Describing function

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

Quantification of Valve Stiction and Dead Band in Control Loops Based on the Harmonic Balance Method

Abstract: The presence of stiction in control valves often causes oscillations in control loops, with negative effects on quality and cost of goods. To address this issue, it is necessary to quantify this stiction to decide about maintenance or to implement compensators that can improve control loop performance until the next plant stop. The describing function (DF) method is a well-known scheme to predict the period and amplitude of limit cycles in control loops, requiring the knowledge of linear and nonlinear parameters of the system model. In the present study, a method has been proposed to estimate these nonlinear parameters using the parameters of linear model and amplitude and period of limit cycle produced by nonlinearity. A procedure is proposed to overcome the case of unknown process model. In addition, generalization of this method to the case of parametric uncertainties in the linear part of the control loop has also been presented. The result is a simple and efficient algorithm that can be easily extended to other nonlinearities. Furthermore, the conditions for existence and uniqueness of solution for dead band and stiction estimations have been obtained. The usefulness of the proposed method has been demonstrated through simulations and its applications to a pilot plant and to real industrial data.

Augmented nonlinear differentiator design and application to nonlinear uncertain systems.

Abstract: In this paper, an augmented nonlinear differentiator (AND) based on sigmoid function is developed to calculate the noise-less time derivative under noisy measurement condition. The essential philosophy of proposed AND in achieving high attenuation of noise effect is established by expanding the signal dynamics with extra state variable representing the integrated noisy measurement, then with the integral of measurement as input, the augmented differentiator is formulated to improve the estimation quality. The prominent advantages of the present differentiation technique are: (i) better noise suppression ability can be achieved without appreciable delay; (ii) the improved methodology can be readily extended to construct augmented high-order differentiator to obtain multiple derivatives. In addition, the convergence property and robustness performance against noises are investigated via singular perturbation theory and describing function method, respectively. Also, comparison with several classical differentiators is given to illustrate the superiority of AND in noise suppression. Finally, the robust control problems of nonlinear uncertain systems, including a numerical example and a mass spring system, are addressed to demonstrate the effectiveness of AND in precisely estimating the disturbance and providing the unavailable differential estimate to implement output feedback based controller.

Reduced fractal model for quantitative analysis of averaged micromotions in mesoscale: Characterization of blow-like signals

Abstract: It has been shown that many micromotions in the mesoscale region are averaged in accordance with their self-similar (geometrical/dynamical) structure. This distinctive feature helps to reduce a wide set of different micromotions describing relaxation/exchange processes to an averaged collective motion, expressed mathematically in a rather general form. This reduction opens new perspectives in description of different blow-like signals (BLS) in many complex systems. The main characteristic of these signals is a finite duration also when the generalized reduced function is used for their quantitative fitting. As an example, we describe quantitatively available signals that are generated by bronchial asthmatic people, songs by queen bees, and car engine valves operating in the idling regime. We develop a special treatment procedure based on the eigen-coordinates (ECs) method that allows to justify the generalized reduced fractal model (RFM) for description of BLS that can propagate in different complex systems. The obtained describing function is based on the self-similar properties of the different considered micromotions. This kind of cooperative model is proposed here for the first time. In spite of the fact that the nature of the dynamic processes that take place in fractal structure on a mesoscale level is not well understood, the parameters of the RFM fitting function can be used for construction of calibration curves, affected by various external/random factors. Then, the calculated set of the fitting parameters of these calibration curves can characterize BLS of different complex systems affected by those factors. Though the method to construct and analyze the calibration curves goes beyond the scope of this paper, this result could benefit future studies that will employ the developed reduced models in diagnosis, prevention, and control of unpredicted and undesired phenomena of some engineering applications that possibly exhibit such BLS.