Proportional-integral-derivative frequency response

In this section the frequency response of a PID controller will be discussed. The transfer function of a proportional integral derivative controller is ... 

The integral in Eq. 5.92, the other term besides g(co), is of course the intercollisional profile. Its density dependence is more complex it is proportional to the product of densities nA nB because of the appearance of PA and vc in the numerator of the first fraction under the integral. Furthermore, nB appears in the form of the collision frequency once more in the denominator of that fraction, as well as in the denominator of the last term. In deriving Eq. 5.92, we have summed over many collisions of a selected atom of type A with the various atoms B. This summation is responsible for the complex density dependence observed here. 

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