Describing function

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

Novel controller design for plants with relay nonlinearity to reduce amplitude of sustained oscillations: Illustration with a fractional controller.

Abstract: This paper proposes a novel constrained optimization problem to design a controller for plants containing relay nonlinearity to reduce the amplitude of sustained oscillations. The controller is additionally constrained to satisfy desirable loop specifications. The proposed formulation is validated by designing a fractional PI controller for a plant with relay.

Bifurcations in Systems with a Rate Limiter

Abstract: Limit cycles analysis of feedback systems with rate limiters in the actuator can be implemented by a classical method in the frequency domain, the harmonic balance method. In this paper, the rate limiter describing function is obtained and applied to the search for limit cycles in such control systems. Three examples with three different bifurcations (saddle-node bifurcation of limit cycles, subcritical Hopf bifurcation at infinity and supercritical Hopf-like bifurcation) are included. The method is approximate but its main advantage is that intuition is gained into a difficult problem.

Simultaneous Closed-loop Identification of Nonlinear and Linear part of a Hammerstein-type Nonlinear Model

Abstract: A procedure for the closed-loop identification of some class of non-linear plants of Hammerstein type, based on a generalization of the well-known Ziegler-Nichols' (ZN) experiment, is proposed It may be used for the simultaneous estimation of the plant dynamic and the describing function of the plant nonlinearity As in the ZN method, no extra equipment is needed for performing the experiment

Sampled describing function analysis of second order sliding modes

Abstract: The describing function method is applied to characterize the steady state behavior of the linear sampled data systems stabilized by a second-order sliding mode algorithm. A describing function of the nonlinearity including a sample and hold element is derived. The proposed method allows to predict the amplitude, frequency and phase of occurring limit cycles caused by the discrete time implementation of discontinuous control algorithms. It is shown that the derived describing function is closely related to its classical continuous time counterpart. The proposed approach is demonstrated using a numerical simulation example as well as a real world experiment.

Dual-input describing function of ‘switching-type’ double-valued non-linearities†

Abstract: The ‘switching-type’ double-valued non-linearities are defined and general relations concerning their modified characteristics and their dual-input describing functions (DIDF) for two sinusoidal inputs with unrelated frequencies are derived. An illustrative example is also presented.