Describing function

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

Parameter plane analysis of neurocontrol vehicle systems for limit cycle prediction

Abstract: The main purpose of this paper is to predict the limit cycles of neurocontrol system with perturbed parameters by combining the approaches of stability equation, describing function and parameter plane. The neurocontroller is first linearized by using the describing function method. The stability of equivalent linearized system is then analyzed by using stability equations and the parameter plane method. According to this procedure, the amplitude and frequency of limit cycles can be figured out clearly in the parameter plane. Moreover, the limit cycle may be suppressed by adjusting the control parameters carefully. Finally, a vehicle model is illustrated to demonstrate its validity.

Identifying A(s) and β(s) in Single-Loop Feedback Circuits Using the Intermediate Transfer Function Approach

Abstract: It is common practice to model the input–output behavior of a single-loop feedback circuit using the two parameters, A and β. Such an approach was first proposed by Black to explain the advantages and disadvantages of negative feedback. Extensive theories of system behavior (e.g., stability, impedance control) have since been developed by mathematicians and/or control engineers centered around these two parameters. Circuit engineers rely on these insights to optimize the dynamic behavior of their circuits. Unfortunately, no method exists for uniquely identifying A or β in terms of the components of the circuit. Rather, indirect methods, such as the injection method of Middlebrook or the break-the-loop approach proposed by Rosenstark, compute the return ratio RR of the feedback loop and inferred the parameters A and β. While one often assumes that the zeros of (1 + RR) are equal to the zeros of (1 + A × β), i.e., the closed-loop poles are equivalent, this is not true in general. It is the objective of this paper to present an exact method to uniquely identify each feedback parameter, A or β, in terms of the circuit components. Further, this paper will identify the circuit conditions for which the product of A × β leads to the correct closed-loop poles.

A describing function analysis in closed loop systems with pulse frequency modulators

Abstract: Describing functions for stability analysis of integral pulse frequency modulated unity feedback closed loop system