Showing papers on "Describing function published in 1969"

A Technique for Control of Traffic at Critical Intersections

Abstract: An algorithm for control of queue lengths at oversaturated intersections oriented towards delaying spillback across upstream intersections as long as possible is described. It is based on determining the change in queue and the allotment of available green time so as to keep the ratio of the actual queues to the maximum link storage space on both phases equal. The mathematical development of the algorithm is described in terms of a Z transform analysis, and the conditions for stability are derived. The resulting mathematical model is linear with the exception of a saturation type nonlinearity caused by the physical requirement to limit split. A describing function analysis is used to demonstrate loop stability in the presence of the nonlinearity.

Response of delta modulation to Gaussian signals

Abstract: Analytical, experimental, and computer simulation results are given for the error spectrum of a delta modulator when probed by stationary, band limited, gaussian noise. These three complementary methods are used to increase our quantitative understanding of the nonlinear system with memory. The error is conveniently split into two components: one linearly dependent on the input signal and one linearly independent of the input signal. In order to isolate these two types of errors we use two measurement techniques. For purposes of analysis we show that the delta modulator can be replaced by an equivalent linear system with additive noise at its output which is linearly uncorrelated with the input. The equivalent linear system may be approximated by using methods involving statistical linearization or the deterministic describing function. Alternately, the equivalent linear system may be obtained from computer simulation.

Quantizer-induced digital controller limit cycles

Abstract: Limit-cycle oscillations can occur in recursive digital controllers, due to the finite resolution of the computational data word. Controllers are usually formed from first- and second-order structures, arranged in parallel, in cascade, or in a combination of these. A first-order structure cannot sustain a stable limit cycle, but a second-order structure can. A simple criterion, based on the describing function of a quantizer, is developed and presented for predicting the amplitudes and frequencies of quantizer-induced limit-cycle oscillations in second-order digital filter structures.

Dual input discrete describing function

Abstract: The definition and development of a modified discrete describing function, referred to as dual input discrete describing function, is considered. High-frequency signal is injected into the non-linearity to quench the limit cycles in closed-loop autonomous relay-type sampled-data systems. An analytic procedure is described, which aims at deriving the dual input discrete describing function for a relay in the Z domain.

Jump-resonance criteria for systems containing double-valued and frequency-dependent nonlinearities

Abstract: A procedure is developed for evaluating the jump-resonance frequencies for feedback systems containing nonlinearities which have complex and frequency-dependent describing functions. The method permits the determination of the multimodal region on the input amplitude/frequency plane, as well as other information concerning the system behaviour at the jump-resonance point. It is therefore convenient for use in the design of multimodal systems. The procedure is illustrated by means of two examples.

Dual-input describing function of double-valued nonlinearities

Abstract: A general method of obtaining the altered characteristic, and hence the dual-input describing function (d.i.d.f.), of double-valued nonlinearities subjected to two sinusoidal signals whose frequencies are incommensurate has been presented with illustrative examples and experimental verification.

On/off servo compensation by logic circuits

Abstract: The on/off servo is analysed in the frequency domain by the Describing Function Method. Compensation using logic circuits to simulate a positive hysteresis type relay is discussed next. Finally the description of a practical positive hysteresis simulator is presented.

On the determination of limit cycles in relay control systems with additional saturation type non-linear elements†

Abstract: Exact and approximate methods of determination of limit cycles in a relay control system including an actuator with PI transfer function and limited output are given. No restrictions are imposed on the order of the plant transfer function. The stability of the limit cycles may be checked using one of the well-known methods, using the describing function concept. With the help of an example it is indicated that the methods suggested give reliable results in eases where the use of the conventional describing function fails.

The effects of limiting on angle- and amplitude-modulated signal

Abstract: The AM compression, AM-PM and PM-AM conversion of a limiter is determined from its describing function.

Development of human describing function models for nonlinear control elements.

Abstract: : The purpose of the thesis is twofold. First, the usefulness of human pilot describing function models in nonlinear control systems was to be experimentally determined. Secondly, parameter adjustment rules which would extend the usefulness of the describing function models into the nonlinear region of operation were determined. The approach to this problem was to operate a pilot model and human tracker control system simultaneously with the same inputs and compare the performance of the two systems as nonlinear elements were introduced. Gaussian nonlinear describing function theory and existing pilot adjustment rules were used to predict model parameter adjustment changes as the level of saturation of the nonlinear elements were decreased. Where these prediction techniques failed, the necessary adjustment rules were experimentally determined. Saturation of the nonlinear elements were decreased. Where these prediction techniques failed, the necessary adjustment rules were experimentally determined. Saturation limiting and rate limiting were the nonlinearities employed with three controlled element characteristics. (Author)

Extension of pilot describing functions to multiple compensatory tracking tasks.

Abstract: : An investigation of the extension of a continuous attention pilot model describing function to a sampling environment through the use of two tasks was undertaken. Three different transfer functions were used as controlled elements in a compensatory tracking task. The technique of electro-oculography was used to monitor eye movements. Performance of the pilots was compared to the continuous attention pilot model with the effective time delay of the model varied to match the performance of the subject. This yielded an increased time delay factor which could be translated into a regression of the error signal bandwidth. The actual error signal bandwidth was determined and comparisons were made. Other parameters were compared with theoretical developments which indicate that sampling should result in an additional time delay to the basic pilot model. Quite good agreement was obtained, and the theory which predicts an additional time delay factor to be added to the pilot model describing function is substantiated. Additionally, a method for predicting performance is outlined. Workload measurement techniques were investigated, and a proposed measure of workload as mean dwell time divided by mean sample time was verified. (Author)

Real and complex-exponential describing functions for transient analysis of non-linear control systems†

Abstract: A real exponential describing function as an analysis tool for studying the transient response of a class of non-linear feedback systems was developed by Bickart (1966). In this paper describing functions are developed for similar analysis more suitable to higher-order non-linear feedback systems. The two classes of describing functions developed are identified as real exponential or complex exponential. Here, signals in ℒ2 ( − ∞, t] a space of the space of square integrable signals defined on (−∞, t ], are approximated by the sum of n signals in ℒ2 1, m (−∞, t)one-dimensional sub-spaccs of ℒ2 ( − ∞, t] having the mth function from the set of reversed time orthogonalized real or eponential functions as a basis. A system mapping ℒ2 1, m(−∞, t] into itself is associated with a system mapping ℒ2 1, m(−∞, t] into itself; the latter system is characterized by a gain—real or exponential describing function. These multiple one-dimensional system mappings give rise to approximation components of the response whos...

The parametric describing function

Abstract: The determination of the amplitude of the self-excited oscillations of a system with only one non-linearity using the describing function method, is generally only approximate, because the wave is supposed to be of a certain form stateda priori (for instance, sinusoidal).