Optimal control of temperature and fuel consumption for soaking pits in a steel plant-A distributed parameter approach

An optimal control theory for a class of non-linear distributed parameter control systems in the general setting involving more than one spatial co-ordinate is developed for use on control of a typical soaking pit in a steel industry. The system is described by a set of non-linear partial differential equations in multidimensional spatial-co-ordinates and non-linear boundary conditions with time-dependent boundary controls as well as a spatially independent parameter vector which is governed by its own set of dynamic equations. The set of necessary conditions for optimality obtained from the theoretical development is directly applied to the optimal heating control of the soaking pit with rectangular ingots. The numerical solution by iterations demonstrates the success of the technique and the algorithm leading to the optimal policy for heating control of a typical soaking pit with minimum fuel consumption.