Predictive LPV control of a liquid–gas separation process

Abstract

The problem of controlling a liquid–gas separation process is approached by using LPV control techniques. An LPV model is derived from a nonlinear model of the process using differential inclusion techniques. Once an LPV model is available, an LPV controller can be synthesized. The authors present a predictive LPV controller based on the GPC controller [Clarke D, Mohtadi C, Tuffs P. Generalized predictive control – Part I. Automatica 1987;23(2):137–48; Clarke D, Mohtadi C, Tuffs P. Generalized predictive control – Part II. Extensions and interpretations. Automatica 1987;23(2):149–60]. The resulting controller is denoted as GPC–LPV. This one shows the same structure as a general LPV controller [El Gahoui L, Scorletti G. Control of rational systems using linear-fractional representations and linear matrix inequalities. Automatica 1996;32(9):1273–84; Scorletti G, El Ghaoui L. Improved LMI conditions for gain scheduling and related control problems. International Journal of Robust Nonlinear Control 1998;8:845–77; Apkarian P, Tuan HD. Parametrized LMIs in control theory. In: Proceedings of the 37th IEEE conference on decision and control; 1998. p. 152–7; Scherer CW. LPV control and full block multipliers. Automatica 2001;37:361–75], which presents a linear fractional dependence on the process signal measurements. Therefore, this controller has the ability of modifying its dynamics depending on measurements leading to a possibly nonlinear controller. That controller is designed in two steps. First, for a given steady state point is obtained a linear GPC using a linear local model of the nonlinear system around that operating point. And second, using bilinear and linear matrix inequalities (BMIs/LMIs) the remaining matrices of GPC–LPV are selected in order to achieve some closed loop properties: stability in some operation zone, norm bounding of some input/output channels, maximum settling time, maximum overshoot, etc., given some LPV model for the nonlinear system. As an application, a GPC–LPV is designed for the derived LPV model of the liquid–gas separation process. This methodology can be applied to any nonlinear system which can be embedded in an LPV system using differential inclusion techniques.