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It is shown that the fundamental structure of Galois switching functions follows naturally from that of Boolean switching functions. An expanded formula for deriving multimomial Galois switching functions is provided with illustrations of its application.
Piecewise linear switching functions design for suboptimal regulation of linear plants with relay controller in regard to transient response performance criterion
Optimum design of piecewise-linear switching functions for linear, constant, lumped systems with single ideal relay controller
Minimization algorithm for complex and switching functions using unique identifiers on Karnaugh map
In connection with investigations conducted by Menger (1969), Benjauthrit and Reed (1976), and Pradhan (1978) two methods have been reported for deriving a unique Galois switching function from a given truth table description of the function. However, neither of the two methods appears satisfactory. One method often contains many redundant terms in its formulation, whereas the second method requires a great number of multiplications and additions. By some algebraic manipulations, an expanded formula is obtained which combines the best features of both methods. This formula makes it possible to compute the coefficients of the desired function more directly and probably with less effort. The conduction of calculations by means of the new formula is illustrated with the aid of examples.
A mathematical modeling technique was developed for the lift characteristics of straight wings throughout a very wide angle of attack range. The technique employs a mathematical switching function that facilitates the representation of the nonlinear aerodynamic characteristics in the partially and fully stalled regions and permits matching empirical data within + or - 4 percent of maximum values. Although specifically developed for use in modeling the lift characteristics, the technique appears to have other applications in both aerodynamic and nonaerodynamic fields.
Fuswitch provides both switch and fuse functions within a single housing. A mercury capillary is used to alternately vaporize and condense the mercury within a reservoir. The housing is impervious to mercury and the fuse portion of the device operates on the principle of the self-healing mercury fuse.
A limit and position sensing system includes a sensor assembly and an emitter. The sensor assembly includes first and second electrical conductors arranged in opposing parallel planes. The first electrical conductor is coiled outwardly from either end thereof in a clockwise fashion to form a first coil region and a second coil region. The second electrical conductor forms a single coil with portions of the single coil's rings lying between the first end and second end of the first electrical conductor being parallel to an axis of the first electrical conductor's plane. Ferromagnetic material is aligned with the first and second electrical conductors and spans beyond (a) the first and second ends of the first electrical conductor, and (b) the portions of the rings of the second electrical conductor's single coil that lie between the first end and second end of the first electrical conductor. The emitter is spaced apart from the sensor assembly and transmits a periodic electromagnetic wave towards the sensor assembly.
A hybrid model for continuum phase-change problems is presented. The hybrid model accounts for flow in regions of concentrated mush, dilute mush, and single-phase liquid. Scale analysis shows that, in dilute mush, the Blake-Kozeny-Carman relation may lead to inaccuracy in the continuum formulation for certain values of the Rayleigh and Darcy numbers. The hybrid model uses arctangent switching functions to switch on the Darcy flow and variable viscosity terms depending on the local value of the fraction solid. Two-dimensional example calculations suggest that the hybrid model more accurately accounts for transport in the dilute mush region.
Device performs same switching functions as mechanical switches, occupies same or less panel space, requires only one power source (which is compatible with the load), and operates under severe conditions of temperature, vibration, and shock.
An analytical investigation was conducted concerning the design of an attitude-stabilization system for stabilizing a vehicle experiencing negligible external moments. The system studied was an automatic discontinuous control system employing a linear switching function including effects of pure time delays, rise and decay time, and neutral zone. Equations were developed which generalize the transient and limit-cycle performance of the control system. understanding of how the physical constants of the system affect its performance, the equations enable the optimization of the system with regard to most considerations that can be expressed mathematically. Design charts are presented which enable rapid calculation of the best thrust level and switching-function coefficient for minimizing power required to stabilize the vehicle within some amplitude, minimizing attitude error, and minimizing angular-velocity error after a period of operation.
A mechanically operable solid state switch suited for use in achieving a variable circuit-switching function is described. This switch is characterized by an annular array of photoresponsive switching devices, disposed in communication with an included source of radiation, and a plurality of interchangeable, mechanically operable interrupter disks. Each disk has a predetermined pattern of transparent and opaque portions. Operative displacement of each disk serves to make and break selected electrical circuits through the photo responsive devices of said array.
In designing a satellite system with on-board processing, the selection of a switching architecture is often critical. The on-board switching function can be implemented by circuit switching or packet switching. Destination-directed packet switching has several attractive features, such as self-routing without on-board switch reconfiguration, no switch control memory requirement, efficient bandwidth utilization for packet switched traffic, and accommodation of circuit switched traffic. Destination-directed packet switching, however, has two potential concerns: (1) contention and (2) congestion. And this report specifically deals with the first problem. It includes a description and analysis of various self-routing switch structures, the nature of contention problems, and contention and resolution techniques.
