An Improved Method for Nonlinear Model Reduction Using Balancing of Empirical Gramians

Nonlinear model predictive control has become increasingly popular in the chemical process industry. Highly accurate models can now be simulated with modern dynamic simulators combined with 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. One possible solution to this is the application of model reduction techniques. The method introduced here reduces nonlinear systems while retaining most of the input-output properties of the original system. The technique is based on empirical gramians that capture the nonlinear behavior of the system near an operating point. The gramians are then balanced and the less important states reduced via a Galerkin projection which is performed onto the remaining states. This method has the advantage that it only requires linear matrix computations while being applicable to nonlinear systems.