Response of more complex systems to forcing functions

Response of More Complex Systems to Forcing Functions 

Transfer functions involving polynomials of higher degree than two and decaying exponentials (distance-velocity lags) may be dealt with in the same manner as above, i.e. by the use of partial fractions and inverse transforms if the step response or the transient part of the sinusoidal response is required, or by the substitution method if the frequency response is desired. For example, a typical fourth-order transfer function  

If is desired to determine the frequency response of this system and if the amplitude ratio and phase shift due to Ga(s) are (AR) and % respectively (and similarly), then the amplitude ratio and the phase shift of G(s) are given by  

Consider G(s) ATG (s)G2(r). Putting j = ioiwe obtain a relationship in terms of the complex variable of the form  

In the heat exchanger arrangement illustrated in Fig. 7.32 the following are known  

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