Showing papers in "Journal of Guidance Control and Dynamics in 1985"

An eigensystem realization algorithm for modal parameter identification and model reduction

Abstract: A method, called the Eigensystem Realization Algorithm (ERA), is developed for modal parameter identification and model reduction of dynamic systems from test data. A new approach is introduced in conjunction with the singular value decomposition technique to derive the basic formulation of minimum order realization which is an extended version of the Ho-Kalman algorithm. The basic formulation is then transformed into modal space for modal parameter identification. Two accuracy indicators are developed to quantitatively identify the system modes and noise modes. For illustration of the algorithm, examples are shown using simulation data and experimental data for a rectangular grid structure.

Distributed Piezoelectric-Polymer Active Vibration Control of a Cantilever Beam

Abstract: An active vibration damper for a cantilever beam was designed using a distributed-parameter actuator and distributed-parameter control theory. The distributed-parameter actuator was a piezoelectric polymer, poly (vinylidene fluoride). Lyapunov's second method for distributed-parameter systems was used to design a control algorithm for the damper. If the angular velocity of the tip of the beam is known, all modes of the beam can be controlled simultaneously. Preliminary testing of the damper was performed on the first mode of the cantilever beam. A linear constant-gain controller and a nonlinear constant-amplitude controller were compared. The baseline loss factor of the first mode was 0.003 for large-amplitude vibrations (± 2 cm tip displacement) decreasing to 0.001 for small vibrations (±0.5 mm tip displacement). The constant-gain controller provided more than a factor of two increase in the modal damping with a feedback voltage limit of 200 V rms. With the same voltage limit, the constant-amplitude controller achieved the same damping as the constant-gain controller for large vibrations, but increased the modal loss factor by more than an order of magnitude to at least 0.040 for small vibration levels.

Quaternion feedback for spacecraft large angle maneuvers

Abstract: This paper presents the stability and control analysis for large angle feedback reorientation maneuvers using reaction jets. The strapdown inertial reference system provides spacecraft attitude changes in terms of quaternions. Reaction jets with pulse-width pulse-frequency modulation provide nearly proportional control torques. The use of quaternions as attitude errors for large angle feedback control is investigated. Closed-loop stability analysis for the three-axis maneuvers is performed using the Liapunov stability theorem. Unique characteristics of the quaternion feedback are discussed for single-axis motion using a phase-plane plot. The practical feasibility of a three-axis large angle feedback maneuver is demonstrated by digital simulations.

The implementation of modal filters for control of structures

Abstract: The most common technique for the control of structures is modal control. In modal control, the differential equations in terms of actual coordinates are replaced by a set of ordinary differential equations in terms of the modal coordinates known as modal equations. In designing feedback controls in conjunction with the modal equations, one must know the modal states for the modes targeted for control. The sensors measure actual states, however. The modal states can be estimated by means of a Luenberger observer or modal filters. The modal filters produce estimates of the modal states from distributed measurements of the states. If distributed measurements are not available, then they can be reconstructed from measurements at discrete points via interpolation. This paper examines various questions associated with the implementation of modal filters, such as the effect of choice of interpolation functions and sensors locations, as well as of measurement errors, on the state estimation process. The method is demonstrated by means of two numerical examples.

Optimal simultaneous structural and control design of maneuvering flexible spacecraft

Abstract: An optimization problem for maneuvering flexible spacecraft is discussed wherein both structural parameters and active control forces are to be determined so that a specific cost functional is minimized. The problem is an application of the general theory of optimal control of parametric systems. For simplicity, only maneuvers from a specified initial state to a specified final state in a specified time interval are considered. Numerical examples are presented for single-axis slew maneuvers of a symmetric four-boom flexible structure. The mass and stiffness distributions of the booms are determined as part of the optimization problem.

