Showing papers on "Describing function published in 1983"
22 Jun 1983
TL;DR: In this paper, the authors provide an overview of one school of thought in this area, typified by the following key ideas: 1. Quasilinear models of the nonlinear system that account for the operating range of system variables must be more realistic than conventional linear models. 2. The designer should be led to a nonlinear controller design if and only if it is really required.
Abstract: Recent research in the area of describing function approaches (both random-input and sinusoidal-input) has laid the foundation for a systematic approach to designing controllers for nonlinear plants. This paper provides an overview of one school of thought in this area, typified by the following key ideas: 1. Quasilinear models of the nonlinear system that account for the operating range of system variables must be more realistic than conventional linear models. 2. A staged design approach that applies more power to "difficult" nonlinear plants than to "easy" ones is more sensible than a single design method. 3. The designer should be led to a nonlinear controller design if and only if it is really required. These points will be developed, illustrated and justified in this presentation.
53 citations
TL;DR: A unifying approach based on methods of linear and nonlinear systems engineering theory to conveniently analyze the metal electrode polarization is presented and is equally appropriate to the study of a wide class of interfacial and dielectric polarization phenomena characterized by a special dispersion behavior.
Abstract: A unifying approach based on methods of linear and nonlinear systems engineering theory to conveniently analyze the metal electrode polarization is presented. The polarization phenomenon is modeled in the linear and nonlinear range. The linear model is based on an exentension of Bode's method consisting of a number of time constant distributions of the Davidson?Cole type. In the nonlinear range, the describing function method is used to analyze the interface in terms of a modified saturation element in cascade with a linear part. The linear part of the nonlinear model has the same form as the linear model with shorter "apparent" average time constants than the corresponding linear representation. The applicability of the method is illustrated using the platinum electrode data. However, the methodology is equally appropriate to the study of a wide class of interfacial and dielectric polarization phenomena characterized by a special dispersion behavior.
50 citations
TL;DR: In this paper, the authors established computable conditions for the stability and instability of limit cycles in nonlinear feedback systems, which in part justify the popular quasistatic stability analysis (Loeb's criterion).
Abstract: In this paper we establish computable conditions for the stability and instability of limit cycles in nonlinear feedback systems. In the proof of the present results, we make use of several novel transformations, of averaging, and of a result on integral manifolds and we assume that we can establish the existence of limit cycles by means of the describing function method. Our results, which in part justify the popular quasistatic stability analysis of limit cycles (Loeb's criterion), are significantly different from existing results dealing with the stability analysis of limit cycles. We demonstrate the applicability of our results by means of specific examples.
25 citations
TL;DR: In this paper, sufficient conditions for the existence of oscillations are obtained for an autonomous single-loop feedback system when the nonlinear elements belong to a class of polynomials.
Abstract: Sufficient conditions for the existence of oscillations are obtained in the case of an autonomous single-loop feedback system when the nonlinear elements belong to a class of polynomials. Both a graphical procedure and an algebraic technique are presented for use with describing function analysis, and a graphical procedure is given for use with multiple input describing functions. Graphing is done in a parameter space of the solution, rather than in the complex plane.
12 citations
01 Jan 1983
TL;DR: The describing function method can be considered as an extension to nonlinear systems of the usual Nyquist stability criterion as discussed by the authors, and the first workers to apply the approach specifically to control systems were Tustin (1947) and Kochenburger (1950).
Abstract: The describing function method can be considered as an extension to nonlinear systems of the usual Nyquist stability criterion. The origins of the method can be traced back to nonlinear mechanics (Krylov and Bogoliuboff, 1932) but the first workers to apply the approach specifically to control systems were Tustin (1947) and Kochenburger (1950).
7 citations
TL;DR: Novel concepts related to the characteristic loci are defined and employed for the derivation of new graphical tests in a method which is based on a set of non-sinusoidal functions.
7 citations
TL;DR: The design method is based on recent breakthroughs in describing function theory that uses a modern algebraic problem formulation to remove all previous nonlinear system restrictions and arrive at quasilinear models of the plant that will serve as a realistic basis for control system design.
4 citations
TL;DR: An exact analysis of a mutually coupled relay oscillator based on a method orignated by Tsypkin is presented, and limit-cycle frequencies and phases can be determined exactly using this method, unlike other approximate methods based on describing functions and harmonic balance techniques.
2 citations
22 Jun 1983
TL;DR: An approach for determining the characteristics of limit cycles in higher order systems with multiple nonlinearities is described, and a search procedure employing eigenvalue derivatives finds limit cycle conditions, when they exist.
Abstract: An approach for determining the characteristics of limit cycles in higher order systems with multiple nonlinearities is described. This method utilizes sinusoidal input describing functions to convert the nonlinear problem to an eigenvalue problem. A search procedure employing eigenvalue derivatives finds limit cycle conditions, when they exist. This technique is efficient, reasonably reliable, and able to treat problems with strong nonlinearities such as Coulomb friction or relays. Two applications are presented, a mechanical servo positioner system and a railway bogie dynamics problem. Comparison of results with simulation is made.
2 citations
Dissertation•
01 Jan 1983
2 citations
02 May 1983
TL;DR: In this article, a more accurate representation of the aerodynamic forces is presented, and compared with those of brute force time marching solutions, and it is concluded that describing function analyses provide useful results for small amplitude motion, e.g., oscillatory angles of attack of.25O +.so or less.
Abstract: Mach number of uniform airflow Previous work on describing function analysis is extended to include a more accurate representation of the aerodynamic forces. Results from such analysis are compared with those of brute force time marching solutions. It is concluded that describing function analyses provide useful results for small amplitude motion, e.g., oscillatory angles of attack of .25O + .so or less. Numerical instabilities encountered using the time marching method at larger oscillatory angles of attack preclude a definitive comparison in that range. However it appears that the describing function method becomes less accurate for larger amplitude motion. frequency ratio; see equation (2c)
01 Dec 1983
TL;DR: In this article, a modification of Tsypkin's method is demonstrated in the analysis of limit cycle behavior of a certain class of systems for which the Sinusoidal Describing Function method of analysis is not valid.
Abstract: The application of a modification of Tsypkin's method is demonstrated in the analysis of limit cycle behavior of a certain class of systems for which the Sinusoidal Describing Function method of analysis is not valid. A set of modified periodicity conditions is shown to be necessary, and is derived for the class of systems of interest.
01 Jan 1983
TL;DR: In this article, the authors describe the method used to obtain visual-cortical describing functions, results for different subjects under different cognitive processing demands, and discusses of what these results indicate.
Abstract: Publisher Summary This chapter describes the method used to obtain visual-cortical describing functions, results for different subjects under different cognitive processing demands, and discusses of what these results indicate. The describing function is a complex measure of the input–output relationship of a system. This measure is viewed in terms of amplitude ratio and phase angle. The Nicolet Fast Fourier Transform (FFT) analyzer provides these measurements. The measurements are valid only where input sinusoids are provided. Only those values are used where the signal-to-noise ratio is greater than 6 dB. The major driver of investigations of steady state evoked response (SSER) at AFAMRL is the question of whether it is possible to alternate responses to evoking stimuli with systematic variations in cognitive demand. Some changes were noted between workload conditions of decision making versus a no demand condition of simply looking at flickering lights.