Showing papers in "Journal of Guidance Control and Dynamics in 1995"

Smooth Sliding-Mode Control for Spacecraft Attitude Tracking Maneuvers

Abstract: A sliding-mode control (SMC) algorithm is derived and applied to quaternion-based spacecraft attitude tracking maneuvers. Based on some interesting properties related to the spacecraft model, a class of linear sliding manifolds is selected. Significantly, a Lyapunov function is introduced in the SMC design, which can avoid the inverse of the inertia matrix and thus simplify the controller design. To improve the transient response before reaching the sliding manifold, the smoothing model-reference sliding-mode control (SMRSMC) is further developed, which requires well-estimated initial conditions. Simulation results are included to demonstrate the usefulness of the SMRSMC method.

Vibration reduction in rotorcraft using active control - A comparison of various approaches

Abstract: This paper presents a concise review of the state of the art for vibration reduction in rotorcraft using active controls. The principal approaches to vibration reduction in helicopters described in the paper are 1) higher harmonic control, 2) individual blade control, 3) vibration reduction using an actively controlled flap located on the blade, and 4) active control of structural response. The special attributes of the coupled rotor/flexible fuselage vibration reduction problem are also briefly discussed to emphasize that vibration reduction at the hub is not equivalent to acceleration reduction at specific fuselage locations. Based on the comparison of the various approaches, it appears that the actively controlled flap has remarkable potential for vibration reduction.

Feedback control logic for spacecraft eigenaxis rotations under slew rate and control constraints

Abstract: The problem of reorienting a rigid spacecraft as fast as possible within the physical limits of actuators and sensors is investigated. In particular, a nonlinear feedback control logic which accommodates the actuator and sensor saturation limits is introduced. The nearminimum-time eigenaxis reorientation problem of the Xray Timing Explorer spacecraft under slew rate and control torque constraints is used as an example to demonstrate the effectiveness and simplicity of the proposed nonlinear feedback control logic.

Robust Dynamic Inversion for Control of Highly Maneuverable Aircraft

Abstract: This paper presents a methodology for the design of flight controllers for aircraft operating over large ranges of angle of attack. The methodology is a combination of dynamic inversion and structured singular value (p) synthesis. An inner-loop controller, designed by dynamic inversion, is used to linearize the aircraft dynamics. This inner-loop controller lacks guaranteed robustness to uncertainties in the system model and the measurements; therefore, a robust, linear outer-loop controller is designed using /i synthesis. This controller minimizes the weighted HQO norm of the error between the aircraft response and the specified handling quality model while maximizing robustness to model uncertainties and sensor noise. The methodology is applied to the design of a pitch rate command system for longitudinal control of a high-performance aircraft. Nonlinear simulations demonstrate that the controller satisfies handling quality requirements, provides good tracking of pilot inputs, and exhibits excellent robustness over a wide range of angles of attack and Mach number. The linear controller requires no scheduling with flight conditions. HE objective of this paper is to present a method for design of flight controllers that provides desired handling qualities over a wide range of flight conditions with minimal scheduling. Acceptable stability and performance robustness must be maintained in the presence of unmodeled dynamics, uncertainties in the aircraft design model, and noisy sensor measurements. The aircraft considered in this paper is the NASA high angle-ofattack research vehicle (HARV), which is typical of future fighter aircraft. It is capable of flight at very high angles of attack and has thrust vectoring as well as conventional aerodynamic control surfaces.1 The unaugmented aircraft does not meet handling quality requirements and some type of augmentation is necessary. This paper considers only the longitudinal control. The controller relates pilot longitudinal stick input to the symmetric deflection of the stabilizer and the longitudinal deflection of the thrust vectoring vanes. The control design philosophy is to use an inner-loop, dynamic inversion controller and an outer-loop, linear \JL controller. The dynamic inversion controller linearizes the pitch rate dynamics of the aircraft; however, since model uncertainties prevent exact linearization, there will always be errors associated with this controller. A simple linear fractional transformation model of these errors is developed for use in design of the outer-loop /^ controller. This controller provides pitch rate following by minimizing the weighted //oo-norm of the difference between the actual aircraft pitch rate response to pilot stick inputs and the desired response to these inputs as given by a transfer function model based on standard handling quality specifications. Thus the outer-loop \Ji controller is an implicit model following design, which provides robustness to errors due to the lack of exact cancellation of the pitch rate dynamics by the dynamic inversion controller. Recently a number of papers have appeared that describe controllers for a highly maneuverable aircraft. In Refs. 2-5, application of linear multi-input/multi-output (MIMO) control design techniques to this problem were presented. In every case, excellent