Formationkeeping for a Pair of Satellites in a Circular Orbit

Abstract: Certain future missions will require that a pair of satellites—ma ster and slave—fly in a fixed relative formation. Active control is required to maintain this formation in spite of disturbances such as aerodynamic drag and solar radiation pressure. This paper develops a closed-loop formationkeeping controller for satellites in any circular orbit using digital optimal control theory. A formationkeepi ng sensor concept, tradeoffs, design, brassboard demonstration, and modeling are discussed. The formationkeeping actuators are assumed to be chemical thrusters on the slave satellite. Two satellites flying in trail 700 m apart in geosynchronou s orbit are used as an example to present closed-loop formationkeeping simulation plots. The results show that formation is maintained to within the ±21 m allocated requirement in the in-track and out-of-plane directions.

Dynamics of flexible bodies in tree topology - A computer oriented approach

Abstract: An approach suited for automatic generation of the equations of motion for large mechanical systems (i.e., large space structures, mechanisms, robots, etc.) is presented. The system topology is restricted to a tree configuration. The tree is defined as an arbitrary set of rigid and flexible bodies connected by hinges characterizing relative translations and rotations of two adjoining bodies. The equations of motion are derived via Kane's method. The resulting equation set is of minimum dimension. Dynamical equations are imbedded in a computer program called TREETOPS. Extensive control simulation capability is built in the TREETOPS program. The simulation is driven by an interactive set-up program resulting in an easy to use analysis tool.

A design methodology for pitch pointing flight control systems

Abstract: A methodology is developed for designing pitch pointing flight control laws by using eigenstructure assignment and command generator tracking. Eigenvalues are chosen to obtain desired damping and rise time, and eigenvectors are chosen to decouple the pitch attitude and flight path angle. Feedforward gains are computed which ensure steady-state tracking of the pilot's command. The design methodology is illustrated by application to an AFTI F- 16 aircraft.

Space structure control design by variance assignment

Abstract: The performance requirements of spacecraft missions are usually specified in terms of root-mean-squared (rms) values on both the input and output variables. The rms contribution of each input or output in the overall system performance metric is called the "input" or "output" cost. A technique is derived that allows a linear controller to assign each of the multi-input or output costs. The procedure is illustrated by the design and shape control for NASA's 64-m Hoop-Column Antenna subject to power-limited actuators. By assigning only the output costs rather than the input costs, the procedure serves to determine the power required of the actuators (required input costs) to achieve the mission requirements (specified output costs). This determination of actuator sizing (and location) for the control of flexible structures is an important feature of the method.

Eigenvalue optimization algorithms for structure/controller design iterations

Abstract: An eigenspace optimization approach is proposed and demonstrated for the design of feedback controllers for the maneuvers/vibration arrests of flexible structures. The algorithm developed is shown to be equally useful in sequential or simultaneous design iterations that modify the structural parameters, sensor/actuator locations, and control feedback gains. The approach is demonstrated using a differential equation model for the "Draper/RPL configuration." This model corresponds to the hardware used for experimental verification of large flexible spacecraft maneuver controls. A number of sensor/actuat or configuration s are studied vis-a-vis the degree of controllabili ty. Linear output feedback gains are determined using a novel optimization strategy. The feasibility of the approach is established, but more research and numerical studies are required to extend these ideas to truly high-dimensioned systems. Parameterization of the Controlled System's Eigenvalues and Eigenvectors C ONSIDER a linear structure (modeled by a finite element or similar discretization scheme) in which the configuration vector jc is governed by the system of differential equations

Star-Sensor-Based Satellite Attitude/Attitude Rate Estimator

Abstract: Recent advancements in star sensor technology suggest that implementations of spacecraft on-orbit attitude determination and control systems based solely On star sensor measurements may soon become practical This paper defines the requirements such applications impose on the star sensors and the algorithms used to estimate attitude and attitude rate A practical filter implementation is described Its open-loop performance is evaluated, and simulation results are presented which suggest that performance consistent with a broad class of spacecraft applications is indeed achievable

Development of the F/A-18A automatic carrier landing system

Abstract: The F/A-18A Automatic Carrier Landing System integrates the aircraft flight control system, throttle control system, inertial navigation sensors, and shipboard SPN-42 tracking radar and computer system to achieve fully automatic approach control to the carrier deck in all weather conditions. Accurate touchdown position and sink rate must be achieved under varying conditions of visibility, deck motion, air turbulence, and ship air wake downdraft. Design analysis of this integrated digital control system is described, including digital synthesis methods used and projected performance under wind and deck motion conditions, two shipboard trials have verified the high touchdown accuracy potential of the system, resulting in along-deck touchdown dispersion of only 19 ft for 91 automatic landings.

