Showing papers in "Journal of Guidance Control and Dynamics in 1993"

Constrained Control Allocation

Abstract: This paper addresses the problem of the allocation of several airplane flight controls to the generation of specified body-axis moments. The number of controls is greater than the number of moments being controlled, and the ranges of the controls are constrained to certain limits. They are assumed to be individually linear in their effect throughout their ranges of motion and independent of one another in their effects. The geometries of the subset of the constrained controls and of its image in moment space are examined. A direct method of allocating these several controls is presented that guarantees the maximum possible moment can be generated within the constraints of the controls. It is shown that no single generalized inverse can yield these maximum moments everywhere without violating some control constraint. A method is presented for the determination of a generalized inverse that satisfies given specifications which are arbitrary but restricted in number. We then pose and solve a minimization problem that yields the generalized inverse that best approximates the exact solutions. The results are illustrated at each step by an example problem involving three controls and two moments.

Gain-Scheduled Missile Autopilot Design Using Linear Parameter Varying Transformations

Abstract: This paper presents a gain-scheduled design for a missile longitudinal autopilot. The gain-scheduled design is novel in that it does not involve linearizations about trim conditions of the missile dynamics. Rather, the missile dynamics are brought to a quasilinear parameter varying (LPV) form via a state transformation. An LPV system is defined as a linear system whose dynamics depend on an exogenous variable whose values are unknown a priori but can be measured upon system operation. In this case, the variable is the angle of attack. This is actually an endogenous variable, hence the expression "quasi-LPV." Once in a quasi-LPV form, a robust controller using H synthesis is designed to achieve angle-of-attack control via fin deflections. The final design is an inner/outerloop structure, with angle-of-attack control being the inner loop and normal acceleration control being the outer loop.

Identification of observer/Kalman filter Markov parameters - Theory and experiments

Abstract: An algorithm to compute Markov parameters of an observer or Kalman filter from experimental input and output data is discussed. The Markov parameters can then be used for identification of a state space representation, with associated Kalman gain or observer gain, for the purpose of controller design. The algorithm is a non-recursive matrix version of two recursive algorithms developed in previous works for different purposes. The relationship between these other algorithms is developed. The new matrix formulation here gives insight into the existence and uniqueness of solutions of certain equations and gives bounds on the proper choice of observer order. It is shown that if one uses data containing noise, and seeks the fastest possible deterministic observer, the deadbeat observer, one instead obtains the Kalman filter, which is the fastest possible observer in the stochastic environment. Results are demonstrated in numerical studies and in experiments on an ten-bay truss structure.

Sun-Perturbed Earth-to-Moon Transfers with Ballistic Capture

Abstract: A method is described for constructing a new type of low energy transfer trajectory from the Earth to the moon leading to ballistic capture. This is accomplished by utilizing the nonlinear Earth-moon-sun perturbations on a point mass in three dimensions. The interaction of the gravitational fields of the bodies defines transition regions in the position-velocity space where the dynamic effects on the point mass tend to balance. These are termed weak stability boundaries. The transfer is obtained by the use of trajectories connecting the weak stability boundaries. It uses approximately 18 percent less Delta-V than the Hohmann transfer to insert a spacecraft into a circular orbit about the moon. The use of this transfer has recently been demonstrated by Japan's Hiten spacecraft, which arrived at the moon on October 2, 1991. Application of the transfer method is also made to the Lunar Observer Mission.

Time-optimal three-axis reorientation of a rigid spacecraft

Abstract: New results are presented for the minimum-time rest-to-rest reorientation control problem of a rigid spacecraft with independent three-axis control. It is shown that in general the eigenaxis rotation maneuver is not time optimal. An inertially symmetric (e.g., spherical or cubical) rigid body is examined to demonstrate that an eigenaxis rotation about a control axis of even such a simple body is not time optimal. The computed optimal solution is bang-bang in all three control components and has a significant nutational component of motion. The total number of switches is found to be a function of the specified reorientation angle.

