Control of the fast dynamics

Owing to the dependence of the state space where the slow dynamics evolves on the large flow rates (Remark 3.1), the fast-controller design must precede the slow-controller design. 

The design of the fast distributed controllers for the individual units can, in general, be addressed as a collection of individual control problems, where the strictness of the operational requirements for each unit dictates the complexity of the corresponding controller typical applications rely on the use of simple linear controllers, e.g., proportional (P), proportional-integral (PI) or proportional-integral-derivative (PID). 

Tikhonov s theorem (Theorem 2.1) indicates a further requirement that must be fulfilled by the controllers in the fast time scale in order for the time-scale decomposition developed above to remain valid, these controllers must ensure the exponential stability of the fast dynamics. From a practical point of view, this is an intuitive requirement one cannot expect stability and control performance at the process level if the operation of the process units is not stable. 

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The previous chapters have concentrated on analyzing the material-balance dynamics of several classes of integrated process systems. We demonstrated that the dynamic behavior of the systems considered exhibits several time scales and described a method for the derivation of reduced-order models describing the dynamics in each time scale. Also, a hierarchical controller design framework was introduced, with distributed control of the fast dynamics and supervisory control of the dynamics at the systems level. 

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