Modeling Plant Non-Linearities for Instantaneous Optimal Control

Frequently, one will find that the conditions for optimality in chemical production are determined by the non-linearities in the plant itself, while the economic objective function might be linear. If the control variables do not enter the objective function, it is found that the instantaneous optimal conditions are found where the product of the sensitivity matrix of the state variables to the control and the gradient of the objective function in the state space is zero. In some cases, this means that the process state is insensitive to the control at the optimum, which makes traditional proportional control instable. Therefore, the modeling and parameter estimation for process non-linearities to identify an optimum become essential. The control problem becomes a tracking problem. This paper describes the application of those ideas to a simple continuous stirred tank reactor with multi-component and multi-reaction kinetics.