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At least 163 records · Page 9

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NASA NTRS1988

Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

Gibson, J. S.↗

NASA NTRS1992

Subsonic flight test evaluation of a performance seeking control algorithm on an F-15 airplane

The subsonic flight test evaluation phase of the NASA F-15 (powered by F 100 engines) performance seeking control program was completed for single-engine operation at part- and military-power settings. The subsonic performance seeking control algorithm optimizes the quasi-steady-state performance of the propulsion system for three modes of operation. The minimum fuel flow mode minimizes fuel consumption. The minimum thrust mode maximizes thrust at military power. Decreases in thrust-specific fuel consumption of 1 to 2 percent were measured in the minimum fuel flow mode; these fuel savings are significant, especially for supersonic cruise aircraft. Decreases of up to approximately 100 degree R in fan turbine inlet temperature were measured in the minimum temperature mode. Temperature reductions of this magnitude would more than double turbine life if inlet temperature was the only life factor. Measured thrust increases of up to approximately 15 percent in the maximum thrust mode cause substantial increases in aircraft acceleration. The system dynamics of the closed-loop algorithm operation were good. The subsonic flight phase has validated the performance seeking control technology, which can significantly benefit the next generation of fighter and transport aircraft.

Gilyard, Glenn B.↗

NASA NTRS1988

The 15-meter antenna performance optimization using an interdisciplinary approach

A 15-meter diameter deployable antenna has been built and is being used as an experimental test system with which to develop interdisciplinary controls, structures, and electromagnetics technology for large space antennas. The program objective is to study interdisciplinary issues important in optimizing large space antenna performance for a variety of potential users. The 15-meter antenna utilizes a hoop column structural concept with a gold-plated molybdenum mesh reflector. One feature of the design is the use of adjustable control cables to improve the paraboloid reflector shape. Manual adjustment of the cords after initial deployment improved surface smoothness relative to the build accuracy from 0.140 in. RMS to 0.070 in. Preliminary structural dynamics tests and near-field electromagnetic tests were made. The antenna is now being modified for further testing. Modifications include addition of a precise motorized control cord adjustment system to make the reflector surface smoother and an adaptive feed for electronic compensation of reflector surface distortions. Although the previous test results show good agreement between calculated and measured values, additional work is needed to study modelling limits for each discipline, evaluate the potential of adaptive feed compensation, and study closed-loop control performance in a dynamic environment.

Grantham, William L.↗

NASA NTRS1992

Air-breathing hypersonic vehicle guidance and control studies: An integrated trajectory/control analysis methodology, phase 2

An integrated trajectory/control analysis algorithm has been used to generate trajectories and desired control strategies for two different hypersonic air-breathing vehicle models and orbit targets. Both models used cubic spline curve fit tabulated winged-cone accelerator vehicle representations. Near-fuel-optimal, horizontal takeoff trajectories, imposing a dynamic pressure limit of 1000 psf, were developed. The first model analysis case involved a polar orbit and included the dynamic effects of using elevons to maintain longitudinal trim. Analysis results indicated problems with the adequacy of the propulsion model and highlighted dynamic pressure/altitude instabilities when using vehicle angle of attack as a control variable. Also, the magnitude of computed elevon deflections to maintain trim suggested a need for alternative pitch moment management strategies. The second analysis case was reformulated to use vehicle pitch attitude relative to the local vertical as the control variable. A new, more realistic, air-breathing propulsion model was incorporated. Pitch trim calculations were dropped and an equatorial orbit was specified. Changes in flight characteristics due to the new propulsion model have been identified. Flight regimes demanding rapid attitude changes have been noted. Also, some issues that would affect design of closed-loop controllers were ascertained.

Hattis, Philip D.↗

NASA NTRS1976

Trajectory optimization for the Atlas/Centaur launch vehicle

A state-of-art survey of computational techniques employed in design and optimization of trajectories for the Atlas/Centaur launch vehicle is presented. Attention is focused on the constrained optimization technique, related to Hestenes' (1969) method of multipliers, with various formulas used in updating the multipliers. Advantages of applying multiplier method to trajectory optimization, with gains in computing speed, are argued, and optimization of the HEAO-A (high energy astronomical observatory) is discussed. Open-loop atmospheric guidance strategy and closed-loop exoatmospheric pitch and yaw guidance equations are dealt with, and the full range of constraints to be observed during the flight is discussed.

Brusch, R. G.↗

NASA NTRS1977

Tracking performance of symbol synchronizers for Manchester coded data

The implementation and tracking performance of symbol synchronizers for Manchester coded data is presented with motivation provided by maximum a posteriori (MAP) estimation theory. Certain physically relizable closed-loop structures, readily implemented in practice, are suggested by the theory for uncoded data symbols with arbitrary data transition probabilities. The tracking performance of these loops is optimized and comparisons are made among the various configurations over a wide range of system parameters. Although not the major intent of the paper, the acquisition problem is briefly addressed.

