Feedback loop (CV changes input) SP Controller Gc Plant Gp Sensor Gs E MV (Manipulated Variable CV Controlled Variable +-+- S

The input of each block determines the output CV = Gp(s)*MV Plant Gp MV (Manipulated Variable CV Controlled Variable

MV = Gc E Controller Gc E MV (Manipulated Variable

Combine blocks CV = Gp*Gc*E Controller Gc Plant Gp E MV (Manipulated Variable CV Controlled Variable

E = SP – S S = Gs*CV or E = SP – Gs*CV Sensor Gs E+-+- SP S CV Controlled Variable

Do the math to get the closed loop transfer function CV = Gp*Gc*E E = SP – Gs*CV CV = Gp*Gc*(SP – Gs*CV) Solve for CV