The measurement selection of inventory control

This work addresses how input-output pairing is related to stability of inventory control systems. Input-output pairing divides the process dynamics into a measured subset and an unmeasured subset. The unmeasured dynamics are called the zero dynamics. We demonstrate that if the input-output pairing is chosen so that the zero dynamics are stable, then the overall stability of the system is guaranteed. Otherwise, the unmeasured inventories do not converge to setpoints due to the instability of internal dynamics. A system with stable zero dynamics is called a minimum phase system. The impact of different input-output pairings on the stability of the overall system is illustrated with two typical examples characterized by nonlinearities. The capability of inventory control is illustrated with an industrial solar grade silicon production process.