Research Area 4: Optimization-based control of large transients with discrete manipulated variables

During normal operation, processing plants usually run smoothly and with little intervention by the operators. In contrast, large transitions, in particular during start-up and shut-down, often cause severe stress on the operators because of significant risks of failure, e.g. when safety trips during start-up bring the plant fully or partly back to a safe state. We will investigate how model- and optimization-based control schemes can be extended to the handling of situations where discrete changes of the operation of the plant (switching of flows, start-up of pieces of equipment) occur. The start-up and changeover of complex plants is currently predominantly based on heuristic procedures and the availability of experienced operators. A rigorous model-based approach now comes within reach due to the increasing number of operator training systems that are being developed and deployed in the industry. For medium-sized and large new investments often operator training systems (OTS) are ordered with the goal to reduce the time and in particular the risk of delays in the commissioning and start-up phases. These simulators contain detailed dynamic models that represent the behavior of the plant over its full range of operation and are accurate enough that the operators do not realize the difference to the real plant. We believe that the knowledge and effort that have been invested in the development of OTS can and should be used to develop optimal start-up and changeover procedures and to implement them under advanced control.

This work builds upon a substantial progress in the solution of dynamic optimization problems with integer degrees of freedom that has been made by IWR recently. Despite the practical relevance and ubiquity of integer or logical decision variables such as valves, gears or the start-up of sub-units, numerical optimization methods capable of solving nonlinear mixed-integer optimal control problems for large-scale systems, and possibly in real-time, have only recently come within reach. The indirect approach by Pontryagin's Maximum Principle is applicable in principle, but certainly not suitable for large-scale online problems. The new approach developed at IWR builds on the direct multiple shooting method as an "all-at-once" approach. The resulting MINLP is solved by a relaxation approach which convexifies the velocity space rather than the control region. Using deep arguments from functional analysis it was shown that the optimal solution of the relaxed problem will deliver an optimal lower bound, without integer gap . Moreover, it can be arbitrarily closely approximated by an integer solution, which can be computed by sophisticated but very fast rounding procedures. The gain in performance is enormous, several orders of magnitude of speed-up over a state-of-the-art MINLP solver even for smaller instances where the NP hardness of the problem is not yet computationally prohibitive for the latter, as e.g. in a moderate horizon automobile test drive problem . Meanwhile, even the minimum time problem of a race car including the changing of gears on a whole formula 1 track has been solved numerically. Encouraged by these results, we want to develop new algorithms to optimally steer a chemical plant to its desired operating point with minimized losses of valuable materials, ecologic impact and unused production capacity.