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Two methods for stabilizing constant linear systems, namely, the extended Bass algorithm for continuous systems and a discrete system analog, are discussed. For the continuous algorithm, a new result on the degree of stability of the closed-loop eigenvalues is presented, and for both methods, typical results and asymptotic trends in the data are illustrated through an example computation.
A design procedure based on Gilbert's decoupling parameters for determining a fixed state feedback control law which decouples a linear system with discrete parameter uncertainties is described. Perfect decoupling conditions are established which involve a test for the existence of a solution to a system of linear equations. An actual solution of the linear equations yields the decoupling control law.
This tutorial paper reviews some of the advantages and disadvantages of a discrete time representation of a signal. Also reviewed are some of the recent theoretical advances in digital signal processing which can be implemented by the use of charge transfer signal processing devices. In particular, the design and implementation of transversal filters and spectrum analyzers will be discussed.
Technique encoding and decoding color-image signals from array of discrete sensors can simplify fabrication of remote-sensing imaging system. Imaging system projects output on charge-coupled-device array. Computerized matrix decoding scheme decodes image.
A suboptimal dynamic compensator to be used in conjunction with the ordinary discrete time Kalman filter was derived. The resultant compensated Kalman Filter has the property that steady state bias estimation errors, resulting from modelling errors, were eliminated.
The design of an optimal dynamic compensator for a multivariable discrete time system is studied. Also the design of compensators to achieve minimum variance control strategies for single input single output systems is analyzed. In the first problem the initial conditions of the plant are random variables with known first and second order moments, and the cost is the expected value of the standard cost, quadratic in the states and controls. The compensator is based on the minimum order Luenberger observer and it is found optimally by minimizing a performance index. Necessary and sufficient conditions for optimality of the compensator are derived. The second problem is solved in three different ways; two of them working directly in the frequency domain and one working in the time domain. The first and second order moments of the initial conditions are irrelevant to the solution. Necessary and sufficient conditions are derived for the compensator to minimize the variance of the output.
Attitude control techniques for the pointing and stabilization of very large, inherently flexible spacecraft systems were investigated. The attitude dynamics and control of a long, homogeneous flexible beam whose center of mass is assumed to follow a circular orbit was analyzed. First order effects of gravity gradient were included. A mathematical model which describes the system rotations and deflections within the orbital plane was developed by treating the beam as a number of discretized mass particles connected by massless, elastic structural elements. The uncontrolled dynamics of the system are simulated and, in addition, the effects of the control devices were considered. The concept of distributed modal control, which provides a means for controlling a system mode independently of all other modes, was examined. The effect of varying the number of modes in the model as well as the number and location of the control devices were also considered.
For certain long transform lengths, Winograd's algorithm for computing the discrete Fourier transform is extended considerably. This is accomplished by performing the cyclic convolution, required by Winograd's method, with the Mersenne-prime number theoretic transform. This new algorithm requires fewer multiplications than either the standard fast Fourier transform or Winograd's more conventional algorithm.
The computed RMS and peak responses due to atmospheric turbulence and discrete wind shears, respectively, are presented for several aircraft in different flight conditions. The responses are presented with and without the effects of a typical second order washout filter. A complete set of dimensional stability derivatives for each aircraft/flight condition combination evaluated is also presented.
Using discrete time state variable representation, a generalized computer-aided modeling and analysis of dc-dc converters is presented. The methodology provides exact modeling and is applicable to all types of power stages and duty-cycle control, including continuous and discontinuous inductor current operation. Converter stability, transient behavior and audio susceptibility can be analytically evaluated and predicted. The generalized theory of the proposed approach to converter modeling and analysis is presented first, followed by a demonstrative example applying the theory to a constant frequency buck converter operating in continuous and discontinuous inductor current mode. Excellent agreement with laboratory test data has been observed.