System identification for adaptive and reconfigurable control

Abstract: In this work, an efficient static system identification method is developed that incorporates prior information. The prior information from flight mechanics enhances the performance of the identification algorithm, yielding more accurate parameter estimates. The proposed static system identification approach is superior to dynamic system identification for on-line identification of rapidly varying plant parameters, making it suitable for adaptive and reconfigurable control. The effectiveness of the static system identification scheme is illustrated in an example problem. A derivative F-16 aircraft control surface (elevator) failure is simulated and the abruptly changing pitch channel control system's stability and control derivatives are successfully identified on-line in the presence of unmodeled dynamics, process noise (clear air turbulence), and realistic measurement noise.

Bayesian State Estimation for Tracking and Guidance Using the Bootstrap Filter

Abstract: The bootstrap filter is an algorithm for implementing recursive Bayesian filters. The required density of the state vector is represented as a set of random samples that are updated and propagated by the algorithm. The method is not restricted by assumptions of linearity or Gaussian noise: It may be applied to any state transition or measurement model. A Monte Carlo simulation example of a bearings-only tracking problem is presented, and the performance of the bootstrap filter is compared with a standard Cartesian extended Kalman filter (EKF), a modified gain EKF, and a hybrid filter. A preliminary investigation of an application of the bootstrap filter to an exoatmospheric engagement with non-Gaussian measurement errors is also given.

Precision position control of piezoelectric actuators using charge feedback

Abstract: The issue of precision position control is critical if piezoelectric actuator technology is to be applied in increasingly demanding applications. In one particular application, the NASA NAOMI project, piezoelectric actuators have been proposed as the pointing and focusing elements for thousands of small mirror-lenslets because of their fast response time and load- carrying ability. In this application the positions of these actuators must be precisely controlled both statically and dynamically to the nanometer level. This requirement necessitates a careful study of the concept and design of the driving electronics of the system. This paper is focused on finding an appropriate method for driving piezoelectric stack actuators for ultraprecision position and motion control. In this paper the theoretical basis of the electrical control of piezoelectric stack actuators is derived using the fundamental physical laws governing dielectrics and piezoceramics. It is shown that the relationships used for voltage control of piezoelectric actuators result from an approximation of the constitutive equations. An exact input/output relationship for piezoelectric actuators is derived and shows that displacement relies fundamentally on charge, not voltage. Experimental verification was obtained to illustrate the differences between driving piezoactuators with voltage control and charge control.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Direct Adaptive and Neural Control of Wing-Rock Motion of Slender Delta Wings

Abstract: The question of wing-rock suppression of slender delta wings is considered. Based on a nonlinear model, an adaptive control law for wing-rock control is derived. In this derivation, it is assumed that the aerodynamic parameters in the nonlinear model are not known. The derivation of a control law for wing-rock suppression using neural networks when the dynamics of wing rock are completely unknown is also treated. A radial basis function network is used for synthesizing the controller. An adaptation law is derived for adjusting the parameters of the network. Digital simulation results show that in the closed-loop system wing-rock motion is suppressed using the adaptive and neural controllers.

Closed-form solutions to constrained control allocation problem

Abstract: This paper describes the results of recent research into the problem of allocating several flight control effectors to generate moments acting on a flight vehicle. The results focus on the use of various generalized inverse solutions and a hybrid solution utilizing daisy chaining. In this analysis, the number of controls is greater than the number of moments being controlled, and the ranges of the controls are constrained to certain limits. The control effectors are assumed to be individually linear in their effects throughout their ranges of motion and independent of one another in their effects. A standard of comparison is developed based on the volume of moments or moment coefficients a given method can yield using admissible control deflections. Details of the calculation of the various volumes are presented. Results are presented for a sample problem involving 10 flight control effectors. The effectivenesses of the various allocation schemes are contrasted during an aggressive roll about the velocity vector at low dynamic pressure. The performance of three specially derived generalized inverses, a daisy-chaining solution, and direct control allocation are compared.

