Computation of the near‐optimal temperature and initiator policies for a batch polymerization reactor

Abstract

Optimal control theory is applied to a batch polymerization reactor for PMMA to calculate the near‐optimal temperature and initiator policies that are required to produce a polymer with a desired final conversion, and desired number average and weight average molecular weights. The two‐point boundary value problem that results from the application of the Pontryagin minimum principle to the mathematical model of the reactor is solved by the discretization control method. According to this, the total reaction time is divided into N equal subintervals. It is assumed that the control variables remain constant in each interval and the Hamiltonian is minimized by a first‐order gradient technique. It is shown that the introduction of the “target set” concept, which is well suited to industrial practice, simplifies the numerical solution of the TPBV problem. Results of the simulations demonstrate the potential gains possible from the application of the optimal control theory to the batch polymerization of PMMA.

Cascade closed-loop optimization and control of batch reactors

“…There are two main optimization approaches used with batch reactors. The classical approach involves the use of Pontryagin's principle, which results in a two-point boundary value problem (TPBVP) (Hicks et al, 1969;Denn, 1969;Kirk, 1970;Bryson and Ho, 1975;Sage and White III, 1977;Thomas and Kiparissides, 1984;Bryson, 1999). The major drawback of this approach is that the optimal solution is very sensitive to changes in initial conditions.…”

Molecular‐weight distribution attainable in a batch free‐radical polymerization

“…Many researchers have used the optimal-control theory in order to determine a recipe that minimizes the reaction time and produces the polymer with the desired average MWs in a Ž batch reactor Hicks et al, 1969;Sacks et al, 1972;Chen and Jeng, 1978;Thomas and Kiparissides, 1984;Ponnuswamy et . al., 1987;Ahn et al, 1998 .…”

Optimal State Estimation and on-Line Optimisation of a Biochemical Reactor

“…The optimal control policies that ensure the satisfaction of the product property requirements and the operational constraints can be calculated off-line, which are then implemented on-line so that the system is operated in accordance with these control policies. Optimal control is a widely used approach and various techniques have been reported for chemical processes including bioreactors (Bryson and Ho, 1975;Catalina and Gabriela, 2007;Jimmy et al, 2010;Jin et al, 2011;Peroni et al, 2005;Thomas and Kiparissides, 1984;Xie et al, 2001). However, on-line optimising control is a promising approach to fulfill the requirement of monitoring and control of bioreactors.…”