4. Comparison between Non-interacting and Interacting Systems

Non-interacting: \[\frac{H_2(s)}{Q(s)} = \frac{R_2}{ (\tau_1s+1)(\tau_2s+1)} = \frac{R_2}{\tau_1\tau_2 s^2 + (\tau_1+\tau_2)s + 1}\]

Interacting: \[\frac{H_2(s)}{Q(s)} = \frac{R_2}{\tau_1\tau_2s^2 + (\tau_1+\tau_2+A_1R_2)s + 1}\] The difference between the transfer function for the non-interacting system, and that for the interacting system, is the presence of cross-product term \(A_1R_2\) in the coefficient of \(s\).


Here, \(\tau_1=\tau_2\), and \(A_1=A_2\).

Interacting system is more sluggish than the noninteracting system.