Autonomous rendezvous using artificial potential function guidance

Abstract: A novel methodology has been developed for the guidance and control of a maneuvering chase vehicle undergoing terminal rendezvous in the presence of path constraints and multiple obstructions. The method hinges on defining a suitable scalar function which represents an artificial potential field describing the locality of the target vehicle. Using a set of bounded impulses the chase vehicle is guided by the local topology of this potential function. Obstructions and path constraints are introduced by superimposing regions of high potential around these regions. Exact, analytical expressions are then obtained for the required control impulse magnitude, direction and switching times using the second method of Lyapunov. These control impulses ensure that the potential function monotonically decreases so that convergence of the chaser to the target is ensured analytically, without violating the path constraints. Since the components of the potential and control impulses may be represented analytically, the method appears suitable for autonomous, real-time control of complex maneuvers with a minimum of onboard computational power.

Attitude stabilization of a rigid spacecraft using two momentum wheel actuators

Abstract: It is well known that three momentum wheel actuators can be used to control the attitude of a rigid spacecraft and that arbitrary reorientation maneuvers of the spacecraft can be accomplished using smooth feedback. If failure of one of the momentum wheel actuators occurs, we demonstrate that two momentum wheel actuators can be used to control the attitude of a rigid spacecraft and that arbitrary reorientation maneuvers of the spacecraft can be accomplished. Although the complete spacecraft equations are not controllable, the spacecraft equations are controllable under the restriction that the total angular momentum vector of the system is zero. The spacecraft dynamics under such a restriction cannot be asymptotically stabilized to any equilibrium attitude using a timeinvariant continuous feedback control law, but discontinuous feedback control strategies are constructed that stabilize any equilibrium attitude of the spacecraft in finite time. Consequently, reorientation of the spacecraft can be accomplished using discontinuous feedback control.

Proportional navigation and weaving targets

Abstract: Sinusoidal or weave maneuvers on the part of the target can make it particularly difficult for a pursuing missile to hit. Normalized design curves are presented so that the guidance system designer can easily assess the influence of weave maneuvers on missile system performance. These curves show how the target weave frequency and amplitude along with the interceptor guidance system tune constant and effective navigation ratio determine the size of the miss distance. Acceleration saturation effects also are considered as a further important influence on system performance. Finally, suggestions are made showing how to improve system performance.

Optimization of low-thrust interplanetary trajectories using collocation and nonlinear programming

Abstract: The method of collocation with nonlinear programming is applied to the determination of minimum-time, low-thrust interplanetary transfer trajectories. Since the vehicle motor operates continuously, the minimum-time trajectories are also propellant minimizing. The numerical solution method requires that the transfer be divided into three phases: escape from the departure planet, heliocentric flight, and arrival at the destination planet. Two-body gravitational models are used in each phase and the transformation from planetocentric coordinates to heliocentric coordinates and vice-versa is incorporated as a set of nonlinear constraints on the problem variables. No a priori assumptions on the optimal control time history are required. An Earth-to-Mars transfer with a very low thrust acceleration of 0.0001 g is used as an example.

Guidance of a homing missile via nonlinear geometric control methods

Abstract: This paper examines the guidance problem of an acceleration constrained homing missile when the initial missile heading is far from intercept course. A guidance strategy based on the theory of feedback linearization is presented, and simulation results are given comparing miss distance performance of the feedback linearized guidance law to proportional navigation. It is demonstrated that the feedback linearized guidance law is a viable option under these conditions. aT L*A(r) LgLkfh(x) N'

Application of Direct Transcription to Commercial Aircraft Trajectory Optimization

Abstract: One of the most effective numerical techniques for the solution of trajectory optimization and optimal control problems is the direct transcription method. This approach combines a nonlinear programming algorithm with a discretization of the trajectory dynamics. When the resulting mathematical programming problem is solved using a sparse sequential quadratic programming algorithm, the technique produces solutions very rapidly and has demonstrated considerable robustness when applied to atmospheric and orbital trajectories. This paper describes the application of the direct transcription technique to the optimal design of a commercial aircraft trajectory, subject to realistic constraints on the aircraft flight path. A primary result of the paper is to demonstrate that the transcription formulation leads to a very natural treatment of realistic Federal Aviation Administration (FAA) imposed path constraints within a high fidelity simulation. A second important result is to demonstrate that modeling tabular data using smooth approximations significantly improves the speed of convergence.

Neural-network-based scheme for sensor failure detection, identification, and accommodation

Abstract: This paper presents a neural-network-based approach for the problem of sensor failure detection, identification, and accommodation for a flight control system without physical redundancy in the sensors. The approach is based on the introduction of on-line learning neural network estimators. For a system with n sensors, a combination of a main neural network and a set of n decentralized neural networks achieves the design goal. The main neural network and the ith decentralized neural network detect and identify a failure of the ith sensor, whereas the output of the ith decentralized neural network accommodates for the failure by replacing the signal from the failed ith sensor with its estimate. The on-line learning for these neural network architectures is performed using the extended back-propagation algorithm. The document describes successful simulations of the sensor failure detection, identification, and accommodation process following both soft and hard sensor failures. The simulations have shown remarkable capabilities for this neural scheme.

