The Optimization Algorithm rFSQP with Application to Nonlinear Model Predictive Control of Grate Sintering

Abstract

This thesis contributes to the research on optimization algorithms for nonlinear programming, and to the application of such algorithms to nonlinear model predictive control.

Regarding the contribution to research on algorithms for nonlinear programming, a novel algorithm is put forward with a complete theory for global and local convergence. This is the main contribution of the thesis. The algorithm, named rFSQP, is a reduced Hessian Feasible Sequential Quadratic Programming method. It remains feasible with respect to nonlinear inequalities at all SQP iterations, but nonlinear equality constraints are treated as in general reduced Hessian SQP methods. The rFSQP algorithm is implemented in MATLAB and tested on a number of small scale problems with encouraging results. However, the algorithm is designed for large scale problems with few degrees of freedom. Some preliminary testing of the algorithm on large scale problems are investigated.

The thesis also contributes to the understanding of the relation between sequential and simultaneous reduced gradient methods, and to the understanding of the relation between discretization methods for dynamical systems and the choice of optimization algorithms.

The thesis also contributes to model based control approaches of grate sintering. Grate sintering is a complex metallurgical process, where melting of solids and fast gas dynamics give rise to stiff process models, i.e. the "time constants" of the system differ by many decades in magnitude. Hence, application of real-time optimization methods like nonlinear model predictive control to the grate sintering process is challenging. The thesis gives a framework for implementing nonlinear model based control of grate sintering by giving a control objective, a nonlinear model and choosing an appropriate discretization scheme. The thesis gives a reduced order model which is less computationally demanding. Data from industrial experiments are used to adapt the model and to assess the control objective.