H(infinity) optimized wave-absorbing control - Analytical and experimental results

Abstract: The wave-absorbing control is a control concept to absorb waves traveling in a flexible structure at actuator positions. This paper presents an approach to design a broadband compensator by applying the //«, control theory to the wave-absorbing control method. This approach aims to minimize effects of the incoming waves on the outgoing waves at the actuator positions in the sense that the //«, norm of the closed-loop scattering matrix is minimum. Vibration suppression control for a flexible beam is studied analytically and demonstrated experimentally to exemplify the controller design approach. Compensators are designed for a collocated torque actuator and angle sensor and also for a noncollocated torque actuator and bending moment sensor. Performance of the compensators is analyzed in the frequency domain, and measured open- and closed-loop transfer functions are obtained from random excitation tests. The designed compensators are shown to attain good broadband damping, and results of the experiments are shown to agree well for the range of frequency below 50 Hz with those of the numerical simulations. I. Introduction A CTIVE control of vibrations in large flexible structures has received considerable attention in recent years. The modal model is a powerful technique both for the dynamic analysis and for the control design. However, limitations on the applicability of the structural modal analysis exist1 when the requirements for vibration suppression and pointing accuracy for flexible structures become stringent. The flexible mode frequencies and shapes are extremely sensitive to inevitable modeling errors, and modal analysis cannot provide a sufficiently accurate design model over a modally rich frequency range. One alternative is the traveling wave approach. This approach is based on the property that the response of a flexible structure to a typical locally applied force can be viewed in terms of traveling elastic disturbances. Mathematically, traveling waves belong to homogeneous solutions of partial differential equations describing the vibration of continua. At controller positions, relations between incoming and outgoing wave vectors and control inputs are derived in a matrix form by representing boundary conditions in terms of the traveling wave vectors. Outgoing waves are produced by the reflection of the incoming waves and are generated by control inputs. Transfer functions from the incoming wave and control input vectors to the outgoing wave vector are called scattering and generating matrices, respectively. Control inputs are set to be in the output-feedback form. This leads to the closed-loop relations between outgoing and incoming waves. Compensators are selected so that the effects of the incoming waves on the outgoing waves are reduced in some sense by adequately selecting elements of the closed-loop scattering matrix. Characteristic elements of the wave-propagation model, such as a scattering matrix, are smooth functions with respect to frequency and are more insensitive to model uncertainties than mode frequencies and shapes. The approach can provide a sufficiently accurate model for a controller design over a modally dense frequency region, and considerable research has been done on the wave control methods.1"8 However these methods also have drawbacks, such as 1) the designed compensator is not guaranteed to be a causal and real function with

Identification of aerodynamic coefficients using computational neural networks

Abstract: Precise, smooth aerodynamic models are required for implementing adaptive, nonlinear control strategies. Accurate representations of aerodynamic coefficients can be generated for the complete flight envelope by combining computational neural network models with an Estimation-Before-Modeling paradigm for on-line training information. A novel method of incorporating first-partial-derivative information is employed to estimate the weights in individual feedforward neural networks for each aerodynamic coefficient. The method is demonstrated by generating a model of the normal force coefficient of a twin-jet transport aircraft from simulated flight data, and promising results are obtained.

Path-constrained trajectory optimization using sparse sequential quadratic programming

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 discretization of the trajectory dynamics. The resulting mathematical programming problem is characterized by matrices that are large and sparse. Constraints on the path of the trajectory are then treated as algebraic inequalities to be satisfied by the nonlinear program. This paper describes a nonlinear programming algorithm that exploits the matrix sparsity produced by the transcription formulation. Numerical experience is reported for trajectories with both state and control variable equality and inequality path constraints. T is well known that the solution of an optimal control or trajectory optimization problem can be posed as the solution of a two-point boundary value problem. This problem requires solving a set of nonlinear ordinary differential equations; the first set defined by the vehicle dynamics and the second set (of adjoint differential equations) by the optimality conditions. Boundary conditions are imposed from the problem requirements as well as the optimality criteria. By discretizing the dynamic variables, this boundary value problem can be reduced to the solution of a set of nonlinear algebraic equations. This approach has been successfully utilized1'5 for applications without path constraints. Since the approach requires adjoint equations, it is subject to a number of difficulties. First, the adjoint equations are often very nonlinear and cumbersome to obtain for complex vehicle dynamics, especially when thrust and aerodynamic forces are given by tabular data. Second, the iterative procedure requires an initial guess for the adjoint variables, and this can be quite difficult because they lack a physical interpretation. Third, convergence of the iterations is often quite sensitive to the accuracy of the adjoint guess. Finally, the adjoint variables may be discontinuous when the solution enters or leaves an inequality path constraint. Difficulties associated with adjoint equations are avoided by the direct transcription or collocation methods.6'10 In this approach, the dynamic equations are discretized, and the optimal control problem is transformed into a nonlinear program, which can be solved directly. The nonlinear programming problem is large and sparse and a method for solving it is presented in Ref. 7. This paper extends the method of Ref. 7 to efficiently handle inequality constraints and presents a nonlinear programming algorithm designed to exploit the properties of the problem that results from direct transcription of the trajectory optimization application.

