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At least 955 records · Page 53

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NASA NTRS1975

A numerical method for the prediction of high-speed boundary-layer transition using linear theory

A method is described of estimating the location of transition in an arbitrary laminar boundary layer on the basis of linear stability theory. After an examination of experimental evidence for the relation between linear stability theory and transition, a discussion is given of the three essential elements of a transition calculation: (1) the interaction of the external disturbances with the boundary layer; (2) the growth of the disturbances in the boundary layer; and (3) a transition criterion. The computer program which carried out these three calculations is described. The program is first tested by calculating the effect of free-stream turbulence on the transition of the Blasius boundary layer, and is then applied to the problem of transition in a supersonic wind tunnel. The effects of unit Reynolds number and Mach number on the transition of an insulated flat-plate boundary layer are calculated on the basis of experimental data on the intensity and spectrum of free-stream disturbances. Reasonable agreement with experiment is obtained in the Mach number range from 2 to 4.5.

Mack, L. M.↗

NASA NTRS1975

The generation of gravitational waves. 2: The post-linear formalism revisited

Two different versions of the Green's function for the scalar wave equation in weakly curved spacetime (one due to DeWitt and DeWitt, the other to Thorne and Kovacs) are compared and contrasted; and their mathematical equivalence is demonstrated. The DeWitt-DeWitt Green's function is used to construct several alternative versions of the Thorne-Kovacs post-linear formalism for gravitational-wave generation. Finally it is shown that, in calculations of gravitational bremsstrahlung radiation, some of our versions of the post-linear formalism allow one to treat the interacting bodies as point masses, while others do not.

Crowley, R. J.↗

NASA NTRS1976

Solution of linear systems by a singular perturbation technique

An approximate solution is obtained for a singularly perturbed system of initial valued, time invariant, linear differential equations with multiple boundary layers. Conditions are stated under which the approximate solution converges uniformly to the exact solution as the perturbation parameter tends to zero. The solution is obtained by the method of matched asymptotic expansions. Use of the results for obtaining approximate solutions of general linear systems is discussed. An example is considered to illustrate the method and it is shown that the formulas derived give a readily computed uniform approximation.

Ardema, M. D.↗

NASA NTRS1975

On the time-weighted quadratic sum of linear discrete systems

A method is proposed for obtaining the time-weighted quadratic sum for linear discrete systems. The formula of the weighted quadratic sum is obtained from matrix z-transform formulation. In addition, it is shown that this quadratic sum can be derived in a recursive form for several useful weighted functions. The discussion presented parallels that of MacFarlane (1963) for weighted quadratic integral for linear continuous systems.

Jury, E. I.↗

NASA NTRS1976

On optimal control of linear systems in the presence of multiplicative noise

This correspondence considers the problem of optimal regulator design for discrete time linear systems subjected to white state-dependent and control-dependent noise in addition to additive white noise in the input and the observations. A pseudo-deterministic problem is first defined in which multiplicative and additive input disturbances are present, but noise-free measurements of the complete state vector are available. This problem is solved via discrete dynamic programming. Next is formulated the problem in which the number of measurements is less than that of the state variables and the measurements are contaminated with state-dependent noise. The inseparability of control and estimation is brought into focus, and an 'enforced separation' solution is obtained via heuristic reasoning in which the control gains are shown to be the same as those in the pseudo-deterministic problem. An optimal linear state estimator is given in order to implement the controller.

Joshi, S. M.↗

NASA NTRS1975

Development of a digital adaptive optimal linear regulator flight controller

Digital adaptive controllers have been proposed as a means for retaining uniform handling qualities over the flight envelope of a high-performance aircraft. Towards such an implementation, an explicit adaptive controller, which makes direct use of online parameter identification, has been developed and applied to the linearized lateral equations of motion for a typical fighter aircraft. The system is composed of an online weighted least-squares parameter identifier, a Kalman state filter, and a model following control law designed using optimal linear regulator theory. Simulation experiments with realistic measurement noise indicate that the proposed adaptive system has the potential for onboard implementation.

Berry, P.↗

NASA NTRS1975

Some estimation formulae for continuous time-invariant linear systems

In this brief paper we examine a Riccati equation decomposition due to Reid and Lainiotis and apply the result to the continuous time-invariant linear filtering problem. Exploitation of the time-invariant structure leads to integration-free covariance recursions which are of use in covariance analyses and in filter implementations. A super-linearly convergent iterative solution to the algebraic Riccati equation (ARE) is developed. The resulting algorithm, arranged in a square-root form, is thought to be numerically stable and competitive with other ARE solution methods. Certain covariance relations that are relevant to the fixed-point and fixed-lag smoothing problems are also discussed.

