Differential Dynamic Programming as a Tool for Dynamic Optimization in a Travelling-Grate Pelletizing Plant

Abstract

Induration in a travelling-grate pelletizing plant is a nonlinear distributed parameter process. A high-order dynamic model of the induration zone has been simplified into a model of low order using the method of subdomains. The Differential Dynamic Programming (DDP) method is used for solving an optimal control problem containing the simplified model. The problem of minimizing the inlet gas energy necessary for the induration is considered. The purpose is to examine the feasibility of the DDP method as a tool for dynamic optimization in this kind of process.The approach of the method of subdomains used in the simplification is briefly that the distributed variables are approximated by truncated power series, in the space variable, with time-dependent coefficients. The approximations are inserted into the partial differential equations, forming residuals which are integrated over certain subdomains. The result of this procedure is a non-linear model of low order with time as the independent variable. The optimal control problem treated here has the inlet gas temperature as the control variable. The greater loss of energy at high temperatures is covered by using a quadratic function of the inlet gas temperature in the cost functional. Furthermore, the derivative of pellet temperature with respect to time is limited by a specified value in order to avoid heat shock. The influence of the energy obtained through the exothermal reaction of magnetite into hematite is considered. Variations in the model parameters bed height and pressure drop are performed to determine a defined efficiency of the energy of the inlet gas.Results of the optimization would be to use high beds and as high as possible a gas temperature. The results also show that the method of subdomains in combination with DDP forms a powerful tool for the discovery and verification of control strategies in processes of this type.