Station-keeping method for libration point trajectories

Abstract: Three-dimensional orbits in the vicinity of the interior libration point (Li) of the Sun-Earth/Moon barycenter system are currently being considered for use with a number of missions planned for the 1990s. Since such libration point trajectories are, in general, unstable, spacecraft moving on these paths must use some form of trajectory control to remain close to their nominal orbit. The primary goal of this effort is the development of a Stationkeeping strategy applicable to such trajectories. A method is presented that uses maneuvers executed (impulsively) at discrete time intervals. The analysis includes some investigation of a number of the problem parameters that affect the overall maneuver costs. Simulations are designed to provide representative station- keeping costs for a spacecraft moving in a libration point trajectory, and preliminary results are summarized. RAJECTORY planning for a number of scientific mis- sions scheduled for launch in the 1990s includes the possi- ble use of three-dimensi onal halo or Lissajous orbits in the vicinity of the interior L! libration point of the Sun-Earth/ Moon barycenter system.1 This effort is directed toward the development of a Stationkeeping strategy that can be used to maintain spacecraft near such nominal libration point trajec- tories. A significant number of analyses have been completed that involve Stationkeeping methods for Earth orbiting satel- lites; maintaining a spacecraft on a libration point orbit, how- ever, has received limited attention. In the late 1960s, Far- quhar2 developed a number of possible Stationkeeping strat- egies for libration point orbits. Later, in 1974, a station- keeping method for spacecraft moving on halo orbits in the vicinity of the Earth-Moon translunar libration point L2 was published by Breakwell et al. 3 In contrast, specific mission requirements influenced the design of the Stationkeeping strat- egy for the first libration point mission. When the Interna- tional Sun-Earth Explorer-3 (ISEE-3) satellite was injected into a halo orbit associated with the interior L! libration point of the Sun-Earth system in 1978, a series of maneuvers exe- cuted at approximately three-month intervals was used for Stationkeeping.4 More recently, a series of papers have pre- sented results from studies that use Floquet and invariant manifold theories to develop a ''loose" Stationkeeping strat- egy for halo-type orbits.5"8 Similar to ISEE-3, the method also uses discrete maneuvers, applied at varying time intervals, that control the trajectory near the nominal path. A significant goal of this study is the development of a potentially ''tight" control strategy for Stationkeeping that can be applied to both halo and Lissajous trajectories (as well as other possible types of libration point paths). In this approach, the allowable deviation of the actual trajectory relative to the nominal path can be varied over a wide range depending on mission require- ments. Of course, low costs are desirable as well.

Piezoelectric actuator design for vibration suppression - Placement and sizing

Abstract: The authors consider the problem of simultaneous placement and sizing of distributed piezoelectric actuators to achieve the control objective of damping vibrations in a uniform beam. For several closed-loop performance measures they obtain optimal placement and sizing of the actuators using a simple numerical search algorithm. These measures are applied to a specific example of a simply supported beam with piezoelectric actuators, and their relative effectiveness is discussed. >

Optimal periodic control for spacecraft pointing and attitude determination

Abstract: A new approach to autonomous magnetic roll/yaw control of polar-orbiting, nadir-pointing momentum bias spacecraft is considered as the baseline attitude control system for the next Tiros series. It is shown that the roll/yaw dynamics with magnetic control are periodically time varying. An optimal periodic control law is then developed. The control design features a state estimator that estimates attitude, attitude rate, and environmental torque disturbances from Earth sensor and sun sensor measurements; no gyros are needed. The state estimator doubles as a dynamic attitude determination and prediction function. In addition to improved performance, the optimal controller allows a much smaller momentum bias than would otherwise be necessary. Simulation results are given.

