Model predictive control of high-index DAE systems without index reduction

Abstract

Process control has in its traditional mathematical representation the process description by means of ordinary di erential equations, ODEs. A more general alternative for representing the dynamic process to be simulated and controlled is through its discription in di erential-algebraic equations, DAEs. The process control is classically represented by PID controllers (Proportional, Integral and Derivative) and having in the upper layer the model predictive control strategies, MPC. It presenting nowadays a growing research activity on the development of optimal control, a control technique also based on a model, in which optimization techniques are used. The present work employs a computational simulation technique for DAE systems, known as direct initialization, which consists of initializing the model from a stationary condition and using a regularization function to carry out the transition from one condition to the other. This approach was used to identify and control four processes described by high-index DAEs. The processes are described by index 2 DAEs being the benchmark model of a condenser used by Pantelides, two models of reactors, one isothermal and other non-isothermal, and a non-dimensional model of reactive ash drum. The processes described by models were identi ed to transfer functions and controlled with MPC controller of the GPC (Generalized Predictive Control) type. It was evidenced that the index reduction can lead to incoherent behaviors and the identi ed linear models, based on transfer function, adequately represented the local behavior of high-index DAE models.