Modern Control System Theory and Design, 2nd Edition

2.13.  TRANSFER FUNCTIONS OF SYSTEMS

In order to determine the transfer function of complex systems, it is necessary to eliminate intermediate variables of the elements that comprise the system. This will enable the designer to obtain a relation between the input and output of the overall system. This section will consider the transfer functions of cascaded elements, single-loop feedback systems, and multiple-loop feedback systems. A nonloading cascaded system is shown in Figure 2.9. We assume that the input impedance of each system is infinite, and the outputs of the preceding systems are not affected by connecting to the succeeding element. The transfer function of the overall system can be obtained by solving the following set of equations:

By inspection, it can be seen that the transfer function of the cascaded system, E₅(s)/E₁(s) is the product of the transfer functions of the individual elements:

Consider the elementary linear feedback system in Figure 2.10. G(s) and H(s) represent ...