Robust time-optimal control of uncertain structural dynamic systems

Abstract: A time-optimal open-loop control problem of flexible spacecraft in the presence of modeling uncertainty has been investigated. The results indicate that the proposed approach significantly reduces the residual structural vibrations caused by modeling uncertainty. The results also indicate the importance of proper jet placement for practical tradeoffs among the maneuvering time, fuel consumption, and performance robustness.

Inversion-Based Nonlinear Control of Robot Arms with Flexible Links

Abstract: The design of inversion-bas ed nonlinear control laws solving the problem of accurate trajectory tracking for robot arms having flexible links is considered. It is shown that smooth joint trajectories can always be exactly reproduced preserving internal stability of the closed-loop system. The interaction between the Lagrangian/assumed modes modeling approach and the complexity of the resulting inversion control laws is stressed. The adoption of clamped boundary conditions at the actuation side of the flexible links allows considerable simplification with respect to the case of pinned boundary conditions. The resulting control is composed of a nonlinear state feedback compensation term and of a linear feedback stabilization term. A feedforward strategy for the nonlinear part is also investigated. Simulation results are presented for a planar manipulator with two flexible links, displaying the performance of the proposed controllers also in terms of end-effector behavior.

Aircraft failure detection and identification using neural networks

Abstract: In this paper, a neural network is proposed as an approach to the task of failure detection following damage to an aerodynamic surface of an aircraft flight control system. Several drawbacks of other failure detection techniques can be avoided by taking advantage of the flexible learning and generalization capabilities of a neural network. This structure, used for state estimation purposes, can be designed and trained on line in flight and generates a residual signal indicating the damage as soon as it occurs. From an analysis of the cross-correlation functions between some key state variables, the identification of the damage type can also be achieved. The results of a nonlinear numerical simulation for a damaged control surface are reported and discussed.

Digital simulation of atmospheric turbulence for Dryden and von Karman models

Abstract: Algorithms are presented for generating discrete sample time histories of random atmospheric turbulence having statistical characteristics as prescribed by the Dryden and von Karman models defined in MIL-F-8785C. When these algorithms are incorporated into a dynamic simulation, response of an aircraft to the turbulence can be predicted. Such information is useful both in the design stage and during the development phase of the aircraft. The von Karman model is generated using a variation of the sum-of-sinusoids method, modified to reduce computation time. Techniques for improving computational speed are considered, and results of test runs are presented. The Dryden model is generated by passing band-limited white noise through appropriate linear filters. The input variance required to produce the desired output variance is determined as a function of the sample frequency. Generation of roll gust velocities is also addressed, as well as the application of lateral and vertical velocities to the computation of yaw and pitch moments on an aircraft.

Control of Wing-Rock Motion of Slender Delta Wings

Abstract: A theoretical analysis is conducted to determine the optimal control input for wing-rock suppression through a Hamiltonian formulation. The optimality equations are analyzed through Beecham-Titchener's averaging technique and numerically integrated by a backward-differentiation formulas method developed for implicit differential equations. The weighting factors in the cost function are shown to be related explicitly to the system output damping and frequency. A numerical model constructed for an 80-deg delta wing is solved to illustrate the results. It is shown that Beecham-Titchener's technique is accurate in determining the necessary control function to suppress wing rock. From the numerical results, it is also shown that an effective way to suppress wing rock is to control the roll rate. System sensitivity is investigated by determining variations in system output damping and frequency with aerodynamic model coefficients. The results show that higher sensitivity corresponds to lower system damping.

