Describing function

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

Non-linear aspects and selection of microprocessor controllers†

Abstract: Stability aspects of non-linearities introduced by using a microprocessor digital controller in a feedback loop are investigated, using the describing function analysis. In particular, 8- and 16-bit types of equipment are compared. The conclusion reached is that from the practical standpoint, there is no difference between the two types as far as stability is concerned. A system selection procedure, proposed in a previous paper, is implemented in the selection of microprocessor equipment to satisfy specified design criteria. The procedure is composed of stages involving curve-fitting and minimization. A particular example, illustrating the implementation of the procedure, along with final recommendations, is presented.

Limit cycle prediction of a neurocontrol vehicle system based on gain-phase margin analysis

Abstract: Based on some useful frequency domain methods, this paper proposes a systematic procedure to address the limit cycle prediction of a neural vehicle control system with adjustable parameters. A simple neurocontroller can be linearized by using describing function method firstly. According to the classical method of parameter plane, the stability of linearized system with adjustable parameters is then considered. In addition, gain margin and phase margin for limit cycle generation are also analyzed by adding a gain-phase margin tester into open loop system. Computer simulations show the efficiency of this approach.

Analysis of a System Controlled by a Relay with Dead Zone, Hysteresis and Integral Feedback

Abstract: The applicability of the describing function method of analysis to a plant/controller system containing a nonlinear relay with feedback is investigated. A second order plant model is employed, with system parameters based on a ship steering system application. Analytical predictions of limit-cycle behavior are made and are found to be in disagreement with time-domain results. It is hypothesized that the theory fails due to insufficient filtering of harmonics in the relay feedback loop. The system is theoretically modified to include additional filtering in the feedback loop to test this hypothesis, and good correlation between theory and time-domain results is observed. Implications for plant/controller design and the ship steering problem are discussed.

On the identification of a nonlinear function in a feedback loop

Abstract: Many models of systems, important in practice have the form of an interconnection of a known linear model and an unknown nonlinear function. One example of such a system is a model of thermoacoustic instability affecting gas turbine engines and rockets (so-called thermoacoustic feedback loop). In this paper, we propose a computationally attractive algorithm for identifying static nonlinearity in a thermoacoustic feedback loop which is either in a limit cycle or is being, driven by Gaussian noise. The algorithm is based upon functional analytic treatment of the describing function method and lends itself nicely to a class of limit cycling or noise driven feedback systems where the nonlinearity is of a special type. We present examples as well as a simulations with the thermoacoustic feedback loop as an application of the identification algorithm.

Biologically-Inspired Impedance Control With Hysteretic Damping

Abstract: Recent experiments have shown that human joints can maintain a constant damping ratio across a wide range of external loads. This behavior can be explained by the use of a “complex stiffness” frequency-domain model approximating the impedance of the human joint. However, for a robot to replicate this naturally beneficial human behavior would require a time-domain model of this nonlinear joint impedance. This letter demonstrates that there exists a nonlinear time-domain model (originally from the structural mechanics community) that has a frequency-domain “describing function” that matches the complex stiffness model observed in humans. We provide an extension of this nonlinear time-domain model that removes the need to implement hard-switching control input. In addition, we demonstrate that this proportional-and-hysteretic-damping controller has inertia-invariant overshoot and therefore offers an advantage over the more common proportional-derivative control approach. Implementing the proposed proportional-and-hysteretic-damping control in a single-joint test-robot, we demonstrate for the first time that the desired frequency domain behavior can be reproduced in practice.