Model reduction and hierarchical controller design

Let us employ the ratio of the nominal, steady-state values (denoted by the subscript s) of the feed-stream and recycle-stream flow rates to define the recycle number 

Process systems with significant material recycling 

Ignoring the two-time-scale behavior, a single j x 4 (1 j 5) multivariable optimization- or inversion-based controller could be designed for the overall system, using any combination of the flow rates of the five available material streams (F, V, B, R, and D) to address the four control objectives stated above (Mr, Mo, Mb, and x2jB). 

However, the stiffness/ill conditioning of the model (3.31) will strongly impact on the implementation of optimization controllers (e.g., a model predictive controller) (Baldea et al. 2010). On the other hand, for any choice of four flow rates as manipulated inputs (keeping the remaining one constant at its nominal value), the system is non-minimum phase (Kumar and Daoutidis 2002) and thus potentially closed-loop unstable with an inversion-based controller.3 As discussed in the previous section, a more systematic controller-design approach would 

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