Switched band-pass filters are key components of proposed adaptive, software- defined radio transceivers that would be parts of envisioned digital-data-communication networks that would enable real-time acquisition and monitoring of data from geographically distributed sensors. Examples of sensors to be connected to such networks include security cameras, radio-frequency identification units, and geolocation units based on the Global Positioning System. Through suitable software configuration and without changing hardware, these transceivers could be made to operate according to any of a number of complex wireless-communication standards that could be characterized by diverse modulation schemes, bandwidths, and data-handling protocols. The adaptive transceivers would include field-programmable gate arrays (FPGAs) and digital signal-processing hardware. In the receiving path of a transceiver, the incoming signal would be amplified by a low-noise amplifier (LNA). The output spectrum of the LNA would be processed by a band-pass filter operating in the frequency range between 900 MHz and 2.4 GHz. Then a down-converter would translate the signal to a lower frequency range to facilitate analog-to-digital conversion, which would be followed by baseband processing by one or more FPGAs. In the transmitting path, a digital stream would first be converted to an analog signal, which would then be up-converted to a selected frequency band before being applied to a transmitting power amplifier. The aforementioned band-pass filter in the receiving path would be a combination of resonant inductor-and-capacitor filters and switched band-pass filters. The overall combination would implement a switch function designed mathematically to exhibit desired frequency responses and to switch the signal in each frequency band to an analog-to-digital converter appropriate for that band to produce a digital intermediate-frequency signal for digital signal processing.
This report presents the formulation of the optimal low- and medium-thrust orbit transfer control problem and methods for numerical solution of the problem. The problem formulation is for final mass maximization and allows for second-harmonic oblateness, atmospheric drag, and three-dimensional, non-coplanar, non-aligned elliptic terminal orbits. We setup some examples to demonstrate the ability of two indirect methods to solve the resulting TPBVP's. The methods demonstrated are the multiple-point shooting method as formulated in H. J. Oberle's subroutine BOUNDSCO, and the minimizing boundary-condition method (MBCM). We find that although both methods can converge solutions, there are trade-offs to using either method. BOUNDSCO has very poor convergence for guesses that do not exhibit the correct switching structure. MBCM, however, converges for a wider range of guesses. However, BOUNDSCO's multi-point structure allows more freedom in quesses by increasing the node points as opposed to only quessing the initial state in MBCM. Finally, we note an additional drawback for BOUNDSCO: the routine does not supply information to the users routines for switching function polarity but only the location of a preset number of switching points.
Optoelectronic switching employs a hybrid optical/electronic principle to perform the switching function and is applicable for either analog broadband or high-bit rate digital switching. The major advantages of optoelectronic switching include high isolation, low crosstalk, small physical size, light weight, and low power consumption. These advantages make optoelectronic switching an excellent candidate for on-board satellite switching. This paper describes a number of optoelectronic switching architectures. System components required for implementing these switching architectures are discussed. Performance of these architectures are evaluated by calculating their crosstalk, isolation, insertion loss, matrix size, drive power, throughput, and switching speed. Technologies needed for monolithic optoelectronic switching are also identified.
To make satellite channels cost competitive with optical cables, the use of small, inexpensive earth stations with reduced antenna size and high powered amplifier (HPA) power will be needed. This will necessitate the use of high e.i.r.p. and gain-to-noise temperature ratio (G/T) multibeam satellites. For a multibeam satellite, onboard switching is required in order to maintain the needed connectivity between beams. This switching function can be realized by either an receive frequency (RF) or a baseband unit. The baseband switching approach has the additional advantage of decoupling the up-link and down-link, thus enabling rate and format conversion as well as improving the link performance. A baseband switching satellite requires the demultiplexing and demodulation of the up-link carriers before they can be switched to their assigned down-link beams. Principles of operation, design and implementation issues of such an onboard demultiplexer/demodulator (bulk demodulator) that was recently built at COMSAT Labs. are discussed.
A comprehensive discussion of the problem of singular control is presented. Singular control enters an optimal trajectory when the so called switching function vanishes identically over a finite time interval. Using the concept of domain of maneuverability, the problem of optical switching is analyzed. Criteria for the optimal direction of switching are presented. The switching, or junction, between nonsingular and singular subarcs is examined in detail. Several theorems concerning the necessary, and also sufficient conditions for smooth junction are presented. The concepts of quasi-linear control and linearized control are introduced. They are designed for the purpose of obtaining approximate solution for the difficult Euler-Lagrange type of optimal control in the case where the control is nonlinear.