1. A COMPARISON OF PERFORMANCE AND IMPLEMENTATION CHARACTERISTICS OF NMPC FORMULATIONS
Guilherme A. A. Gonçalves, Evandro L. Alvaristo, Guilherme C. Silva, Maurício B. Souza Jr., Argimiro R. Secchi
Chemical Engineering Program –PEQ/COPPE, Universidade Federal do Rio de Janeiro, Brazil
Goal
To compare different approaches for predictive control, applied to a highly nonlinear chemical reactor
Why?
Different approaches, such as linear MPC, sequential NMPC, neural network NMPC, Adaptive MPC, are being developed for nonlinear predictive control, however a fair comparison is difficult to find in the literature.
Technique
2. The techniques differ primarily in the form of process model used in the controller, leading to different methodologies for solving the optimization problem and, consequently, different computational burden.
1. Four approaches were chosen for solving the NMPC problem: a classical sequential approach using a parallel integration-optimization method, An Neural Network NMPC that uses this type of model to avoid the model integration, An adaptive MPC that linearize the model in each sampling time and the classical QP-linear approach in state space form.
Sequential NMPC
Adaptive MPC
Neural Network NMPC
Linear MPC
Nonlinear ODE model
Sequential problem using a NLP solver coupled with a numerical integration routine
Replaces de ODE model with a neural network model
NLP solver and evaluation of a neural network model
Linearization along the prediction horizon
NLP/QP solver and evaluation of a linear model
Linear model
QP solver
Sequential NMPC
Adaptive MPC
Nonlinear chemical process
(van de Vusse Reaction)
Predictive control problem
Neural Network NMPC
Computational Burden
Linear MPC
4. The results show that:
The superiority of the NMPC against the linear version was shown in regions of pronounced nonlinearity. It was also demonstrated that the NMPC approaches based on simplified process models (adaptive linear and neural networks) demand a reduced computational burden than the one that depend on the integration of the full model, with similar performance.
3. The system chosen has a singular behavior with two gain inversions while vary the input flow. The comparison was made considering isothermal conditions, which result in only one gain inversion. Then, the system was divided in two regions: one of them cover the left side of the gain curve, and the other comprising the right side.
Comparison between controllers for an initial steady-state to the left of the maximum
Acknowledgments
Comparison between controllers for an initial steady-state to the right of the maximum
The authors acknowledge financial support from the Brazilian National Council for Scientific and Technological Development (CNPq).
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