Compensation Of Valve Deadzone Using Mixed Integer Predictive Control

Stiction is a nonlinear friction phenomenon that causes poor performance of control loops in the process industries. In this work, we develop a mixed-integer MPC (Model Predictive Control) formulation including valve dynamics for a sticky valve in order to improve control loop performance. The introduction of the valve nonlinearity into the model prevents the MPC from requesting physically unrealistic control actions due to valve stiction. Simulation studies using a two-tank systems show that, if the deadband value is known apriori, the Mixed-Integer Quadratic Programming (MIQP) can effectively improve the closed-loop performance in the presence of valve stiction. INTRODUCTION Model Predictive Control has become one of the most widespread modern control strategies which have been successfully applied in many industrial applications. The idea of MPC is to determine an optimal control at the current time instant by solving an optimal control problem on a prediction horizon. The main reason for the wide-scale adoption of MPC is its ability to handle constraints on inputs and states that arise in most applications. MPC also naturally handles the multidimensional systems. Control valves are necessary elements in many chemical process control systems and are equipped for manipulating mass flows, energy flows or pressure. In general, they contain static and dynamic nonlinearities including saturation, backlash, stiction, deadband and hysteresis. If these nonlinearities are present, the valve is not capable of following the command signals provided by the controller thus leading to control performance degradation. A limit cycle is typically produced around the steady-state operating points if these nonlinearities are not included explicitly in the controller design. To compensate for valve malfunction several methods based on MPC has been developed. The framework developed in (Rodrıguez and Heath 2012) used the inverse of the nonlinearity in series with the original nonlinearity to overcome the problem. General compensation formulation that includes dynamics of sticky valve and additional constraints on inputs rate of change have been introduced in (Durand and Christofides 2016). A significant contribution in the area of valve nonlinearities compensation has been done in the work by (Zabiri and Samyudia 2006) which used a hybrid formulation of the input constraint within the MPC design to express the actuator backlash. The controller was used only in the only in the proximity of steady state operating points. Strategy that uses twomove stiction compensation have been revised in (Bacci di Capaci et al 2016) and successfully applied to the pilot plant. In this paper, nonlinear model of the process with defined valve dead-zone was developed and used for optimization of the control signal via MPC strategy. The valve nonlinearity is expressed in terms of IF THEN conditions resulting in the hybrid model. Hybrid systems represent a unified framework for modelling such processes that combine continuous and discrete dynamic with logical rules and appear in various applications like robotic systems and automotives. A special class of hybrid systems called Mixed Logical Dynamical (MLD) systems has been introduced in (Bemporad and Morari 1999). Hybrid systems can effectively model a variety of systems: hybrid automata, nonlinear systems with the nonlinearity represented by the piece-wise affine functions, linear systems with constraints, etc. MPC is a general approach for control of such systems. However, the optimization problem is no longer quadratic programming (QP) problem but a Mixed-Integer Quadratic Programming problem. The inclusion of integer variables turns the easily solved QP problem, into an NP-hard problem (Borrelli et al 2006). VALVE NONLINEARITY DESCRIPTION A common process nonlinearity affecting the performance of control circuits with control valves (Fig. 1) is known as ‘stiction’ which exhibits a range of nonlinear behaviour including hysteresis, backslash and deadzones, both dynamic and static. In this paper, the model that includes deadband in every valve move was chosen. In Figure 1 the signal u is the process input, that is, the valve output, y is the process output, uMPC is the MPC output, w and v are white Gaussian noises. Proceedings 31st European Conference on Modelling and Simulation ©ECMS Zita Zoltay Paprika, Péter Horák, Kata Váradi, Péter Tamás Zwierczyk, Ágnes Vidovics-Dancs, János Péter Rádics (Editors) ISBN: 978-0-9932440-4-9/ ISBN: 978-0-9932440-5-6 (CD) Figure 1: The Closed-loop System with the (sticky) Control Valve followed by the Process. The sticky valve has a nonlinear dynamics expressed by the following relations: