Structured Model Order Reduction of Parallel Models in Feedback

Parallel working units in closed-loop operation are frequently encountered in industrial applications of advanced process control (boilers, turbines, chemical reactors, etc.). Control strategies typically require different low-order models for each configuration of parallel units. These different models are usually obtained by heuristics applied to the parallel models. To replace these heuristics, this paper proposes a systematic solution based on structured model order reduction. Two methods are considered, the first has general applicability to stable closed-loop systems, but gives no a priori error bounds; the second linear matrix inequality (LMI)-based method comes with an explicit error bounds, but cannot be applied to general models. However, it is shown that for models composed of cascades of stable subsystems and negative feedbacks of strictly positive real subsystems, the LMIs are always feasible. Both methods are demonstrated on a practical example of a cogeneration power plant with multiple boilers. It is proved that the second LMI-based method can always be applied to general problems with structures similar to the boiler-header systems considered in this paper.