Ground Tests of Magnetometer- Based Autonomous Navigation (MAGNAV) for Low-Earth-Orbiting Spacecraft

Abstract: Actual spacecraft data have been used to test two filters that rely solely on magnetometer measurements to determine spacecraft ephemeris. This work proves the potential of a novel autonomous orbit determination scheme. One of the filters is an extended Kalman-type filter. It estimates a position and velocity, and it uses equations of motion to propagate these estimates. The other filter is a batch least-squares filter. It estimates static Keplerian parameters along with magnetometer biases. Tests of these filters involve filtering of magnetometer data followed by comparison of estimated position with position derived from ground-based tracking. Both filters perform well on the MAGSAT spacecraft, achieving accuracies from 4 to 8 km. Tests of the batch filter on the DE-2 spacecraft yield somewhat larger position uncertainties, 17-18 km. Batch filter tests on the LACE spacecraft yield much larger position errors, 120 km. This poor LACE performance can be attributed partly to solar-array-g enerated low-frequency noise.

Inverse dynamics approach to trajectory optimization for an aerospace plane

Abstract: An inverse dynamics approach for trajectory optimization is proposed. This technique can be useful in many difficult trajectory optimization and control problems. The application of the approach is exemplified by ascent trajectory optimization for an aerospace plane. Both minimum-fuel and minimax types of performance indices are considered. When rocket augmentation is available for ascent, it is shown that accurate orbital insertion can be achieved through the inverse control of the rocket in the presence of disturbances.

Classical and robust H(infinity) control redesign for the Hubble Space Telescope

Abstract: A control redesign problem of the Hubble Space Telescope for reducing the effects of solar array vibrations on telescope pointing jitter is investigated. Both classical and H, control design methodologies are employed for such a control problem with a non-colocated actuator and sensor pair. This paper successfully demonstrates the effectiveness of a dipole concept for precision line-ofsight pointing control in the presence of significant structural vibrations. Proposed controllers with two dipoles effectively reduce the effects of the solar array induced disturbances at 0.12 Hz and 0.66 Hz on pointing jitter.

Attitude control with realization of linear error dynamics

Abstract: An attitude control law is derived to realize linear unforced error dynamics with the attitude error defined in terms of rotation group algebra (rather than vector algebra). Euler parameters are used in the rotational dynamics model because they are globally nonsingular, but only the minimal three Euler parameters are used in the error dynamics model because they have no nonlinear mathematical constraints to prevent the realization of linear error dynamics. The control law is singular only when the attitude error angle is exactly pi rad about any eigenaxis, and a simple intuitive modification at the singularity allows the control law to be used globally. The forced error dynamics are nonlinear but stable. Numerical simulation tests show that the control law performs robustly for both initial attitude acquisition and attitude control.

Asymptotic stability theorem for autonomous systems

Abstract: ENGINEERING NOTES are short manuscripts describing new developments or important results of a preliminary nature. These Notes cannot exceed 6 manuscript pages and 3 figures; a page of text may be substituted for a figure and vice versa. After informal review by the editors, they may be published within a few months of the date of receipt. Style requirements are the same as for regular contributions (see inside back cover).

Quasi-Closed-Form Solution to the Time-Optimal Rigid Spacecraft Reorientation Problem

Abstract: The problem of slewing a rigid body from an arbitrary initial orientation to a desired target orientation in minimum time is addressed. The nature of the time-optimal solution is observed via an open-loop solution using the switch time-optimization algorithm developed by Meier and Bryson. Conclusions as to the number and timing of control switches are drawn and substantiated analytically. The solution of the kinematic differential equations for Euler parameters is examined for systems in which the applied torque is much greater than the nonlinear terms in Euler's equations. An approximate solution to these equations is used to construct the state transition matrix as a function of a given control sequence and control intervals. This allows a rapid solution for the required switch times for all admissible control sequences. Uncoupled switching functions can be generated given the approximate switch times for the optimal sequence. The resulting feedforward/feedback control is suitable for online computation.