Optimum estimates of nonobservable random variables or random processes which influence the rate functions of a discrete time jump process (DTJP) are derived. The approach used is based on the a posteriori probability of a nonobservable event expressed in terms of the a priori probability of that event and of the sample function probability of the DTJP. Thus a general representation is obtained for optimum estimates, and recursive equations are derived for minimum mean-squared error (MMSE) estimates. In general, MMSE estimates are nonlinear functions of the observations. The problem is considered of estimating the rate of a DTJP when the rate is a random variable with a beta probability density function and the jump amplitudes are binomially distributed. It is shown that the MMSE estimates are linear. The class of beta density functions is rather rich and explains why there are insignificant differences between optimum unconstrained and linear MMSE estimates in a variety of problems.
An approach to one-on-one air-combat analysis is described which employs discrete gaming of a parameterized model featuring choice between several closed-loop control policies. A preference-ordering formulation due to Falco is applied to rational choice between outcomes: win, loss, mutual capture, purposeful disengagement, draw. Approximate optimization is provided by an active-cell scheme similar to Falco's obtained by a 'backing up' process similar to that of Kopp. The approach is designed primarily for short-duration duels between craft with large-envelope weaponry. Some illustrative computations are presented for an example modeled using constant-speed vehicles and very rough estimation of energy shifts.
The calculation procedure is based on the method of characteristics for steady three-dimensional flow. The bow shock wave and the internal shock wave system were computed using a discrete shock wave fitting procedure. The general structure of the computer program is discussed, and a brief description of each subroutine is given. All program input parameters are defined, and a brief discussion on interpretation of the output is provided. A number of sample cases, complete with data deck listings, are presented.
Pilot behavior is considered as a discrete-time process where the decision making has a sequential nature. This model differs from both the quasilinear model which follows from classical control theory and from the optimal control model which considers the human operator as a Kalman estimator-predictor. An additional factor considered is that the pilot's objective may not be adequately formulated as a quadratic cost functional to be minimized, but rather as a more fuzzy measure of the closeness with which the aircraft follows a reference trajectory. All model parameters, in the digital program simulating the pilot's behavior, were successfully compared in terms of standard-deviation and performance with those of professional pilots in IFR configuration. The first practical application of the model was in the study of its performance degradation when the aircraft model static margin decreases.
The current program had the objective to modify a discrete vortex wake method to efficiently compute the aerodynamic forces and moments on high fineness ratio bodies (f approximately 10.0). The approach is to increase computational efficiency by structuring the program to take advantage of new computer vector software and by developing new algorithms when vector software can not efficiently be used. An efficient program was written and substantial savings achieved. Several test cases were run for fineness ratios up to f = 16.0 and angles of attack up to 50 degrees.
The users manual for the Discrete Vortex Cross flow Evaluator (DIVORCE) computer program is presented. DIVORCE was developed in FORTRAN 4 for the DCD 6600 and CDC 7600 machines. Optimal calls to a NASA vector subroutine package are provided for use with the CDC 7600.
An analysis is presented for calculating the flow field in supersonic mixed-compression aircraft inlets operating at angle of attack. The flow field is computed by a steady three-dimensional bicharacteristic method. The bow shock wave and the reflected internal shock wave system are computed by a three-dimensional discrete shock wave fitting procedure. Viscous and thermal diffusion may be included as source terms in the bicharacteristic method. A production type computer program capable of determining the flow field in a variety of axisymmetric mixed-compression supersonic inlets is available. The results of the present analysis agree well with those produced by the two-dimensional method of characteristics when axisymmetric flow fields are computed. For three-dimensional flow fields, the results of the present analysis agree well with experimental data except in regions of high viscous interaction and boundary layer removal. The present analysis does not compute the boundary layer, nor does it account for boundary layer bleed.
A suboptimal dynamic compensator to be used in conjunction with the ordinary discrete-time Kalman filter is derived. The resultant compensated Kalman filter has the property that steady-state bias estimation errors, resulting from modelling errors, are eliminated. The implementation of the compensated Kalman filter involves the use of accumulators in the residual channels in addition to the nominal dynamic model of the stochastic system.