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

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 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.