Decouplers and their design

Suppose that, in the system represented by the block diagram shown in Fig. 7.74, both controlled variables Ct and C2 are at their respective set point values / , and R2. A perturbation in either R2 or in the load U2 will cause a consequent change in 

This will not only act as a suitable control signal for C2 but will also produce an undesired disturbance in control loop 1 and cause C, to deviate from its desired value. However, A/Vl can be varied by a quantity M t which compensates for this interaction effect from A/v2. If the deviation in C, due to interaction is %, then My can be determined from equation 7.166a, i.e.  

If there is to be no deviation in Clt then the appropriate control criterion is that = 0. Applying this to equation 7.169 gives  

The same procedure can be used to design a decoupler D2(s) to compensate for the interaction effects caused in loop 2 (Fig. 7.74) by disturbances in loop 1. In this case, from equation 7.166b  

From Fig. 7.15b (which illustrates both decouplers applied at the same time) and equation 7.166a  

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