Decentralized control system design using mixed integer optimization

Decentralized control system design comprises the selection of a suitable control structure and controller parameters. In the present paper, mixed integer optimization is used to determine the optimal control structure and the optimal controller parameters simultaneously. The process dynamics is included explicitly into the constraints using a rigorous nonlinear dynamic process model. Depending on the objective function, which is used for the evaluation of competing control systems, we propose two different formulations. These formulations lead to a mixed integer dynamic optimization (MIDO) problems. Two different solution approaches are considered to solve the resulting MIDO problem and compared with each other. The first is based on the simultaneous dynamic optimization approach. In this approach, the differential state and control variables are discretized using orthogonal collocation on finite elements. Hence the MIDO problem is transformed into a large scale mixed integer non-linear programming (MINLP) problem which is solved with some standard MINLP solvers. The second is based on the sequential dynamic optimization approach, in which the MIDO problem is decomposed into a series of primal problems (dynamic optimization) where the binary variables are fixed, and MILP master problems which determine a new binary configuration for the next primal problem using Generalized Benders Decomposition (GBD). The proposed methodology is applied to an inferential control of a reactive distillation column as a challenging benchmark problem for chemical process control. Results are compared with previous studies and conclusions are drawn for future work in this field