Observer based nonlinear quadratic dynamic matrix control for state space and input/output models

Abstract

An observer based nonlinear Quadratic Dynamic Matrix Control (QDMC) algorithm is developed for use with nonlinear input-output (I/O) and state space models. It generalizes and extends previously published nonlinear QDMC algorithms. The extension to I/O models is particularly important due to the increased use of neural networks and other types of nonlinear black box models in the chemical industry. Disturbance rejection and offset free tracking is addressed in a general setting utilizing concepts from filtering theory. Various kinds of disturbance models can be incorporated in the formulation. Even though nonlinear models are utilized for model prediction, the on-line optimization is formulated as a single Quadratic Program, thus preserving the computational advantages of nonlinear QDMC as compared to Model Predictive Control algorithms based on nonlinear programming techniques. The examples illustrate parameter tuning for open-loop unstable and stable processes and point out both benefits and shortcomings of the algorithm.On a mis au point un algorithme de contr8le matriciel dynamique quadratique (QDMC) non linhire bast sur un observateur destint aux modbles entr&/sortie (E/S) non lineaires et aux modkles d'espace des ttats. Cet algorithme gCntralise et &end les algorithmes QDMC non lineaires publits andrieurement. Cette gtntralisation aux modkles E/S est particulitrement importante du fait de I'utilisation accrue des rtseaux neuronaux et d'autres types de modtles boite noire non linhires dans I'industrie chimique. La rtjection et le suivi sans compensation des perturbations est considtrk dans le contexte gCntral de la thbrie du filtrage. Diffkrents types de modbles de perturbation peuvent &tre introduits dans la formulation. M&me si des modbles non lineaires sont utilids pour la prkdiction des modbles, I'optimisation en ligne est effectuk avec un programme quadratique unique, ce qui permet de conserver les avantages du calcul du QDMC non linhire comparativement aux algorithmes de contrdle prkdictif des modbles b&s sur des techniques de programmation non linhires. Les exemples illustrent I'ajustement des parambtres pour des prockdts en boucle ouverte stables ou instables et soulignent tant les avantages que les limites de I'algorithme.

Comparison of model predictive control strategies for a fluidized catalytic cracker

“…In particular, it can be performed by local linearization of the nonlinear state space model [59,60] at each sampling instant. In the three previously described versions of MPC (DMC, QDMC, MPC with penalty on y), the outputs were predicted using the linear model based on the step response coefficients.…”

“…An important drawback of such a nonlinear optimization problem to be solved for control and on-line implementation is that it is required to guarantee successful optimization at each sampling instant. Other forms of nonlinear control are presented in the literature such as by [59,60], but the local linearization which is proposed by these latter authors make it closer to linear MPC than real Nonlinear MPC. Figure 13 shows that the regulation and tracking are well performed, but that the way to reach the setpoints and the interactions shows significant improvement with respect to the linear MPC strategies as the outputs exhibit lower deviations with respect to their respective set points around the set point changes.…”

Optimal Design of a Solar Desalination Unit with Heliostats

“…After implementation of the control law, the sequence of calculation is repeated at the next sampling instant according to the receding horizon methodology. Many synthesis articles [20,[25][26][27][28][29][30][31][32] and textbooks [33][34][35] have been published which show the development of MPC and its application in the industrial world [36]. Compared to most usual control possibilities, the main advantages of MPC are the multivariable character by means of the internal model based on step or pulse responses or state space model and the consideration of constraints [24].…”