A Reduced Linear Model Predictive Control Algorithm for Nonlinear Distributed Parameter Systems

A novel model reduction-based framework for linear Model Predictive Control ( MPC) of Distributed Parameter Systems is presented. It exploits the separation of scales exhibited in many systems of engineering interest. It is based on the online, adaptive identification of the dominant modes of the system using the Arnoldi method. The low-dimensional dominant subspace corresponding to those modes is exploited for the linearization of the model. Only low-dimensional Jacobian and sensitivity matrices are involved in this framework. They are projections of the original matrices onto the dominant subspaces, computed efficiently with numerical directional perturbations. The low-order linear model from this procedure is utilized in the context of a MPC scheme. The efficiency of the proposed methodology is illustrated using a temperature tracking control of a tubular reactor which also involves measurement noise and disturbances.