Describing function

About: Describing function is a research topic. Over the lifetime, 1742 publications have been published within this topic receiving 26702 citations.

A software tool for the design and simulation of PID with event based sampling

Abstract: In this work we present a free software tool for the design and simulation of PID controllers with event based sampling. The tool allows to easily obtain the PID that minimizes the disturbance IAE while maintains the control action jumps under a desired bound, for a given robustness. The application calculates the phase and gain margins with respect the existence of limit cycles for SSOD sampling and RQ sampling, taking into account the describing function approximation. Therefore, the application can be used to design a PID that guarantees the absence of oscillations due to limit cycles with certain margins. A time response simulation window allows to simulate the response of the event based controlled system to setpoint and disturbance changes, choosing between SSOD and RQ with hysteresis. Performance data are automatically calculated and shown. The application is useful to analyze the implications of using PI and PID controllers with different event based sampling strategies, especially the existence of limit cycles and the compromise between control action jumps and performance.

The Use of an R.M.S. Describing Function for the Study of Low-order Systems Incorporating Backlash

Abstract: In this paper the stability problem of a low-order non-linear feedback control system is investigated with the help of an r.m.s. describing function. A second-order system incorporating a backlash non-linearity is considered and it is shown that the r.m.s. describing function for the backlash element provides a more reliable locus in predicting the existence of ‘ limit cycle ’ oscillation in the system and in computing the value of the limit cycle parameters. The magnitude of this r.m.s. describing function is found by taking the ratio of the r.m.s. value of the periodic wave at the output of the non-linearity to the r.m.s. value of its assumed sine wave input, while the phase is determined simply from the knowledge of an r.m.s. quantity oe . The analogue computer results and also the results obtained by using the conventional describing function locus are tabulated for the sake of comparison.

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.

Limitations on the use of describing functions

Abstract: The describing-function method of analysis fails to predict the existence of a limit cycle when applied to a relay control system for a nuclear reactor. This is demonstrated by a direct solution of the system differential equations and by experiment on the Universities' Research Reactor.