Quantificação de não linearidades em malhas de controle pelo método da função descritiva

Abstract

This work presents a new method to quantify the deadband and friction in control valves using the describing function method. This method was originally proposed for predicting the existence of limit cycles in control loops, and also to estimate the amplitude and frequency thereof. In this work the method of describing function is applied to quantify the dead band and the stiction in control valves. The starting point for the application of the methodology developed in this work, is a control loop with the control signal oscillating due to the presence of the dead band, or stiction. The algorithm uses the measures of the amplitude and the frequency of the control signal and the transfer function of the linear part of the loop, i.e the product of transfer functions of the controller and the process. The method is extended to the case of processes with uncertainty, using tools of the robust control theory, such as interval plants and the Kharitonov’s theorem. In the case of first-order processes with or without time delay, the linear part can be approximated by a transfer function with parameters that can be easily identified, and in this case, the quantification algorithm takes a simplified form with simple and explicit formulas for the parameters to be estimated. This results in a non-invasive procedure, computationally light and fast, unlike other methods of quantification, such as grid-based search and optimization, which are more complex and consume more computational resources. Finally, the applicability and effectiveness of the estimation algorithm is demonstrated through simulations, a pilot plant with process with uncertainties and three real cases from industry using only the routine signals from the control loops.