Optimal low-thrust three-dimensional Earth-moon trajectories

Abstract: Minimum-fuel, three-dimensional trajectories from a circular low Earth parking orbit to an inclined circular low lunar parking orbit with a fixed thrust-coast-thrust engine sequence are computed for a low-thrust spacecraft. The problem is studied in the context of the classical restricted three-body problem. The minimum-fuel transfer to a polar lunar orbit is obtained by successively solving a sequence of fixed lunar inclination problems. Minimumfuel three-dimensional transfers to a polar lunar orbit with meridian plane constraints are also computed. The minimum-fuel trajectory problems are solved using a "hybrid" direct/indirect method. The hybrid method utilizes the costate time histories to parameterize the three-dimensional thrust steering angle time histories. Numerical results are presented for the optimal three-dimensional Earth-moon trajectories.

Reconfigurable tracking control with saturation

Abstract: On-line system identification and on-line optimization is used to maximize aircraft tracking performance before and after control surface failure, yet prevent instability and departure. The on-line optimization consists of receding horizon/model predictive optimal control with one-step-ahead actuator rate constraint enforcement. Such hard constraint enforcement is rigorous through use of a linear programming algorithm to include rate saturation in the design. The paper demonstrates that the full, infinity norm solution with one-step-ahead constraint enforcement is equivalent to a simple one-dimensional optimization whose solution is attainable in closed form. This equivalence allows for an efficient on-line implementation of reconfigurable control with hard actuator rate constraints. Good tracking performance after severe failure is demonstrated in realistic simulations.

Fuel/Time Optimal Control of the Benchmark Problem

Abstract: Design of fuel/time optimal control of the benchmark two-mass/spring system is addressed in the frequency domain. The optimal control profile is represented as the output of a time-delay filter, where the amplitude of the time-delayed signals are constrainted to satisfy the control bounds. The time delays of the filter are determined by solving a parameter optimization problem that minimizes a weighted fuel/time cost function subject to the constraint that the tune-delay filter cancel all the poles of the system and the control profile satisfies the rigid-body boundary conditions. It is shown that three control structures exist: a three-switch profile corresponding to the time optimal control problem that changes to a six-switch profile corresponding to a cost function that includes a small weight on the fuel. As the weight on the fuel increases beyond a critical value, the control profile changes to a two-switch profile. The value of the critical weight that represents the transition of the control profile from a six-switch to a two-switch control profile is determined.

Integrated Development of the Equations of Motion for Elastic Hypersonic Flight Vehicles

Abstract: An integrated, consistent analytical framework is developed for modeling the dynamics of elastic hypersonic flight vehicles. A Lagrangian approach is used to capture the dynamics of rigid-body motion, elastic deformation, fluid flow, rotating machinery, wind, and a spherical rotating Earth model and to account for their mutual interactions. The resulting equations of motion govern the rigid-body and elastic degrees of freedom (DOF). The elastic motion is represented in terms of modal displacement coordinates relative to the elastic mean axes system, and the rigid-body motion is represented in terms of the translational and rotational velocities of this axes system. A vector form of the force, moment, and elastic-deformation equations is developed from Lagrange's equation; a usable scalar form of these equations is also presented. The appropriate kinematic equations are developed and are presented in a usable form. The characteristics of the three-DOF point-mass dynamic model are also outlined, and the corresponding equations are presented. A preliminary study of the significance of selected terms in the equations of motion is conducted. Using generic data for a single-stage-to-orbit vehicle, it was found that the Coriolis force can reach values up to 6 % of the vehicle weight and that the forces and moments attributable to fluid-flow terms can be significant.

Satellite autonomous navigation based on magnetic field measurements

Abstract: This paper presents a near-Earth (less than 1000 km altitude) satellite autonomous navigation and orbit determination method using measurements of the Earth magnetic field. An orbit state vector comprised of six Keplerian elements enables the estimation of the instantaneous orbital elements by a relatively simple extended Kalman filter algorithm. The satellite position and velocity are computed as a function of the estimated orbital elements. Several algorithms were developed. The basic algorithm uses a "measurement" of the magnetic field magnitude. Consequently, this algorithm is independent of attitude information. Simulation tests yielded accurate Keplerian element estimation and a few kilometers of position estimation error. More complicated algorithms that estimate drag and/or utilize attitude information were tested. The basic algorithm was successfully applied to real Earth Radiation Budget Satellite data, and a modified version of this algorithm was applied to Gamma Ray Observatory magnetometer readings to yield estimates of the orbital elements and the position and velocity. In both cases of real satellite navigation, the position was estimated within a few tens of kilometers.