Simon, M. K.↗

NASA NTRS1982

Robust Kalman filter design for active flutter suppression systems

Additional insight is provided into the use of the Doyle-Stein (1979, 1981) technique in aeroelastic control problems by examining the application of the method to a flutter control problem. The system to be controlled consists of a full-size wind tunnel model of a wing, plus an aileron, an actuator, and an accelerometer used to sense the motion of the wing. A full-state feedback controller was designed using linear optimal control theory, and a Kalman filter was used in the feedback loop for state estimation. The filter design procedure is explained along with that to improve closed-loop properties of the system. The locus of the poles of the filter is examined as a scalar design parameter is varied. The Doyle-Stein design procedure is shown to substantially improve the stability properties of an active flutter controller designed using the linear quadratic Gaussian control theory.

Garrard, W. L.↗

NASA NTRS1984

Investigation, development and application of optimal output feedback theory. Volume 2: Development of an optimal, limited state feedback outer-loop digital flight control system for 3-D terminal area operation

This report contains the development of a digital outer-loop three dimensional radio navigation (3-D RNAV) flight control system for a small commercial jet transport. The outer-loop control system is designed using optimal stochastic limited state feedback techniques. Options investigated using the optimal limited state feedback approach include integrated versus hierarchical control loop designs, 20 samples per second versus 5 samples per second outer-loop operation and alternative Type 1 integration command errors. Command generator tracking techniques used in the digital control design enable the jet transport to automatically track arbitrary curved flight paths generated by waypoints. The performance of the design is demonstrated using detailed nonlinear aircraft simulations in the terminal area, frequency domain multi-input sigma plots, frequency domain single-input Bode plots and closed-loop poles. The response of the system to a severe wind shear during a landing approach is also presented.

Broussard, J. R.↗

NASA NTRS1983

Closed-form solutions for feedback control with terminal constraints

The problem of closed-loop control of maneuvers between two states for linear dynamical systems, subject to an arbitrarily specified terminal state, is considered. The feedback controller design is based on finite-time quadratic regulator theory. Closed-form expressions for the optimal control law are developed. Solutions are presented for both conventional and smoothed control profiles with fixed and/or free end condition problems. In the maneuvers using control-rate penalties, smooth profiles are generated throughout the maneuvers, in the sense that the initial condition jump discontinuities have been eliminated. Several examples involving large-angle maneuvers of a spacecraft are demonstrated. Results include control maneuvers from one state to another such as rest to rest and spin to rest, which effectively justify the solutions developed in this paper.

Juang, J.-N.↗

NASA NTRS1986

Closed-loop, pilot/vehicle analysis of the approach and landing task

In the case of approach and landing, it is universally accepted that the pilot uses more than one vehicle response, or output, to close his control loops. Therefore, to model this task, a multi-loop analysis technique is required. The analysis problem has been in obtaining reasonable analytic estimates of the describing functions representing the pilot's loop compensation. Once these pilot describing functions are obtained, appropriate performance and workload metrics must then be developed for the landing task. The optimal control approach provides a powerful technique for obtaining the necessary describing functions, once the appropriate task objective is defined in terms of a quadratic objective function. An approach is presented through the use of a simple, reasonable objective function and model-based metrics to evaluate loop performance and pilot workload. The results of an analysis of the LAHOS (Landing and Approach of Higher Order Systems) study performed by R.E. Smith is also presented.

Anderson, M. R.↗

NASA NTRS1986

Integrated aeroservoelastic tailoring of lifting surfaces

An approach to the integration of two design activities, structural design and active control design, for a highly idealized aeroservoelastic system is presented. The particular design goal for this study is the maximization of the stable airspeed envelope of an idealized model of an aeroservoelastic system through rational and systematic variation of structural and control design parameters. The steady-state linear quadratic regulator is used to model the control subsystem; the structural subsystem is assigned characteristic design parameters, such as shear center position. The application of the procedure described here produces optimally controlled structures with stability characteristics superior to those of open-loop and initial closed-loop designs.

Zeiler, T. A.↗

NASA NTRS1986

An estimator-predictor approach to PLL loop filter design

An approach to the design of digital phase locked loops (DPLLs), using estimation theory concepts in the selection of a loop filter, is presented. The key concept is that the DPLL closed-loop transfer function is decomposed into an estimator and a predictor. The estimator provides recursive estimates of phase, frequency, and higher order derivatives, while the predictor compensates for the transport lag inherent in the loop. This decomposition results in a straightforward loop filter design procedure, enabling use of techniques from optimal and sub-optimal estimation theory. A design example for a particular choice of estimator is presented, followed by analysis of the associated bandwidth, gain margin, and steady state errors caused by unmodeled dynamics. This approach is under consideration for the design of the Deep Space Network (DSN) Advanced Receiver Carrier DPLL.

Statman, J. I.↗

NASA NTRS1986

A methodology for designing robust multivariable nonlinear control systems

A new methodology is described for the design of nonlinear dynamic controllers for nonlinear multivariable systems providing guarantees of closed-loop stability, performance, and robustness. The methodology is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate inverse operator for the plant. A major feature of the methodology is a unification of both the state-space and input-output formulations. In addition, new results on stability theory, nonlinear state estimation, and optimal nonlinear regulator theory are presented, including the guaranteed global properties of the extended Kalman filter and optimal nonlinear regulators.

Grunberg, D. B.↗

NASA NTRS1988

The Mark III stellar interferometer

The Mark III interferometer is an operational long baseline stellar interferometer on Mt. Wilson with four-possible baseline configurations from 9m NE-SW to 20m N-S. The interferometer was designed to be a highly automated astronomical instrument to measure stellar positions and diameters to a magnitude limit of seven. Initial fringe observations were made in September 1986 with a 12-m N-S baseline. In the following months, semi-automated astrometric and stellar diameter measurements were also made. This paper describes the hardware and software components of the instrument and its operational characteristics. The interferometer has several novel features. One is the use of optimal estimation and control algorithms (e.g. Kalman filters) in the control loops. Another is the ability to operate both as a closed-loop phased interferometer and eventually as an open-loop or absolute coherent interferometer. High thermal stability and mechanical accuracy should permit the instrument to point blind at an astronomical object and maintain optical path equality to within the limits set by the atmosphere. In this absolute interferometric mode of operation, it should be possible to observe faint astronomical objects that are too dim for phase tracking. In theory, measurements of amplitude, group delay, and closure phase will be possible to 14 mag.

Shao, M.↗

NASA NTRS1988

Load balancing and closed chain multiple arm control

The authors give the general dynamical equations for several rigid link manipulators rigidly grasping a commonly held rigid object. It is shown that the number of arm-configuration degrees of freedom lost due to imposing the closed-loop kinematic constraints is the same as the number of degrees of freedom gained for controlling the internal forces of the closed-chain system. This number is equal to the dimension of the kernel of the Jacobian operator which transforms contact forces to the net forces acting on the held object, and it is shown that this kernel can be identified with the subspace of controllable internal forces of the closed-chain system. Control of these forces makes it possible to regulate the grasping forces imparted to the held object or to control the load taken by each arm. It is shown that the internal forces can be influenced without affecting the control of the configuration degrees of freedom. Control laws of the feedback linearization type are shown to be useful for controlling the location and attitude of a frame fixed with respect to the held object, while simultaneously controlling the internal forces of the closed-chain system. Force feedback can be used to linearize and control the system even when the held object has unknown mass properties. If saturation effects are ignored, an unconstrained quadratic optimization can be performed to distribute the load optimally among the joint actuators.

Kreutz, Kenneth↗

NASA NTRS1989

Transmission-zero bounds for large space structures, with applications

Many large space structure control problems lead quite naturally to the application of an optimal regulator, so the transmission zeros of the open-loop system give fundamental information about the speed of response achievable by the closed-loop system. Despite the importance of this and other well-known zeros properties, little attention has been given to the transmission zeros of large space structures, except for the special case of a rigid spacecraft with flexible appendages. The object of this paper is to remedy this deficiency. In particular, it is proved that the zeros of a structure with colocated sensors and actuators must lie in a region of the complex plane that is defined by its natural frequencies and damping ratios. This generic result, a consequence of the special form of the equations of motion of structural dynamics, admits a very simple graphical interpretation: it is the generalization of the classical pole-zero interlacing property of undamped single-input/single-output structures. The number of sensor/actuator pairs, and their locations, specify where in the permissible region transmission zeros actually lie, thus quantifying the effect of sensor/actuator placement on closed-loop system performance. These points are illustrated by simple examples.

Williams, Trevor↗

NASA NTRS1989

Sequential design of discrete linear quadratic regulators via optimal root-locus techniques

A sequential method employing classical root-locus techniques has been developed in order to determine the quadratic weighting matrices and discrete linear quadratic regulators of multivariable control systems. At each recursive step, an intermediate unity rank state-weighting matrix that contains some invariant eigenvectors of that open-loop matrix is assigned, and an intermediate characteristic equation of the closed-loop system containing the invariant eigenvalues is created.

Shieh, Leang S.↗

NASA NTRS1992

Robust Assignment Of Eigensystems For Flexible Structures

Improved method for placement of eigenvalues and eigenvectors of closed-loop control system by use of either state or output feedback. Applied to reduced-order finite-element mathematical model of NASA's MAST truss beam structure. Model represents deployer/retractor assembly, inertial properties of Space Shuttle, and rigid platforms for allocation of sensors and actuators. Algorithm formulated in real arithmetic for efficient implementation. Choice of open-loop eigenvector matrix and its closest unitary matrix believed suitable for generating well-conditioned eigensystem with small control gains. Implication of this approach is that element of iterative search for "optimal" unitary matrix appears unnecessary in practice for many test problems.

Juang, Jer-Nan↗