GPC-LPV: a predictive LPV controller based on BMIs

In this paper the authors present a predictive linear parameter varying (LPV) controller based on the GPC controller [1]–[3], for nonlinear systems. The resulting controller is denoted as GPC-LPV. This one has the same structure as a general LPV controller [4]–[7], which has a lineal 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 local model of the nonlinear system around that operating point. And second, using bilinear matrix inequalities (BMIs) 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. This methodology of design can be applied to nonlinear systems which can be embedded in a LPV system using differential inclusion techniques. Finally, the GPC-LPV is applied to the nonlinear model of a liquid-gas separation process.