The equivalent unity feedback system

The analysis of feedback control systems can often be facilitated by conversion to an equivalent unity feedback system, i.e. a feedback loop in which the feedback path is represented by a steady-state gain of unity. There are two principal cases to consider. 

Conversion to Unity Feedback when the Transfer Function in the Feedback Part of the Loop is Represented by a Steady-State Gain K 

Consider a simple feedback loop (Fig. 7.3a) in which the feedback path consists of elements which approximate to a steady-state gain K (Fig. 7.37). In this instance, the equivalent unity feedback loop is determined by placing 1 IK in the set point input to the main loop and compensating for this by adding an additional factor K in the forward part of the loop prior to the entry of the load disturbance, as in Fig. 7.38. It is easy to confirm that the standard closed loop transfer functions and are the same for the block diagrams in Figs 7.37 and 7.38. 

In this case H in Fig. 7.3a cannot be treated as a constant and we write  

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