The hunt (self-oscillations) of a physical system may often be removed by the introduction of an appropriate stabilizing signal which changes the open loop gain of a closed loop system in a non-linear manner. The theory of stabilization developed in this paper explains experimental results reported by R. Oldenburger in 1957. With the aid of Fourier series the designer can determine the periodic signal to be inserted at one point in a loop to yield a desired stabilizing input to a nonlinear element in the loop. This is illustrated by sinusoidal and triangular inputs to a nonlinear element. An example where a limiter is the only nonlinearity, is employed to illustrate the theory. The input-output characteristics of non-linear elements are in practice always modified by the presence of extra signals such as "noise." Further, nonlinearities are always present in physical systems. The effect of extra signals on nonlinearities and system performance is thus of concern in the general study of physical systems, regardless of whether or not the problem of stability is involved. The results of this paper for the problem of stability extend readily to the problem of system performance for arbitrary disturbances. This paper is to be published in the Proceedings of the First IFAC Moscow Congress by Butterworth Scientific Publications, in 1960.

Signal stabilization of self-oscillating systems

A new general DIDF (dual input describing function) has been analytically derived for single-valued nonlinearities subjected to two arbitrary noncommensurate sine waves. The development corroborates a previous approximate development for two sine waves widely separated in frequency. The new DIDF is applied to the problem of the stability of nonlinear systems subjected to sinusoidal forcing. It is shown that the conventional DF (describing function) cannot be used for nonautonomous systems without additional safeguards. After it has been shown by the DIDF that no auto-oscillations exist for given input conditions it is proper to employ the conventional DF in any of the methods suggested in the literature to obtain the closed-loop frequency response under those conditions.

A New Dual-Input Describing Function and an Application to the Stability of Forced Nonlinear Systems

A system for controlling the air-fuel ratio for an internal combustion engine having a detector for detecting the concentration of a constituent of exhaust gases passing through the exhaust passage, air-fuel mixture supply device for supplying an air fuel mixture to the induction passage, electromagnetic valves for correcting the air-fuel ratio of the air-fuel mixture supplied by the air-fuel mixture supply device, a comparator for comparing the output signal of the detector with respect to a predetermined value, an integrating circuit having a proportional circuit for integrating the output of the comparator, a driving circuit for driving the electromagnetic valves in dependency upon the output signal of the integrating circuit. The system has a throttle valve switch actuated by the operation of the throttle valve in an idling condition, steady state and full load condition of the engine and a vacuum switch actuated by vacuum pressure in the induction passage of the engine when the throttle valve is opened to a predetermined degree. A switching circuit is provided to change the proportional constant and integrating constant of the integrating circuit and a decision circuit is provided to actuate the switching circuit in dependency on signals from the throttle valve switch and the vacuum switch, whereby the proportional constant and integrating constant may be changed according to the engine operation.

Air-fuel ratio control system

In this article we are concerned with the implementation of a dither signal for a closed-loop DC motor system. Experimental studies show that the system contains two nonlinearities that are saturated with dead zone and backlash. Parameter estimation techniques are used to identify the unknown system parameters with special care due to the existence of system nonlinearities. An analytical method is then presented to deal with the closedloop DC motor system with two nonlinearities in the loop. Self-excited oscillations are found to exist in the system. A good correlation between the theoretical and experimental results indicates the success of the system identification and modelling process. Also the ability of dither to quench the limit cycle is demonstrated from these results.

Experimental And Analytical Studies Of The Sinusoidal Dither Signal In A DC Motor System

Experimental and analytical studies of the sinusoidal dither signal in a DC motor system

FEEDBACK loops, in states of self-oscillation, can often be stabilized by the introduction of an appropriate signal. In this paper a theory is developed to explain this phenomenon. The theory is applied to a system which is linear except for a limiter. Experimental results for the system showing the removal of the hunt by a stabilizing signal are given in a previous paper.1

C. C. Liu

Papers

Signal stabilization of a control system