Measurement-based run-to-run optimization of batch processes

In batch chemical processing, dynamic optimization is the method of choice to reduce production costs while satisfying safety constraints and product specifications. Most of the standard optimization techniques are based on a model of the process, while it is extremely difficult to get a reliable dynamic model for industrial batch processes, due to uncertainty and process variations. Industry typically copes with uncertainty by introducing conservatism, at the cost of optimality, to guarantee constraint satisfaction even in the worst case. Measurement-based optimization via the tracking of the necessary conditions of optimality (NCO tracking) is a method that proposes to reduce this conservatism by using appropriate process measurements. The method enforces the NCO for the real process – and not for a possibly inaccurate model – using appropriate process measurements. The NCO for terminal-time dynamic optimization problems have four parts that correspond to meeting constraints and sensitivities both on-line and at final time. The real challenge lies in the fact that these four parts need to be handled in entirely different ways, the terminal constraints and sensitivities being addressed in this thesis. The objective of this thesis is to formulate the adaptation laws for the input parameters to satisfy the terminal objectives of the NCO. For this purpose, a variational analysis of the NCO is performed that takes into account uncertainty and the presence of constraints. This analysis also indicates the possibility of separating the input parameters depending on the influence of uncertainty and the effect on the terminal constraints. To implement these adaptation laws, a run-to-run scheme is proposed. Next, the convergence of the run-to-run scheme is analyzed. It is shown the scheme with a constant proportional gain converges to the optimal value for a class of systems that exhibit sector nonlinearity. Under the same assumptions, a variablegain algorithm, based on the Quasi-Newton techniques, is then proposed to improve the rate of convergence of the aforementioned scheme. Both algorithms exhibit global convergence. This methodology was applied to optimize copolymerization of acrylamide and cationic monomers in inverse emulsion in a 1-ton industrial reactor. The optimal solution obtained consists of an isothermal arc followed by an adiabatic one. The switching time between these two arcs was adapted to meet the constraint on final reactor temperature. Experimental results show that adaptation of the switching time led to a reduction of one third of the reaction time.