1. Pneumatic circuits: R, C
Pressure is potential, pressure difference is voltage drop
A flow restrictor is a resistance
An air chamber is a capacitance DP
Slope R
Resistance R
P+pc
P+pi q C R Q pc C pi

2. Position to Pressure transducer/amplifierspb Rx ps C pa
Ps is pressure of supply air from wall pipe or air cylinder
X is weighted differential average of input position and the pivot position
X controls the pressure Pb send to the control valve

3. Pneumatic proportional controller
Ps is const parameter
Diaphragm is fast, so pc and pb are equal
x is weighted diff sum of e and y
Notice the direction of x and e:

4. Pneumatic proportional controller
Since pc=pb
Drawing for this part can be simplified

5. Proportional + derivative controller
Recall: bellow pressure is related to input pressure by
1/(RCs+1)
Pbellow

6. Proportional + Integral controller
So, in closed-loop TF, replace (RCs+1) by (RCs+1)/RCs:

7. PID controller

8. Hydraulic servo system

9. Alternative construction

10. Proportional controller
Same as last page
Same as
before

11. Dashpot

12. Proportional + Integral controller
Rest as before
Last
page

13. Proportional +derivative control
Spring force: k(y-z) instead of kz; new TF=1-oldTF

14. PID controller w
Force Balance: k1z=ADP1; k2(y-w)=ADP1+ADP2

15. Block diagram representation

16. e w z

17. Thermal systems
Conservation of heat energy: