Simultaneous optimization and solution methods for batch reactor control profiles

Differential-algebraic optimization problems appear frequently in process engineering, especially in process control, reactor design and process identification applications. For fed-batch reactor systems the optimal control problem is especially difficult because of the presence of singualr arcs and state variable constraints. For problems of this type we propose a simultaneous optimization and solution strategy based on successive quadratic programming (SQP) and orthogonal collocation on finite elements. In solving the resulting nonlinear programming (NLP) problem, a number of interesting analogs can be drawn to more traditional methods based on variational calculus.First, the collocation method has very desirable stability and accuracy properties. Second, it will be shown that NLP optimality conditions have direct parallels to general variational conditions for optimal control. To demonstrate this strategy, we consider the optimization of a fed-batch penicillin reactor using a number of cases. For the simplest case, the results presented here agree well with previously obtained, analytically-based solutions. In addition, accurate results are presented for more difficult cases where no analytic solution is available.