Real-time dynamic optimization of batch systems

In this paper a methodology for designing and implementing a real-time optimizing controller for batch processes is proposed. The controller is used to optimize a user-defined cost function subject to a parameterization of the input trajectories, a nominal model of the process and general state and input constraints. An interior point method with penalty function is used to incorporate constraints into a modified cost functional, and a Lyapunov based extremum seeking approach is used to compute the trajectory parameters. The technique is applicable to general nonlinear systems. A precise statement of the numerical implementation of the optimization routine is provided. It is shown how one can take into account the effect of sampling and discretization of the parameter update law in practical situations. A simulation example demonstrates the applicability of the technique.