Fast Nonlinear Model Predictive Control of Distributed Parameter Systems

Abstract

Data-driven model identification has been widely used in the control of manufacturing systems for decades. Linear input–output models are typically used for the control of multivariable dynamical systems with actuator, state, and output constraints within model predictive control (MPC) algorithms which have low on-line computational cost. The use of nonlinear models within MPC algorithms has been more limited, due to higher computational costs associated with solving the resulting dynamic optimal control problems.A fast MPC algorithm is proposed for control of nonlinear distributed parameter systems (DPS). The input–output behavior of the DPS is represented by a polynomial nonlinear-autoregressive-with-exogenous-inputs model. A machine learning algorithm is used to construct a sparse nonlinear model from the data. The online computational cost of the MPC algorithm is further reduced by incorporating automatic differentiation within the numerical optimization and implementing in the Julia programming language. The methodology is demonstrated for a computational case study of a tubular chemical reactor, in which sparse predictive models are built and incorporated into an on-line implementable nonlinear MPC algorithm.