Reduction of Nonlinear Models using Balancing of Empirical Gramians and Galerkin Projection

Nonlinear model predictive control has become increasingly popular in the chemical process industry. This is due to several reasons, the most important of them being that highly accurate models can now be simulated with modern dynamic simulators and the increased availability of powerful optimization algorithms. However, computational requirements grow with the complexity of the models. Many rigorous dynamic models require too much computation time to be useful for real-time model based controllers. This presents a need for model reduction techniques. The method introduced here reduces nonlinear systems, while retaining most of the input-output properties of the original system. The reduction itself is based on empirical gramians which capture the nonlinear behavior of the system in a region around an operating point. The gramians are then balanced and the less important states reduced. A Galerkin projection is performed onto the remaining states. This method has the advantage that it only requires linear matrix computations while being applicable to nonlinear systems.