptions regarding the uncertainty. It is also shown that the e exible degrees of freedom must be considered in the e ight-control synthesis for this class of vehicle.

Sensitivity of Trajectory Prediction in Air Traffic Management

Abstract: Trajectory prediction in air trafe c management computes the most likely or the most desirable aircraft trajectories by using models of aircraft performance and atmospheric conditions, as well as measurements of aircraft states. In comparison, actual trajectories are obtained using feedback control from a pilot or autopilot to track e ight objectives, while theaircrafte iesthrough an actual atmosphere. This paperintroduces the concept ofclosedloop sensitivities, which are dee ned as differences between actual and computed trajectories per unit of modeling errors, in thepresenceof pilot/autopilotfeedback controls.Modeling errorsareexpressed asuncertain parameters and/or uncertain functions. Pilot/autopilot control actions are approximated by nonlinear feedback control laws, designedwith themethod of feedback linearization. Both theaircraft equations of motion and the feedbackcontrol laws are linearized around computed reference trajectories, and these linearized equations are used to determine expressions for closed-loop terminal sensitivities. The proposed method is applied to the Center/Terminal Radar Approach Control (TRACON) Automation System as well as e ight management systems.

Attitude Commands Avoiding Bright Objects and Maintaining Communication with Ground Station

Abstract: The objective of the paper is to develop attitude commands for slewing a vehicle such that the angle of its boresight with the centroid of a bright object is not less than a minimum angle and its antennae do not lose communication with the ground. These commands involve three angles: the required pitch/yaw slew angle, the bright object’ s exclusion angle normal to the slew angle, and a roll angle for maintaining communication. The location of the bright object’ s centroid is formulated in terms of an angle normal to the ideal slew plane. If the ideal,minimum-angleslew path enters the forbidden perimeteraround thebrightobject, two alternativeexclusion angles are determined so as to pass the object tangentially from either side. Between the two angles, that exclusion angle is selected, which steers the ground station trace, in the communication beam, toward beam axis and not away from it. Communication links of the antennae are maintained by rolling the vehicle before, during, or after slewing. The three-axis attitude and rate commands are illustrated for a stressing scenario in which two bright objects are close by and hence pose special circumstances for the algorithm to tackle.

Autonomous Orbit Determination for Two Spacecraft from Relative Position Measurements

Abstract: A batch filter has been designed and analyzed to autonomously determine the orbits of 2 spacecraft based on measurements of the relative position vector from one spacecraft to the other. This system provides a means for high-precision autonomous orbit determination for systems that cannot be dependent on signals from the GPS constellation or ground stations. The filter uses a time series of the inertially-referenced relative position vector, and it uses orbital dynamics models for the two spacecraft. It estimates the 6element orbital state vectors of both spacecraft along with a drag parameter for each one. The observability of this system is demonstrated in this proof-of-concept study, and the filter's predicted position determination accuracy is analyzed for a number of situations. Position accuracies on the order of 1 m RMS are predicted for certain configurations.

Comparison of Intelligent, Adaptive, and Nonlinear Flight Control Laws

Abstract: Seven different nonlinear control laws for multiaxis control of a high-performance aircraft are compared in simulation. The control law approaches are fuzzy logic control, backstepping adaptive control, neural network augmented control, variable structure control, and indirect adaptive versions of model predictive control and dynamic inversion. In addition, a more conventional scheduled dynamic inversion control law is used as a baseline. In some of the cases, a stochastic genetic algorithm was used to optimize e xed parameters during design. The control laws are demonstrated on a six-degree-of-freedom simulation with nonlinear aerodynamic and engine models, actuator models with position and rate saturations, and turbulence. Simulation results include a variety of single- and multiple-axis maneuvers in normal operation and with failures or damage. The specie c failure and damage cases that are examined include single and multiple lost surfaces, actuator hardovers, and an oscillating stabilatorcase. Therearealso substantial differences between thecontrol law design and simulation models,which are used to demonstrate some robustness aspects of the different control laws.

