Processes with Propagation Without Feedback

The damping of this sytem can be determined by using equation (10.16) for second-order systems  

The damping of the height in the second tank for the process with feedback is 3/2 times the damping of the process without feedback. As can be seen from the data flow diagram, the feedback is positive. The dynamic behavior of the process with feedback is slower than without feedback since the system is stationary when all the individual components are stationary. 

For the two tanks without interaction, Eqn. (10.33) can be used. The responses to a unit change in inlet flow for the two cases, are shown in Fig. 10.19. 

The general equation for propagation without feedback for a section / of the process, can be written as  

An example for two sections is given in the previous paragraph. For n sequential sections the transfer fimction becomes  

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As described in the previous section, propagation without feedback tends to become plug flow when the number of sections is large (Figure 10.27). The response of the process (propagation with feedback), however, tends toward first-order behavior when the number of sections becomes large (Figure 10.28). 

This is in accordance with section 10.6, where propagation without feedback and propagation with feedback were compared. The response of a flow is undamped, whereas the response of a gradient is strongly damped. All sections are intercoimected, and the system is at equilibrium when all sections are at equilibrium. The process response becomes first order ... 

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