Showing papers on "Describing function published in 1979"

Nonlinear Noise Theory for Synchronized Oscillators

Abstract: A nonlinear theory of noise in synchronized oscillators is outlined, thus extending Kurokawa's work from small to arbitrary injection levels. The description is of phenomenological nature: it uses the describing function method of control theory for calculating the carrier waves, and the circuit theory of periodically driven nonlinear systems for an analysis of the noise sidebands. Simple expressions are derived for the various output noise and noise conversion factors in the case when the nonlinear characteristic of the active device can be described by a third-order (van-der-Pol) polynomial.

Model-follower longitudinal control for automated guideway transit vehicles

Abstract: An approach for the design of longitudinal control systems for automated transit vehicles using the vehicle-follower control concept is presented. It is shown that the spacing policy selected for system operations generates a dynamic model for ideal vehicle response during station keeping. The longitudinal control system should force the actual vehicle response to be as close to this model response as possible. Two model-following controller designs are discussed. In one design the command from the controller is acceleration, and in the other design the command from the controller is jerk. The acceleration- and jerk-limited dynamic response of both controllers is examined by the use of describing functions and by computer simulations.

Using characteristic loci in the Hopf bifurcation

Abstract: The Hopf bifurcation theorem is used by physicists, biologists and others interested in oscillations in systems described by differential equations. This paper presents a version of the theorem applicable directly to feedback systems, using the method of characteristic loci in an interpretation which looks rather like a multiple-loop version of the graphical describing function method. Frequency, amplitude and stability of oscillations about an equilibrium state are predicted by an iterative process which starts with a 2nd-order harmonic balance and successively increases the number of harmonics taken into account. The results from each stage of the process are used to define a curve in the complex plane from which the results of the next stage can be read off; consequently, the user has a visual indication of the accuracy and rate of convergence. The main theoretical limitation is that the nonlinear elements in the system must be continuously differentiable at least once more than the order of the highest harmonic used, whereas the main practical limitation is that the formula for the curve becomes extremely complicated if more than about six harmonics are considered.

Attitude Stability of a Pseudorate Jet-Controlled Flexible Spacecraft

Abstract: The small-angle stability of a single-axis spacecraft attitude control system incorporating a nonlinear pseudorate controller, jet actuator, flexible vehicle dynamics, and a loop time delay is analyzed. The dynamics include a low-frequency rigid vehicle mode and a highly underdamped flexible mode that has its modal frequency outside the rigid vehicle control system bandwidth. The single input sinusoidal describing function for the pseudorate controller is derived and used to determine the effect of the controller on each mode individually. A stable limit cycle for the rigid vehicle mode response is predicted. The flexible mode response is predicted to be stable, unstable, or to exhibit a stable limit cycle, depending on the loop time delay and the flexible mode frequency and damping. Simulation results verify the integrity and interpretation of analytically predicted stability conditions.

Analysis and Design of an Adaptive Multi-Loop Controlled Two Winding Buck/Boost Regulator

Abstract: Small signal low frequency linear average model is derived for a multi-loop controlled two-winding buck/boost converter employing average techniques and the describing function method. The model reveals that a well-designed multi-loop control can provide a second-order zero adaptive to output filter parameter changes due to component tolerances, temperature changes, aging, and the effect of duty cycle modulation. It also can provide stabilization effect by shifting the positive zero to the left-half S-plane. Design quidelines are formulated to optimize regulator-loop dependent characteristics.

Susceptibility of 3-phase power systems to ferro-nonlinear oscillations

Abstract: A numerical method is described for predicting the possibility of jump resonance or subharmonic oscillations being sustained by a given 3-phase circuit, based on the describing function and dual-input describing function concepts of control theory The method can be applied to predict asymmetrical jump modes which have no equivalent in single-phase circuits Results predicted by this method are compared with results obtained from laboratory experiments

Third order oscillators with independently adjustable frequency, amplitude and transient response

Abstract: A class of third order harmonic oscillators with frequency, amplitude and transient response controlled by three separate sets of parameters is derived. A simplified group of oscillators is described in which there are only three parameters, one which controls the frequency, another the amplitude, and the third the transient response. Each oscillator contains a single nonlinearity, which can be either of the saturation or the dead space type. The mathematical analysis is based on linearizing the nonlinearity by means of the sinusoidal describing function. The transient response is studied by considering small amplitude perturbations away from the oscillator's limit cycle. The results of analogue computer simulations are presented with emphasis on the relationship between transient response and the gain controlling it.