Three- and four-satellite continuous-coverage constellations

Abstract: This paper addresses the problem of obtaining continuous satellite line-of-sight coverage of every point in either the northern hemisphere or on the entire Earth's surface with the minimum number of satellites. Geometric theorems and corollaries relating to coverage are presented. A three-satellite elliptic-orbit constellation covering the entire northern hemisphere is described. Also, a four-satellite constellation giving continuous global coverage is defined. An extensive search has uncovered no other three-satellite continuous hemispheric or four-satellite continuous global coverage constellations.

Four-dimensional fuel-optimal guidance in the presence of winds

Abstract: The generation of optimal trajectories from cruise altitude to 10,000 ft for a typical commercial jet transport shows that the optimal absorption of delay in arrival time requires speed reduction in conjunction with altitude excursion (the latter not attempted before). Multiple regression methods are used to develop drag and fuel flow models which are smoother and more compact than those of any previous investigation. The concept of optimal cruise descent is introduced and optimal results are compared with suboptimal strategies of constant Mach number/Calibrated Airspeed (CAS) descent and constant flight path angle descent. Finally, wind effects are analyzed, and the cost of delay as a function of wind condition is presented, followed by the effects of wind on the constant flight path angle descent.

Separation of time scales in aircraft trajectory optimization

Abstract: Two methods for analyzing the time-scale properties of aircraft trajectory optimization problems are presented. Time-scale properties must be identified before solutions can be obtained by using singular perturbation methods. Both methods only require a knowledge of the state equations, the aircraft characteristics, and the bounds on the state and control variables. Although these methods give only rough estimates of time-scale separation, they do not require that an 'exact' optimal trajectory be known, as do the more rigorous methods, and they are an improvement on the ad hoc methods currently in use. The two methods are applied to an example problem for a high performance aircraft.

Optimal many-revolution orbit transfer

Abstract: References ^avison, E.J., "A Method for Simplifying Linear Dynamic Systems," IEEE Transactions on Automatic Control, Vol. AC-11, 1966, pp. 93-101. Chen, C.F. and Shieh, L.S., "A Novel Approach to Linear Model Simplifications," International Journal of Control, Vol. 8, 1968, pp. 561-570. Rao, S.V. and Lamba, S.S., "A New Frequency-Domain Technique for the Simplification of Linear Dynamic Systems," International Journal of Control Vol. 20, 1974, pp. 71-79. Reddy, A.S.S.R., "A Method for Frequency Domain Simplification of Transfer Functions," International Journal of Control, Vol. 23, 1976, pp. 403-409. 5 Parthasarthy, R. and Jayashimha, K.N., "System Reduction Using Stability-Equation Method and Modified Cauer Continued Fraction," Proceedings IEEE, Vol. 70, 1982, pp. 1234-1236. Lepschy, A., Mian, G., and Viaro, U., "Frequency Domain Approach to Model Reduction Problems," Electron Letters, Vol. 18, 1982, pp. 829-830.

Minimum energy-loss guidance for aeroassisted orbital plane change

Abstract: Minimum energy-loss guidance for the aero-assisted plane change of an orbiting vehicle is developed and applied to the plane change of a circular orbit. First, trajectories which minimize the fuel required to change the orbital plane are computed for a realistic vehicle. From these trajectories, it is observed that the fuel weight is minimized if the velocity at exit from the atmosphere is maximized. Next, for the atmospheric turn, approximate optimal controls (angle of attack and bank angle) which maximize the exit velocity are derived. Finally, the minimum-fuel problem is resolved using optimal guidance for the atmospheric part of the trajectory, and the optimization problem reduces to a one-dimensional parameter minimization. Successful plane changes up to 40 deg are demonstrated. Optimal guidance requires up to 14 percent more fuel than the 'true' optimum but only 50 percent of the fuel required by the single-impulse maneuver. Finally, the guidance law developed here is implementable because only algebraic manipulations are required.

