Control in the slow time scale

The design and implementation of the fast controllers allows the derivation of a minimal-order realization of the DAE model of the slow dynamics in Equation (3.16). For illustration purposes, let us assume that the fast controllers are defined by the static state-feedback control law 

Using the methods presented in Chapter 2, the above formulation can be used to derive a state-space realization of the slow dynamics of the type in Equation (2.48). The resulting low-dimensional model should subsequently form the basis for formulating and solving the control problems associated with the slow time scale, i.e., stabilization, output tracking, and disturbance rejection at the process level. 

From a practical perspective, this is the model that should be used to design a (multivariable) controller that manipulates the inputs us to fulfill the control objectives ys. It is important to note that the availability of a low-order ODE model of the process-level dynamics affords significant flexibility in designing the supervisory control system, since any of the available inversion- or optimization-based (e.g., Kravaris and Kantor 1990, Mayne et al. 2000, Zavala 

Process systems with significant material recycling 

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