Eigenstructure Assignment Algorithm for Mechanical Second-Order Systems

Abstract: Introduction E IGENSTRUCTURE assignment algorithms are widely used to design control systems.Most of the available eigenstructure assignment algorithms assign all of the eigenvalues to the desired values.The eigenstructureassignmentalgorithmcan be dividedinto two groups, that is, the null space approach and Sylvester equation approach.The null spaceapproachis used to solvemode decoupling problems by assigning a certain set of eigenvectors to the desired values, whereas the Sylvester equationapproach is used to design a controller for the vibration suppressionof  exible structures.3;4 It is known that the dynamics of a large class of mechanical systems can be represented by second-order systems of differential equations. Because the dimension of aerospace structural dynamic systems is usually large, one often encounters an uncomfortably high computational burden to design a controller, especially when an optimizationprocess is involved.4 In thisNote,we proposea specialized version of an eigenstructure assignment algorithm to take advantages of the structure of second-order differential equations for mechanical vibrating systems. Therefore, when we deal with the n second-order differential equation of mechanical vibrating systems,it is notnecessaryto determinethe2n£ 2n eigenvectormatrix for the corresponding2n Ž rst-order state-space equations. The proposed algorithm is more efŽ cient than the conventional eigenstructure assignment algorithm in the sense that it uses less memory and operations. The numerical accuracy and efŽ ciency of the proposed algorithmresults because the conventionaleigenstructure assignment algorithm must solve the Sylvester equation numerically, whereas, in this Note, an analytic formulation for solving the Sylvester equation is derived that takes full advantageof the mathematical structureof mechanical second-ordersystems. It can also be anticipated that numerical accuracywill be superior for most highdimensioned applications; the results of our calculations strongly support this supposition.

Modeling of Variable Length Towed and Tethered Cable Systems

Abstract: An algorithm is presented for modeling the dynamics of towed and tethered cable systems with e xed and varying lengths (specie cally, tethers, towing, reel-in/pay-out cone gurations ). The systems may have one or many open branches, but they must be towed or tethered from a single point. The modeling uses e nite-segment (rigidlink/lumped-parameter ) elements. Cable length changes (reel-in/pay-out ) are modeled by having a link near the towing (or anchoring )vessel change length. Thephysical properties of the cable may change from link to link. The towed bodies may have control surfaces. Effects of e uid drag, lift, and buoyancy are included. Added mass forces and moments are included for the towed bodies but not for the cable itself. An illustrative application is presented for a system with three different pay-out rates. Nomenclature aJ;aK = acceleration of J; K eijk = permutation symbol,

Design of Automatic Landing Systems Using Mixed H/H Control

Abstract: Mixed H2/HX control technique is employed to develop controllers for auto-landing systems for a commercial airplane. A linear model of the aircraft in longitudinal motion is established using the appropriate aerodynamic coefficients. With the control actuator, tracking errors, and altitude motion, the aircraft is shown to be governed by an augmentation system along with its filter model. Two kinds of optimal and robust control requirements are designed, which need to be satisfied simultaneously. One of requirements is with respect to an optimal trajectory selection for landing routes. The H2 method is used to minimize a cost function such that the optimal gain for trajectory optimization can be obtained. The other requirement is with respect to the disturbance attenuation. The Hm technique is employed to obtain the necessary formulation for the robust control gain to minimize the affection of the disturbance to the performance output. An algorithm is developed based on the convex theory for the mixed H2I Hn control and filter gains, which provides a suboptimal solution. A large commercial aircraft (Boeing 747-200) is employed to illustrate the potential of the proposed method. It is shown that the glide slope capture motion and flare maneuver of the aircraft are accomplished quite well, and the amplitudes of all maneuver are within FAA requirements. L INTRODUCTION Control of aircraft under difficult maneuvers is a problem of both theoretical and practical interest. Control under one of these difficult maneuvers, that of landing, is discussed and addressed in this paper. Design of automatic landing systems has been achieved using both robust and optimal control methods [1-3]. Reference [1] employed the #„ synthesis to design an automatic landing controller for an F-14 aircraft. Design of landing systems encountering windshear is given in

Practical View of Redundancy Management Application and Theory

Abstract: A perspective is developed on how redundancy management techniques for e ight-critical systems have matured sincetheearliestapplicationsin the1960s,driven largelybytheintroduction ofmorepowerfulcomputerresources. As this evolution occurred, the basic issues involving system architecture tradeoffs changed very little, although the hardware mechanizations of the earlier analog systems have been replaced largely with the software of the newerdigital systems.Thesebasicissuesarereviewed and howthey tend to beresolvedinpractical mechanizations is shown. The large body of literature on analytic redundancy theory developed since the 1970s is discussed in the context of its applicability to practical systems. It is shown that analytic redundancy has an important role in real-world systems but that it is not a replacement for physical redundancy, and its proper implementation requires that it be embedded within the physical redundancy structure of the system.