Time-domain stability robustness measures for linear regulators

Abstract: The stability robustness aspect of linear systems is analyzed in the time domain. A bound on the perturbation of an asymptotically stable linear system is obtained to maintain stability using Liapunov matrix equation solution. The resulting bound is shown to be an improved upper bound over the ones recently reported in the literature. The proposed methodology is then extended to Linear Quadratic (LQ) and Linear Quadratic Gaussian (LQG) regulators. Examples given include comparison with an aircraft control problem previously analyzed.

Line-of-sight reconstruction for faster homing guidance

Abstract: A novel way to generate the signal required for homing guidance is to reconstruct the line of sight angle by combining seeker boresi ht error with an integrated rate gyro signal (1.2,3,1,5). The paper shows that line-of-sight (LQS) reconstruction allows reduced stabilization loop gain requirements over other guidance implementations. For a given stabilization loop gain, faster guidance system time constants can be achieved with LQS reconstruction, thus enabling the guidance system to achieve more accurate hominq than other implementations.

Sensor failure detection for jet engines using analytical redundancy

Abstract: Analytical redundant sensor failure detection, isolation and accommodation techniques for gas turbine engines are surveyed. Both the theoretical technology base and demonstrated concepts are discussed. Also included is a discussion of current technology needs and ongoing Government sponsored programs to meet those needs.

Predictor laws for pictorial flight displays

Abstract: Two predictor laws are formulated and analyzed: (1) a circular path law based on constant accelerations perpendicular to the path and (2) a predictor law based on state transition matrix computations. It is shown that for both methods the predictor provides the essential lead zeros for the path-following task. However, in contrast to the circular path law, the state transition matrix law furnishes the system with additional zeros that entirely cancel out the higher-frequency poles of the vehicle dynamics. On the other hand, the circular path law yields a zero steady-state error in following a curved trajectory with a constant radius. A combined predictor law is suggested that utilizes the advantages of both methods. A simple analysis shows that the optimal prediction time mainly depends on the level of precision required in the path-following task, and guidelines for determining the optimal prediction time are given.

A multiloop robust controller design study using singular value gradients

Abstract: A method for designing robust feedback controllers for multiloop systems is presented. Robustness is characterized in terms of the minimum singular value of the system return difference matrix at the plant input. Analytical gradients of the singular values with respect to design variables in the controller are derived. A cumulative measure of the singular values and their gradients with respect to the design variables are used with a numerical optimization technique to increase the system's robustness. Both unconstrained and constrained optimization techniques are evaluated. Numerical results are presented for a two-input/two-output drone flight control system.

Minimum-fuel aeroassisted coplanar orbit transfer using lift-modulation

Abstract: Minimum-fuel trajectories and lift controls are computed for aeroassisted coplanar transfer from high orbit to low orbit. The optimal aeroassisted transfer requires less fuel than the all-propulsive Hohmann transfer for a wide range of high orbit to low orbit transfers. The optimal control program for the atmospheric portion of the transfer is to fly at maximum positive L/D initially to recover from the downward plunge, and then, to fly at negative L/D to level off the flight, such that the vehicle skips out of the atmosphere with a flight path angle near zero degrees. To avoid excessive heating rates, the vehicle flies initially at high angle of attack in order to slow down higher in the atmosphere, allowing recovery from the downward plunge, which occurs subsequently using the maximum positive L/D, to take place at a lower atmospheric density, or equivalently, at a higher altitude.

