Overall closed-loop transfer function

A control system may have several feedback control loops. For example, with a ship autopilot, the rudder-angle control loop is termed the minor loop, whereas the heading control loop is referred to as the major loop. When analysing multiple loop systems, the minor loops are considered first, until the system is reduced to a single overall closed-loop transfer function. 

The complete, or overall closed-loop transfer function can now be evaluated... 

Find the overall closed-loop transfer function for the system shown in Figure 4.6. Solution... 

Remark. To expedite the construction of the overall closed-loop transfer functions for any feedback control loop, use the following rules ... 

The numerator of an overall closed-loop transfer function is the product of the transfer functions on the forward path between the set point or the load and the controlled output. Thus ... 

Verify these two rules with the overall closed-loop transfer functions Gsp and Gioad [eqs. (14.6) and (14.7)]. Also, these rules can be used to formulate the closed-loop transfer function between an input anywhere in the loop and the output. 

A change in the demand for shaft power A Pd may be added to the summing point of APref and AP and APref assumed to be zero. Hence the overall closed-loop transfer function gain G, at the speed co is found to be. 

If we substitute for Gpi2 2 (18-8) using (18-10) and then substitute for Y2 using (18-9), the overall closed-loop transfer function between Yi and Ui is... 

From eqs. (14.6) and (14.7) it can be easily seen that the closed-loop overall transfer functions G sp and G ioad depend not only on the process dynamics but also on the dynamics of the measuring sensor, controller and final control element. 

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