Global Positioning System Integer Ambiguity Resolution Without Attitude Knowledge

Abstract: Inthispaper,anewmotion-basedalgorithmforglobalpositioningsystemintegerambiguityresolutionisderived. Thealgorithmrepresentstheglobalpositioningsystem sightlinevectorsinthebodyframeasthesumoftwovectors, onedependingonthephasemeasurementsandtheotherontheunknownintegers.Thevectorcontainingtheinteger phases is found using a procedure developed to solve for magnetometer biases. In addition to a batch solution, this paper also provides a sequential estimate, so that a suitable stopping condition can be found during the vehicle motion. The newalgorithm has several advantages: it doesnot requirean a prioriestimateofthevehicle’ s attitude; it provides an inherent integrity check using a covariance-type expression; and it can sequentially estimate the ambiguitiesduring thevehiclemotion. Itsonly disadvantageisthatit requiresatleastthreenoncoplanar baselines. The performance of the new algorithm is tested on a dynamic hardware simulator.

Finite Dimensional Optimal Control of Poiseuille Flow

Abstract: In this paper we consider linear stabilization of plane, Poiseuille  ow using linear quadratic Gaussian optimal control theory. It is shown that we may signiŽ cantly increase the dissipation rate of perturbation energy, while reducing the required control energy, as compared with that reported using simple, integral compensator control schemes. Poiseuille  ow is described by the inŽ nite dimensional Navier–Stokes equations. Because it is impossible to implement inŽ nite dimensional controllers, we implement high but Ž nite order controllers. We show that this procedure in theory can lead to destabilization of unmodeled dynamics. We then show that this may be avoided using distributed control or, dually, distributed sensing. A problem in high plant order linear quadratic Gaussian controller design is numerical instability in the synthesis equations. We show a linear quadratic Gaussian design that uses an extremely low-order plant model. This low-order controller produces results essentially equivalent to the high-order controller.

H Bounded Fault Detection Filter

Abstract: A key issue in practical fault detection e lter applications is sensitivity to system disturbances and sensor noise. In this paper, a stabilizing fault detection e lter gain is found that bounds the H1 norm of the transfer matrix from system disturbances and sensor noise to the residual. For multidimensional faults, a residual direction is identie ed that enhances the fault signal-to-noise ratio while maintaining the H1 norm bound. By retaining the faultdetection e lterstructure,thepracticalapplicability oftheproposed approach isthesameasforfaultdetection e lter designs found by conventional eigenvector assignment. In contrast to an unknown input observer approach wherein noise is explicitly decoupled from the fault signal, a noise bounding approach does not impose additional geometric constraints on the e lter structure. This allows a given e lter to isolate more faults, an important feature because in practical applications low-order e lter dynamics are common. Further, the possibility of ill-conditioned e lter eigenvectors, occasionally imposed by geometric constraints, may be reduced.

Optimal Combined Reaction-Wheel Momentum Management for Earth-Pointing Satellites

Abstract: When reaction wheels of a satellite drift toward saturation caused by the accumulated effect of external torque, it is common to employ thrusters or magnetorquers to actively unload extra momentum of the wheels. This paper presents several optimal approaches to manage the three-axis reaction wheel momentum of Earth-pointing satellites actuated by three-axis magnetorquers and/or thrusters. The optimalmomentumdumping using magnetorquers only behaves fairly slowly, and there are difŽ culties in solving a two-point boundary problem for onboard applications.Comparatively, thrusters can achieve relatively fastmomentumdumpingat the cost of consuming expendable fuel. Based upon relatively simple optimal algorithmsusing thrusters only, the newly proposed combined algorithmseffectively separate the required torques formagnetorquersand thrusters commandingsimultaneously. They simply employ on-line geomagneticmeasurements. The key beneŽ t of these combined approaches is that they can save a large amount of thruster propellant because of the assistance of the magnetorquers. The realistic simulations showed that the optimal combined method can economize at least 20% thruster fuel within an unloading time of 1 10 of an orbit (about 10 min) for a low-Earth-orbit mini-satellite. The combined controllers are readily applicable to real-time practical momentum dumping.