An off-line model reduction-based technique for on-line linear MPC applications for nonlinear large-scale distributed systems

Linear Model Predictive Control (MPC) has been effectively applied for many process systems. However, linear MPC is often inappropriate for controlling nonlinear large-scale systems. To overcome this, model reduction methodology has been exploited to enable the efficient application of linear MPC for nonlinear distributed-parameter systems. An implementation of the proper orthogonal decomposition method combined with a finite element Galerkin projection is first used to extract accurate non-linear low-order models from the large-scale ones. Then a Trajectory Piecewise-Linear method is developed to construct a piecewise linear representation of the reduced nonlinear model. Linear MPC, based on quadratic programming, can then be efficiently performed on the resulting system. The stabilisation of the oscillatory behaviour of a tubular reactor with recycle is used as an illustrative example to demonstrate our methodology.