Pneumatic circuits: R, C

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Presentation transcript:

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

Position to Pressure transducer/amplifiers pb 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

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:

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

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

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

PID controller

Hydraulic servo system

Alternative construction

Proportional controller Same as last page Same as before

Dashpot

Proportional + Integral controller Rest as before Last page

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

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

Block diagram representation

e w z

Thermal systems Conservation of heat energy: