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Cliff, E. M.

Publications and source records attributed to Cliff, E. M..

31 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

An on-board near-optimal climb-dash energy management

On-board real time flight control is studied in order to develop algorithms which are simple enough to be used in practice, for a variety of missions involving three dimensional flight. The intercept mission in symmetric flight is emphasized. Extensive computation is required on the ground prior to the mission but the ensuing on-board exploitation is extremely simple. The scheme takes advantage of the boundary layer structure common in singular perturbations, arising with the multiple time scales appropriate to aircraft dynamics. Energy modelling of aircraft is used as the starting point for the analysis. In the symmetric case, a nominal path is generated which fairs into the dash or cruise state. Feedback coefficients are found as functions of the remaining energy to go (dash energy less current energy) along the nominal path.

Weston, A. R.↗
NASA NTRS1982

Altitude transitions in energy climbs

The aircraft energy-climb trajectory for configurations with a sharp transonic drag rise is well known to possess two branches in the altitude/Mach-number plane. Transition in altitude between the two branches occurs instantaneously, a 'corner' in the minimum-time solution obtained with the energy-state model. If the initial and final values of altitude do not lie on the energy-climb trajectory, then additional jumps (crude approximations to dives and zooms) are required at the initial and terminal points. With a singular-perturbation approach, a 'boundary-layer' correction is obtained for each altitude jump, the transonic jump being a so-called 'internal' boundary layer, different in character from the initial and terminal layers. The determination of this internal boundary layer is examined and some computational results for an example presented.

Weston, A. R.↗
NASA NTRS1981

Pursuit/evasion in orbit

Maneuvers available to a spacecraft having sufficient propellant to escape an antisatellite satellite (ASAT) attack are examined. The ASAT and the evading spacecraft are regarded as being in circular orbits, and equations of motion are developed for the ASAT to commence a two-impulse maneuver sequence. The ASAT employs thrust impulses which yield a minimum-time-to-rendezvous, considering available fuel. Optimal evasion is shown to involve only in-plane maneuvers, and begins as soon as the ASAT launch information is gathered and thrust activation can be initiated. A closest approach, along with a maximum evasion by the target spacecraft, is calculated to be 14,400 ft. Further research to account for ASATs in parking orbit and for generalization of a continuous control-modeled differential game is indicated.

Kelley, H. J.↗
NASA NTRS1981

Fixed-trim re-entry guidance analysis

The terminal guidance problem for a fixed-trim re-entry body is formulated with the objective of synthesizing a closed-loop steering law. A transformation of variables and subsequent linearization of the motion, with the sight-line to the target as a reference, reduces the order of the state system for the guidance problem. The reduced order system, although nonlinear and time-varying, is simple enough to lend itself to synthesis of a class of guidance laws. A generalization of the feedforward device of classical control theory is successfully employed for compensation of roll autopilot lags. The proposed steering law exhibits superior miss-distance performance in a computational comparison with existing fixed-trim guidance laws.

Gracey, C.↗
NASA NTRS1980

Thrust-vectored differential turns

Barrier surface construction in the joint space of the differential turning game for thrust-vectored vs. conventional aircraft is discussed. Differential-turn studies are based on modifications of existing computer programs including an energy-turn program, and one which generates hodograph data. Optimal turning flight in energy approximation is discussed for the conventional aircraft configurations. It is concluded that any advantages realized from thrust-vectoring are minor, unless hover is possible, where advantages would be major at low energies, and affect tactics at high energies as well.

Kelley, H. J.↗
NASA NTRS1978

Numerical solutions of a control problem governed by functional differential equations

A numerical procedure is proposed for solving optimal control problems governed by linear retarded functional differential equations. The procedure is based on the idea of 'averaging approximations', due to Banks and Burns (1975). For illustration, numerical results generated on an IBM 370/158 computer, which demonstrate the rapid convergence of the method are presented.

Banks, H. T.↗
NASA NTRS1978

On approximating hereditary dynamics by systems of ordinary differential equations

The paper deals with methods of obtaining approximate solutions to linear retarded functional differential equations (hereditary systems). The basic notion is to project the infinite dimensional space of initial functions for the hereditary system onto a finite dimensional subspace. Within this framework, two particular schemes are discussed. The first uses well-known piecewise constant approximations, while the second is a new method based on piecewise linear approximating functions. Numerical results are given.

Cliff, E. M.↗
NASA NTRS1977

A piecewise linear approximation scheme for hereditary optimal control problems

An approximation scheme based on 'piecewise linear' approximations of L2 spaces is employed to formulate a numerical method for solving quadratic optimal control problems governed by linear retarded functional differential equations. This piecewise linear method is an extension of the so called averaging technique. It is shown that the Riccati equation for the linear approximation is solved by simple transformation of the averaging solution. Thus, the computational requirements are essentially the same. Numerical results are given.

Cliff, E. M.↗
NASA NTRS1975

Essential uncontrollability of discrete linear, time-invariant, dynamical systems

The concept of a 'best approximating m-dimensional subspace' for a given set of vectors in n-dimensional whole space is introduced. Such a subspace is easily described in terms of the eigenvectors of an associated Gram matrix. This technique is used to approximate an achievable set for a discrete linear time-invariant dynamical system. This approximation characterizes the part of the state space that may be reached using modest levels of control. If the achievable set can be closely approximated by a proper subspace of the whole space then the system is 'essentially uncontrollable'. The notion finds application in studies of failure-tolerant systems, and in decoupling.

Cliff, E. M.↗
NASA NTRS1972

A problem of collision avoidance

Collision avoidance between two vehicles of constant speed with limited turning radii, moving in a horizontal plane is investigated. Collision avoidance is viewed as a game by assuming that the operator of one vehicle has perfect knowledge of the state of the other, whereas the operator of the second vehicle is unaware of any impending danger. The situation envisioned is that of an encounter between a commercial aircraft and a small light aircraft. This worse case situation is examined to determine the conditions under which the commercial aircraft should execute a collision avoidance maneuver. Three different zones of vulnerability are defined and the boundaries, or barriers, between these zones are determined for a typical aircraft encounter. A discussion of the methods used to obtain the results as well as some of the salient features associated with the resultant barriers is included.

Vincent, T. L.↗