Nonlinear modelling of f.e.t.-input operational amplifiers

Abstract: A square-law model for f.e.t.-input operational amplifiers is applied, by means of describing functions, to the evaluation of slew-induced distortion in a simple active filter. The computed frequency responses are validated by measurements at large signal levels.

Noise in Mutually Coupled Oscillators

Abstract: A general noise theory for microwave oscillators, which is based upon the describing function method, is developed and applied to the cases of mutually coupled and multiple-device oscillators. Explicit expressions are derived for the output power, the FM-and the AM-noise. Both theoretical and experimental results are given concerning the dependence of the output noise on the number of active devices and on the parameters of the coupling network.

An adaptive-control switching buck regulator-implementation, analysis and design

Abstract: Describing function techniques and average methods have been employed to characterize a multiloop switching buck regulator by three functional blocks: power stage, analog signal processor and pulse modulator. The model is employed to explore possible forms of pole-zero cancellation and the adaptive nature of the control to filter parameter changes. Analysis-based design guidelines are provided including a suggested additional RC compensation loop to optimize regulator performances such as stability, audiosusceptibility, output impedance and load transient response.

A Volterra series-derived describing function for a motor/variable gearbox/load combination

Abstract: A solution to the speed variations of a load driven via a variable ratio gearbox from a non constant speed drive is obtained as a Volterra series. A particular solution is found when the gear ratio is varied sinusoidally. This leads to a simple transfer function, with coefficients varying with input amplitude, which is shown to adequately model the overall dynamics.

An application of adaptive control techniques in metrology

Abstract: This paper examines the dynamic performance of an automated optical gauging instrument. A mathematical model of the system is developed which demonstrates the intrinsically non-linear characteristics which provide coupling between two nominally independent control loops. Approximate stability bounds for the closed-loop system are established using the describing function matrix technique. The inverse Nyquist diagram is used to design appropriate compensation networks, taking into account design objectives including the avoidance of various limit cycles and a rapid transient response. The final design is implemented on the instrument and its behaviour compared with the simulated system. It is shown that the response time is reduced to approximately 11% of that of the original system in agreement with design predictions.

A Stability Limit of PWM Control System Using Harmonic Describing Function

Abstract: The limiting gain for the stability of a closed-loop pulse-width modulated control system is obtained by the application of multiple-input describing function technique, particularly when a significant harmonic is present at the input in addition to the fundamental frequency signal. Result shows that the allowable gain thus obtained can be much smaller than that obtained by the application of fundamental frequency describing function.

A study of double mode limit cycles in a resonator controlled oscillator

Abstract: A system is described which excites continuous oscillations in a resonator at two frequencies simultaneously. The resonator, typically in the form of a disc, can have modes which are close together in frequency and a double mode oscillator facilitates measurement of the difference in frequency. Such a measurement can be used to accurately determine Poisson ratio for the material of the disc. The resonator is excited by means of a nonlinear feedback loop which is designed to give stable double mode oscillations with frequencies close to the natural modes of the resonator. Several results from describing function theory are used to predict the behaviour of the system and the analysis is compared with the results of an analogue computer simulation.

Stability Analysis of Chemical Fine-Control Reactor in State Space

Abstract: Stability is studied of a nuclear reactor system which is controlled by the concentration change of poison solution circulating through the pipe installed in the reactor. Particular attention is paid to: (1) nonlinearities due to the reactivity feedbacks, (2) rigorous treatment of nonlinear control elements without employing approximate methods such as the describing function and (3) nonlinear characteristics of the concentration change of poison solution. The stability of this complex reactor system is analyzed in the state space by applying the technique based on Lyapunov's method. A special technique is employed to cope with the difficulty such that the stability of a system with time lag depends on the present state as well as on the past history of the state which is usually indeterminable. Analysis is carried out for both simplified and realistic models. For the former model, one stability region is compared with another by varying the lag time, characteristics of nonlinear elements and the power at...