A novel linear hybrid model predictive control design: application to a fed batch crystallization process

This paper addresses the problem of enabling the use of complex first principles model information as part of a linear Model Predictive Control implementation for improved control. This is achieved by building a hybrid model that uses an approximate implementation of a first principle model and a Subspace Identification (SID) State Space model to explain the error (the residual) between the first principle implementation and the process outputs. The key idea is to utilize the first principles model with the initial conditions consistent with a particular batch, but using a constant value of the control action. Thus, even though the first principles model may be intractable from an optimization perspective, the approximate implementation allows the hybrid model to be linear (in the control input), while allowing the nonlinear dependence on the initial conditions to be captured. The proposed hybrid model based MPC is compared against a previous hybrid model with 2 SID models and a single SID model on a fed batch crystallization process. The paper demonstrates the improved performance achievable by the readily implementable proposed approach.