A Calculation Method of Optimal Actuators Allocation for Controlling Temperature Distribution in a Packed-bed Reactor

This study proposes a method for determining the optimal placement of actuators to achieve the target temperature distribution when designing a bench-scale tubular reactor. Based on the material and heat balances of one-dimensional nonlinear distributed parameter systems representing the dynamics of a tubular reactor with a large exothermic reaction, we optimized the placement and output of multiple actuators with fixed widths in the length of the reactor to achieve the target temperature distribution using a mathematical model converted into nonlinear ordinary differential equations by an orthogonal collocation method. Because this optimization problem is a convex problem with a slightly uneven distribution of the evaluation function for the decision variables owing to the numerical complexity of the collocation method, a genetic algorithm was used to solve this global optimization problem. As a result, it was found that the optimal allocation of multiple actuators could be determined, and the target temperature distribution without hot spots could be realized precisely by several actuators. In addition to the placement and output of the actuators, the widths of the actuators were optimized simultaneously. The results showed that using a few actuators with optimal widths, the target temperature distribution could be achieved more precisely than when using multiple actuators with fixed widths.