Maximum Likelihood Identification of Uncontrollable Linear Time-Invariant Models for Offset-Free Control

Maximum likelihood identification of linear time-invariant models is a difficult problem because it is, in general, a nonlinear semidefinite program, with semidefinite covariance matrix arguments and semidefinite filter stability constraints. To enforce filter stability, we establish a general theory of closed constraints on the system eigenvalues using LMI regions. To solve the identification problem, we employ a Cholesky factorization method that reduces the semidefinite program to a standard nonlinear program. Finally, we apply the identification algorithm to a class of linear plant and disturbance models commonly used in offset-free model predictive control applications. Specifically, we consider models that are structured with uncontrollable, integrating disturbance states. We solve this disturbance modeling problem, and validate the resulting controller and estimator performance, in two real-world case studies: first, a low-cost benchmark temperature control laboratory, and second, an industrial-scale chemical reactor at Eastman Chemical's Kingsport plant.