Showing papers on "Describing function published in 1968"

Multiple-Input Describing Functions and Nonlinear System Design

Abstract: ABRAMSON Information theory and coding BATTIN Astronautical guidance BLACHMAN Noise and its effect on communication BREMER Superconductive devices BROXMEYER Inertial navigation systems GELB AND VANDER VELDE Multiple-input describing functions and nonlinear system design GILL Introduction to the theory of finite-state machines HANCOCK AND WINTZ Signal detection theory HUELSMAN Circuits, matrices, and linear vector spaces KELSO Radio ray propagation in the ionosphere MERRIAM Optimization theory and the design of feedback control systems MUUM Biological control systems analysis NEWCOMB Linear multiport synthesis PAPOULIS The fourier integral and its applications R. N. BRACEWELL) STEINBERG AND LEQUEUX (TRANSLATOR Radio astronomy WEEKS Antenna engineering PREFACE The theory of automatic control has been advanced in important ways during recent years, particularly with respect to stability and optimal control. These are significant contributions which appeal to many workers, including the writers, because they answer important questions and are both theoretically elegant and practically useful. These theories do not, however, lay to rest all questions of importance to the control engineer. The designer of the attitude control system for a space vehicle booster which, for simplicity, utilizes a rate-switched engine gimbal drive, must know the characteristics of the limit cycle oscillation that the system will sustain and must have some idea of how the system will respond to attitude commands while continuing to limit-cycle. The designer of a chemical process control system must be able to predict the transient oscillations the process may experience during start-up due to the limited magnitudes of important variables in the system. The designer of a radar antenna pointing system with limited torque capability must be able to predict the rms pointing error due to random wind disturbances on the antenna, and must understand how these random disturbances will influence the behavior of the system in its response to command inputs. But more important than just being able to evaluate how a given system will behave in a postulated situation is the fact that these control engineers must design their systems to meet specifications on important characteristics. Thus a complicated exact analytical tool, if one existed, would be of less value to the designer than an approximate tool which is simple enough in application to give insight into the trends in system behavior as a function of system parameter values or possible compensations, hence providing the basis for system design. As an analytical tool to answer questions such as these in a way …

Frequency response analysis of two-dimensional nonlinear symmetrical and non-symmetrical control systems,

Abstract: This paper describes an analytical-graphical procedure which permits the closed loop frequency response of two-dimensional, non-linear, control systems to be evaluated. Amplitude and phase response, jump resonance and frequency entrainment are the characteristics which are predicted by this procedure. It is applicable to both symmetrical and non-symmetrical systems and restrictions do not have to be placed on the amplitudes and phase angles of the sinusoidal input signals. Describing functions are used to represent the responses of the non-linear elements.

On the suppression of limit-cycle oscillations

Abstract: A procedure is presented for the suppression of limit-cycle oscillations in unity-feedback control systems which have an on-off type nonlinearity in cascade with a linear transfer function. The procedure is based on the introduction of a minor loop into the system. This produces a high-frequency periodic signal at the input of the nonlinearity, and thereby limit-cycle oscillations are suppressed.

Error bounds for the describing function method

Abstract: An assessment of a method due to Garber and Rozenvasser for constructing bounds on describing function method estimates of amplitude and frequency is reported for the autonomous case. A fundamental problem in applying the method is described. Attempts to improve the bounds and a general critique of the method are outlined.

Response of certain nonlinearities to modulated inputs

Abstract: A method of evaluating the response of zero-memory frequency-independent nonlinearities to a modulated input is presented by representing the response by a Fourier series of the input variable. The special case of a limiter subject to a sinusoidally amplitude-modulated carrier-suppressed input is treated in some detail, and an envelope describing function evaluated. The application to the frequency-domain analysis of a.c. nonlinear carrier-control systems is mentioned.

The frequency response and jump-resonance criteria of non-linear control systems

Abstract: In this paper a simple graphical method of obtaining the frequency response of nonlinear systems along with a criterion for jump resonance is presented when the frequency of the sinusoidal input is varied. The method is applicable whether the system considered contains a non-linearity with a real or complex describing function. As an example a system with saturation non-linearity is considered.

Prediction of jump resonance in systems containing certain multidimensional nonlinearities

Abstract: An expression is derived for the incremental describing function of a nonlinearity whose first-harmonic output has a phase shift with respect to the input. Its application in predicting jump resonance in feedback systems containing certain multidimensional nonlinearities is demonstrated by three typical examples.

Multimodal and transitional behaviour in second-order nonlinear systems

Abstract: Second-order systems with amplitude-dependent nonlinearities can exhibit multirnodal behaviour. A method of finding the range of parameters for which this behaviour is observed is considered, and the method is then extended to predict the type of transients which occur in the system from a given set of initial conditions. The method is based on the describing function of the nonlinearity. The effect of the shape of the nonlinearity on the number of possible fundamental modes of response is discussed, and attention is given to the possibility of exciting subharmonic modes of response, the purpose being to find the range of parameters for which the analysis of the fundamental modes of response is valid.

A describing function analysis in closed loop systems with pulse frequency modulators

Abstract: Describing functions for stability analysis of integral pulse frequency modulated unity feedback closed loop system

Describing-Function Analysis of Thermally Self-Excited Mechanical Oscillators

Abstract: This paper presents an example of the broad applicability of techniques developed initially for use in a specialized field. Describing-function techniques, which are useful in the analysis of nonlinear circuits, are applied to the analysis of thermally selfexcited mechanical oscillators. The amplitude and frequency behavior predicted by this method of analysis are in qualitative agreement with the observed behavior of typical oscillators.

A Comparison between the Fourier and Ritz Describing Functions for the Damped Driven Duffing Equation

Abstract: Fourier and Ritz describing functions are obtained for the damped, driven Duffing equation. These results are compared to the pseudo-describing function, which is defined as the ratio of the first harmonic output amplitude obtained with a real filter to the input amplitude. The results indicate that the Ritz describing function is a better approximation to the pseudo-describing function. Since a number of important nonlinear systems can be represented or approximated by the Duffing equation, it seems that the Ritz describing function has significance as another tool in nonlinear system analysis.