Hybrid equations of motion for flexible multibody systems using quasicoordinates

Abstract: A variety of engineering systems, such as automobiles, aircraft, rotorcraft, robots, spacecraft, etc., can be modeled as flexible multibody systems. The individual flexible bodies are in general characterized by distributed parameters. In most earlier investigations they were approximated by some spatial discretization procedure, such as the classical Rayleigh-Ritz method or the finite element method. This paper presents a mathematical formulation for distributed-parameter multibody systems consisting of a set of hybrid (ordinary and partial) differential equations of motion in terms of quasi-coordinates. Moreover, the equations for the elastic motions include rotatory inertia and shear deformation effects. The hybrid set is cast in state form, thus making it suitable for control design.

Runge-Kutta Algorithm for the Numerical Integration of Stochastic Differential Equations

Abstract: This paper presents a new Runge-Kutta (RK) algorithm for the numerical integration of stochastic differential equations. These equations occur frequently as a description of many mechanical, aerospace, and electrical systems. They also form the basis of modern control design using the linear quadratic regulator/Gaussian (LQR/LQG) method. It is convenient, and common practice, to numerically simulate these equations to generate sample random processes that approximate a solution of the system (often called Monte Carlo simulations). It is shown in the paper that the standard deterministic solution techniques are inaccurate and can result in sample sequences with covariances not representative of the correct solution of the original differential equation. A new set of coefficients is derived for a RK-type solution to these equations. Examples are presented to show the improvement in mean-square performance.

Geometric stiffening in multibody dynamics formulations

Abstract: In this paper we discuss the issue of geometric stiffening as it arises in the context of multibody dynamics. This topic has been treated in a number of previous publications in this journal and appears to be a debated subject. The controversy revolves primarily around the 'correct' methodology for incorporating the stiffening effect into dynamics formulations. The main goal of this work is to present the different approaches that have been developed for this problem through an in-depth review of several publications dealing with this subject. This is done with the goal of contributing to a precise understanding of the existing methodologies for modelling the stiffening effects in multibody systems. Thus, in presenting the material we attempt to illuminate the key characteristics of the various methods as well as show how they relate to each other. In addition, we offer a number of novel insights and clarifying interpretations of these schemes. The paper is completed with a general classification and comparison of the different approaches.

Covariance control design for Hubble Space Telescope

Abstract: To improve the response to unexpected thermally induced disturbances, two new controllers are designed for the Hubble Space Telescope (HST) using covariance control techniques. The first controller minimizes the required control effort subject to inequality constraints on the output covariance matrix. The second controller is designed to satisfy both output covariance constraints and controller covariance constraints. The importance of the controller covariance constraint is to properly scale the controller for digital implementation in the control computer using fixed-point arithmetic. We provide a technique to integrate modeling, control design, and signal processing (in HST's fixed-point control computer), since these problems are not separable. Covariance control can easily accommodate the roundoff error and computational time delay. Compared with the existing HST controller design, the results show that the required pointing error specifications can be achieved with 85% less control effort and that the error due to the finite-wordlength implementation of the controller can easily be included in the optimal control design process.

Nonlinear Predictive Control of Feedback Linearizable Systems and Flight Control System Design

Abstract: The question of output trajectory control of input-output feedback linearizable nonlinear dynamic systems using state variable feedback is considered For the derivation of the predictive control law, a vector function s is chosen as a linear combination of the tracking error, its higher order derivatives, and the integral of the tracking error The control law is obtained by the minimization of a quadratic function of the predicted value of s and the control input It is shown that in the closed-loop system the trajectories are uniformly ultimately bounded in the presence of uncertainty in the system parameters Based on these results, a flight control system for the trajectory control of the output variables pitch, sideslip, and roll angles (0, /3, ) using aileron, rudder, and elevator control is presented Simulation results are obtained to show that precise simultaneous longitudinal and lateral maneuvers can be performed in spite of the uncertainty in the aerodynamic parameters

Calculation of second and higher order eigenvector derivatives

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