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Circuit Theory, IRE Transactions on

Issue 1 • Date March 1954

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Displaying Results 1 - 9 of 9
  • Trends in feedback systems (editorial)

    Publication Year: 1954 , Page(s): 2 - 8
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    There are a number of new and powerful techniques rapidly being developed for the analysis and synthesis of feedback control systems. Four of these techniques are illustrated by some of the papers in this issue. One of the most fruitful of these is in the field of statistics, and in particular its application to nonlinear systems. R. C. Booton presents a paper which derives the cross-power density spectrum for a component with saturation or clipping. From this cross-power operator one can determine the quantity of output signal which is correlated with the input, the amount of harmonic distortion power present in the output, and an equivalent ¿gain¿ term satisfactory for use in testing for the build-up of periodic oscillations. View full abstract»

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  • Nonlinear control systems with random inputs

    Publication Year: 1954 , Page(s): 9 - 18
    Cited by:  Papers (2)
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    The describing-function method for the analysis of nonlinear systems with sinusoidal inputs is interpreted as a mean-square quasi-linearization technique and is generalized to apply to random signals. An amplitude-sensitive (or zero-memory) nonlinearity is interpreted as being approximately equivalent to a linear frequency-insensitive device, and a formula is derived for its equivalent gain. A simple rate-limited control system with a Gaussian input is analyzed as a specific application. Approximation of a general nonlinear element (containing memory) is considered next, and a relation between equivalent-system impulse response and the response of the actual nonlinearity is derived. View full abstract»

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  • A method of analysis and synthesis of closed loop servo systems containing small discontinuous non-linearities

    Publication Year: 1954 , Page(s): 19 - 34
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (986 KB)  

    A method is presented for molding non-linear elements of a system into equivalent linear elements so that existing linear methods of analysis and synthesis may be applied. The method can be applied in a Large number of practical cases, particularly in the more complex systems. It is based upon a Fourier expansion of the output waveform of a sinusoidally excited discontinuous element. Several cases of practical importance are considered, and charts are presented which may be used in analysis or design. View full abstract»

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  • Stability of feedback systems using dual Nyquist diagram

    Publication Year: 1954 , Page(s): 35 - 44
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    This paper introduces a procedure for determing the stability of a feedback system using a dual Nyquist diagram. Such a diagram results when the characteristic equation of the system is interpreted to be the sum of two frequency-dependent functions F1(p) + F2(p) instead of the normal expression 1 + G(p)H(p). This diagram then consists of two polar plots; one plot represents the locus of one of the functions which is contained in the characteristic equation, and the other plot is the negative locus of the other function contained in the characteristic equation. Each of these curves may, if desired, be considered as an individual Nyquist diagram. View full abstract»

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  • Optimum lead-controller synthesis in feedback-control systems

    Publication Year: 1954 , Page(s): 45 - 48
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    The phase lead network, shown in figure 1, had demonstrated its ability to improve the relative stability of linear feedback amplifiers long before it was adopted as one of the principal stabilizing networks by those interested in the newer field of servomechanisms. Its wide acceptance was based upon its simple form when dealing with d.c. signals and its ability to produce rate-type signal components without mechanical devices. When used as a synthesis tool in connection with the Nyquist plot (1)¿ of the loop-transfer characteristics, it allows considerable freedom in shaping the contour to conform to generally acceptable standards of performance to the limited extent with which they can be interpreted on this Nyquist plot. The major drawback of the phase-lead network is its attenuation of the signal components, an attenuation which may be readily appreciated if this network is viewed as a resistance voltage divider under static (d.c.) conditions. This sacrifice is all the more objectionable in applications where higher-frequency noise components are present and the need to maintain the signal-to-noise ratio has virtually eliminated this useful tool from systems whose inputs contain large noise components. A system controlled by a radar signal provides just such a situation. View full abstract»

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  • On the comparison of linear and nonlinear servomschanism response

    Publication Year: 1954 , Page(s): 49 - 55
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    In trying to design or adjust a dynamic system for optimum performance, the engineer is helped by a knowledge of theoretical limits on the capabilities of the system. Examples of such limits are the gain-bandwidth product of amplifier design and the coding theorem of information theory. View full abstract»

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  • Predictor servomechanisms

    Publication Year: 1954 , Page(s): 56 - 70
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    This paper is concerned with the problem of optimizing the transient behavior of a servomechanism. In this instance the term optimum is used in the sense of a transient response in minimum time as compared with the familiar minimum RMS error criteria for an optimum system. The use of the term ¿predictor¿ arises from the fact that the system. utilizes the information contained in the Input and its derivatives in order to reduce the error to zero in an optimum manner. View full abstract»

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  • Conversion of a beline cycle with an ideal transformer into a cycle without an ideal transformer

    Publication Year: 1954 , Page(s): 71 - 75
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (498 KB)  

    O. Brune1 has proved that any rational ¿positive real¿ function possesses a one terminal-pair network configuration containing a finite number of linear passive elements. Brune suggested the ladder synthesis for positive real functions. In general his synthesis procedure contains mutual couplings which are not desirable from a practical standpoint. Thus, there has always been a great desire to eliminate ideal transformers from the picture. As steps towards this goal, H. W. Bode2 suggests resistance padding, and E. A. Guillemin3 often uses some practical methods for eliminating the ideal transformer in special cases. The existence proof, along with a synthesis procedure without an ideal transformer, was first given by R. Bott and R. J. Duffin4. View full abstract»

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  • What is nature's error criterion?

    Publication Year: 1954 , Page(s): 76
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    It is well known that the Fourier series is not the only trigonometric polynomial that may be used to represent a periodic function. It is a polynomial with the property that the mean square error between a partial sum and the given function is a minimum; that is to say, it approximates the given function so as to make the mean square error a minimum. This error criterion is only one of many that could be stipulated as fixing the manner in which the polynomial approximates the given function, and from a practical standpoint it isn't even a good one for many applications because it suffers from the Gibbs phenomenon. A Tschebyscheff-like approximation or the one inherent in the Cesaro sum which converges uniformly even at points of discontinuity may be preferable in many cases. View full abstract»

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