Optimization in process design and control: I. Accelerated global optimization for low-order controller design and process optimization. II. Online control of a distributed parameter process: Applications in composites manufacturing.

摘要

The first paper presents an optimization-based ℓ1–ℓ ∞ optimal fixed-order controller design method. To achieve an optimization search over all stabilizing fixed order controllers, a controller parametrization is used that is based on the Youla parametrization and also includes a quadratic equality constraint. The resulting infinite dimensional optimization problem is nonconvex and is solved by asymptotic approximation. The global optimum is obtained by branch and bound which also employs interval analysis to accelerate convergence. Two implementations of intervals computations are presented, and the most efficient one consists of a novel Interval Newton method that capitalizes on the structure of the problem's equations and speeds up convergence to the global optimum by several orders of magnitude.; The second paper considers the problem of global solution of nonconvex optimization problems that arise in chemical process design. Such problems typically involve a large number of equality constraints and global optimization algorithms exhibit slow convergence. Interval analysis is used in a systematic way that exploits the structure of the equality constraints to accelerate convergence to the global optimum. Heat exchanger network optimization and reactor optimization are used as examples.; In the third paper, the process control of the cure in resin transfer molding (RTM) is studied. During RTM cure, the exothermic reaction that polymerizes the liquid resin causes the development of spatial temperature gradients which lead to non-uniform cure rates. To achieve uniform cure, this work considers a receding horizon, on-line optimization based model predictive controller of the cure. A discretized, finite dimensional model is used for prediction. This model is based on model reduction of an infinite dimensional transport model via Karhunen-Loéve decomposition. Bias calculations are introduced to correct for process-model mismatch. The results of the implementation of this controller are shown, and the identification of optimal tuning parameters and the trade-off between performance and control effort are discussed for a polyester resin system. The simulations indicate that the proposed control algorithm achieves uniform cure.