Dynamic Characteristics of Liquid Motion in Partially Filled Tanks of a Spinning Spacecraft

Abstract: This paper presents a boundary-layer model to predict dynamic characteristics of liquid motion in partially filled tanks of a spinning spacecraft. The solution is obtained by solving three boundary-value problems: an inviscid fluid problem, a boundary-layer problem, and a viscous correction problem. The boundary-layer solution is obtained analytically, and the solutions to inviscid and viscous correction problems are obtained by using finite element methods. The model has been used to predict liquid natural frequencies, mode shapes, damping ratios, and nutation time constants for a spinning spacecraft. The results show that liquid motion in general will contain significant circulatory motion due to Coriolis forces except in the first azimuth and first elevation modes. Therefore, only these two modes can be represented accurately by equivalent pendulum models. The analytical results predict a sharp drop in nutation time constants for certain spacecraft inertia ratios and tank fill fractions. This phenomenon was also present during on-orbit liquid slosh tests and ground air-bearing tests. I. Introduction A RECENT trend in geosynchronou s spacecraft design is to use liquid apogee motors, which results in liquid constituting almost half of the spacecraft mass during transfer orbit. In these spacecraft, liquid motion significantly influences the spacecraft attitude stability and control. LEAS AT, a geosynchronous spacecraft with liquid apogee motor, launched in September 1984, experienced attitude control motion instability1 during the pre-apogee injection phase, immediately following the activation of despin control. The instability was found to be the result of interaction between liquid lateral sloshing modes and the attitude control. This experience demonstrated that the analysis of dynamic interaction between liquid slosh motion and attitude control is critical in the attitude control design of these spacecraft. To perform this analysis, accurate determination of liquid dynamic characteristics, such as natural frequencies, mode shapes, damping, and modal masses becomes important. Accurate prediction of liquid dynamic characteristics is, however, a difficult problem because of the complexity of the hydrodynamical equations of motion. Several investigators have analyzed the fluid motion in rotating containers. Greenspan2 analyzed the transient motion during spin up of an arbitrarily shaped container filled with viscous imcompressible fluid. Stewartson3 developed a stability criterion for a spinning top containing fluid. This stability criterion was corrected by Wedemeyer 4 by considering fluid viscosity. Nayfeh and Meirovitch5 analyzed a spinning rigid body with a spherical cavity partially filled with liquid. Viscous effects are considered only for a boundary layer near the wetted surface. Hendricks and Morton6 analyzed the stability of a rotor partially filled with a viscous incompressible fluid. Stergiopoulous and Aldridge7 studied inertial waves in a partially filled cylindrical cavity during spin up. Pfeiffer8 introduced the concept of homogeneous vorticity to the problem of partially filled containers. El-Raheb and Wagner9 developed a finite element model based on a homogeneous vorticity as

Block-diagonal equations for multibody elastodynamics with geometric stiffness and constraints

Abstract: This paper presents a comprehensive, block-diagonal matrix formulation of the equations of motion of a system of hinge-connect ed flexible bodies undergoing large rotation and translation together with small elastic vibration. The formulation compensates for premature linearization of equations, associated with the customary treatment of small elastic displacement, by accounting for geometric stiffness due to inertia as well as interbody forces. The algorithm is first developed for a tree configuration and is then extended to the case of closed structural loops by cutting the loops and expressing all of the kinematical variables into terms dependent and free of constraint forces/torques. A solution procedure satisfying constraints is given.

Maneuver and vibration control of hybrid coordinate systems using Lyapunov stability theory

Abstract: In this study, we present a generalized control law design methodology that covers a large class of systems, especially flexible structures described by hybrid discrete/distributed coordinate systems. The Lyapunov stability theory is used to develop globally stabilizing control laws. A hybrid version of Hamilton's canonical equations is introduced, which provides a direct path to designing stabilizing control laws for general nonlinear hybrid systems. The usual loss of robustness due to model reduction is overcome by this Lyapunov approach, which does not require truncation of the flexible systems into finite dimensional discrete systems.

Inverse simulation of large-amplitude aircraft maneuvers

Abstract: Inverse simulation techniques are computational methods that determine the control inputs to a dynamic system that will produce desired system outputs. Such techniques can be useful tools for the analysis and evaluation of problems associated with maneuvering flight. As opposed to current inverse simulation methods that require numerical time differentiation in their implementation, the proposed technique is essentially an integration algorithm. It is applicable to cases where the number of inputs equals or exceeds the number of constrained outputs. The algorithm is exercised in determining the trim conditions and then the control inputs that force a nonlinear model of an F-16 fighter to complete large-amplitude maneuvers.