Consider the inverting operational amplifier in Figure AP2.9. Find the transfer function Vo(s)/Vi(s). Show that the transfer function can be expressed as
![](https://test.transtutors.com/qimg/14817b09-dcd3-419a-92fc-3a72422fe408.png)
Where the gains KP, KI and KD are functions of C1, C2, R1, and R2, This circuit is a proportional-integral-derivative (PID) controller (more on PID controllers in Chapter 7).
![](https://test.transtutors.com/qimg/792a64bb-1e70-484e-ac3e-7a5f23c8c024.png)