Periodic optical cruise of an atmospheric vehicle

Abstract: Since the steady-state cruise path of an idealized point mass model of an atmospheric vehicle operating in the hypersonic flight regime is dynamically not fuel minimizing, closed periodic paths are numerically determined. By application of second-order conditions for local optimality, a periodic extremal path for a flat Earth is shown to be locally minimizing and produces an improvement in fuel usage of 4.2% over the steady-state cruise path. Application of these second variational conditions to extremal paths for the spherical Earth failed. Nevertheless, these paths produce improved fuel performance over the associated steady-state cruise path. UEL efficient cruise trajectories for aircraft have been a subject of continuous theoretical interest and are becoming one of practical interest as well. The analysis of aircraft trajectories for fuel minimization was first performed in a reduced state space.1"3 By neglecting the altitude and flight path angle dynamics, the equations of motion of a point mass representation of the aircraft motion reduces to the energy-state approximation where energy and fuel mass are the state variables, thrust and velocity (or altitude) are considered the control variables, and range is the independent variable. The first-order dynamics or rates are represented by the rate of change in the energy and fuel with respect to a change in range. The hodograph3 is formed by determining the boundary of reachable rates for admisible values of the control variables at a given energy value (the rates are independent of the fuel). The steady-state cruise fuel performance is given by the value of the fuel mass rate where the hodograph crosses the zero energy rate axis. If the hodograph is not convex so that a straight line tangent to two points on the hodograph (called the convex hull3) crosses the zero energy rate axis at a smaller value of fuel mass rate than does the hodograph, then the control variables at the points of tangency are used to form a chattering control sequence which theoretically will improve fuel performance over the steadystate cruise path. This chattering sequence, first discussed in Ref. 1, is an unrealizable infinite frequency control sequence between two thrust levels and two altitude and velocity points on the energy manifold where the aircraft is aerodynamic or propulsion efficient. This chattering cruise is also referred to as the relaxed steady state cruise in Ref. 2. Since velocity and altitude chattering is unrealizable, altitude has been added as a state variable in Ref. 4 and thrust and flight path angle are considered the control variables. In Ref. 4 the small angle approximation applied to the flight path angle results in flight path angle and thrust appearing linearly in the aircraft dynamic model and cost function. These control variables which lie interior to their admissible control sets along the extremizing steady-state cruise path form what is called a doubly singular arc in the calculus of variations.5'6 By applications of the matrix generalized Legendre-Clebsch condition due to Robbins, 7 it is demonstrated in Ref. 8 that the steady-state cruise path is not minimizing..

Maximum-information guidance for homing missiles

Abstract: A recently-defined information index is used to enhance the information content of minimum-control-effort trajectories for the homing missile intercept problem. Optimal planar intercept trajectories are obtained for a performance index which is control effort weighted by position information content. The missile and target are assumed to be operating at constant speed. The shooting method is used to compute the optimal paths; but because of the simplicity of the model, on-line optimization yielding a guidance law with information enhancement should be possible.

Experimental research on flexible beam modal control

Abstract: A hardware experiment has been developed to study the active vibration control (low-authority control) of a clamped-free flexible beam, where the design methodology is based on direct velocity feedback control. The objective of the experiment is to demonstrate and verify the dynamics and advanced control laws as applied to a structural element. Another important feature of the experiment is the feasibility of hardware realization, especially the dedicated noncontacting actuating and sensing method. Sensing is provided by a purely optical displacement sensor, while an electrodynamic force system provides the actuation. Experimental results are compared with numerical simulations of open- and closed-loop performance in both the colocated and noncolocated actuator/sensor positions. In most cases, good agreement is achieved between the experiments and theoretical predictions.

Analysis of aircraft control strategies for microburst encounter

Abstract: Analyses have indicated that improved control strategies could reduce the threat posed by the presence of microburst-type wind shear during aircraft takeoffs and landings. The attenuation of flight path response to microburst inputs by feedback control to elevators and throttle was studied for the cases of a jet transport and a general aviation aircraft, using longitudinal equations of motion, root locus analysis, Bode plots of altitude response to wind inputs, and nonlinear numerical simulation. Energy management relative to the airmass, a pitch-up response to the decreasing airspeed, increased phugoid mode damping, and decreased phugoid natural frequency, are found to improve microburst penetration aircraft behavior. Aircraft stall, and throttle saturation, are limiting factors in an aircraft's ability to maintain a given flight path during a microburst encounter.