Control implications and controller implementation

The arguments presented above indicate that the large recycle and coolant flow rates wr and uq are the only manipulated inputs available in the fast time scale, and should be used to control the process temperatures. Likewise, the dynamics of the material-balance variables in the slow time scale are affected only by the small feed and effluent flow rates uq and up, which are thus the manipulated inputs that must be used to tackle control objectives involving the material balance. 6sp, the setpoints of the temperature controllers in the fast time scale, are also available as manipulated inputs in the slow time scale, a choice that leads to cascaded control configurations between the energy- and material-balance controllers. 

In most cases, the only objective in the fast time scale is the control of the reactor temperature, for which there are two available manipulated inputs, r and uc- Thus, several control system design options are available. 

On reverting to the particular case considered in Section 7.6.1, and applying the model-reduction framework outlined above, we obtain the following description of the fast dynamics  

According to our analysis, we address the control of the reactor temperature T in the fast time scale, keeping the ratio wc/wr constant and using the proportional-integral feedback law  

The constraints arising from the fast dynamics (7.36) can now be solved for the quasi-steady-state value, i.e., T = Tsp, which allows us to obtain a description of the slow dynamics  

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