Bierman, G. J.↗

NASA NTRS1977

FM oscillator has improved deviation linearity

Device can be obtained by driving basic circuit through nonlinear FET input stage. Frequency of VCO is linearized with FET and total variance is varactor controlled. Experimental device exhibited linearity of better than plus or minus one percent for total frequency of plus or minus 10 millihertz.

Honnell, M. A.↗

NASA NTRS1975

Closed-loop structural stability for linear-quadratic optimal systems

This paper contains an explicit parameterization of a subclass of linear constant gain feedback maps that never destabilize an originally open-loop stable system. These results can then be used to obtain several new structural stability results for multi-input linear-quadratic feedback optimal designs.

Wong, P. K.↗

NASA NTRS1976

An algorithm for the weighting matrices in the sampled-data optimal linear regulator problem

The sampled-data optimal linear regulator problem provides a means whereby a control designer can use an understanding of continuous optimal regulator design to produce a digital state variable feedback control law which satisfies continuous system performance specifications. A basic difficulty in applying the sampled-data regulator theory is the requirement that certain digital performance index weighting matrices, expressed as complicated functions of system matrices, be computed. Infinite series representations are presented for the weighting matrices of the time-invariant version of the optimal linear sampled-data regulator problem. Error bounds are given for estimating the effect of truncating the series expressions after a finite number of terms, and a method is described for their computer implementation. A numerical example is given to illustrate the results.

Armstrong, E. S.↗

NASA NTRS1976

Closed-loop structural stability for linear-quadratic optimal system

This paper contains an explicit parameterization of a subclass of linear constant gain feedback maps that will not destabilize an originally open-loop stable system. These results can then be used to obtain several new structural stability results for multi-input linear-quadratic feedback optimal designs.

Wong, P. K.↗

NASA NTRS1975

Closed-loop structural stability for linear-quadratic optimal systems

An explicit parametrization of a subclass of linear constant gain feedback maps that never destabilize an originally open-loop stable system is presented. These results are used to obtain several new structural stability results for multiinput linear-quadratic feedback optimal designs.

Wong, P. K.↗

NASA NTRS1977

Symbolic computation of recurrence equations for the Chebyshev series solution of linear ODE's

If a linear ordinary differential equation with polynomial coefficients is converted into integrated form then the formal substitution of a Chebyshev series leads to recurrence equations defining the Chebyshev coefficients of the solution function. An explicit formula is presented for the polynomial coefficients of the integrated form in terms of the polynomial coefficients of the differential form. The symmetries arising from multiplication and integration of Chebyshev polynomials are exploited in deriving a general recurrence equation from which can be derived all of the linear equations defining the Chebyshev coefficients. Procedures for deriving the general recurrence equation are specified in a precise algorithmic notation suitable for translation into any of the languages for symbolic computation. The method is algebraic and it can therefore be applied to differential equations containing indeterminates.

Geddes, K. O.↗

NASA NTRS1976

Linear feedback rate bounds for regressive channels

Bounds for the linear feedback capacity of m-th order Gaussian autoregressive channels are derived. The upper bound is tighter than that found by Tiernan and Schalwijk (1974) for the feedback capacity of a first-order autoregressive Gaussian channel with not necessarily linear processing. The separation between the upper and lower bounds is small, and it is conjectured that the lower bound converges to the feedback capacity of the first-order channel as the number of signals tends to infinity.

Butman, S. A.↗

NASA NTRS1977

Closed-loop structural stability for linear-quadratic optimal systems

This paper contains an explicit parametrization of a subclass of linear constant gain feedback maps that will not destabilize an originally open-loop stable system. These results can then be used to obtain several new structural stability results for multiinput linear-quadratic feedback optimal designs.

Wong, P. K.↗

NASA NTRS1976

A stabilization algorithm for linear discrete constant systems

A procedure is derived for stabilizing linear constant discrete systems which is a discrete analog to the extended Bass algorithm for stabilizing linear constant continuous systems. The procedure offers a method for constructing a stabilizing feedback without the computational difficulty of raising the unstable open-loop response matrix to powers thus making the method attractive for high order or poorly conditioned systems.

Armstrong, E. S.↗

NASA NTRS1976

Closed-loop structural stability for linear-quadratic optimal systems

Wong, P. K.↗

NASA NTRS1977

Optimal filtering and filter stability of linear stochastic delay systems

Optimal filtering equations are obtained for very general linear stochastic delay systems. Stability of the optimal filter is studied in the case where there are no delays in the observations. Using the duality between linear filtering and control, asymptotic stability of the optimal filter is proved. Finally, the cascade of the optimal filter and the deterministic optimal quadratic control system is shown to be asymptotically stable as well.

Kwong, R. H.-S.↗