Transfer functions for feedback controllers

As discussed in Chap. 7, the three common commercial feedback controllers are proportional (P), proportionaMntegral (PI) and proportional-integral-derivative (PID), The transfer functions for these devices are developed below. 

The equation describing a proportional controller in the time domain is  

Equation (9.107) is written in terms of total variables. If we are dealing with perturbation variables, we simply drop the bias term. Laplace transforming gives 

Rearranging to get the output over the input gives the transfer function for the controller. 

So the transfer function for a proportional controller is just a gain. 

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Transfer Functions for Feedback Controllers Conclusion Problems... 

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