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This guide delves into the intricacies of feedback loops within control systems, emphasizing the interaction between controlled and manipulated variables. It covers the mathematical foundation of closed-loop transfer functions and the critical role of the controller in achieving stable operation. By analyzing the relationships among process gain, setpoint, and the sensor’s output, readers will learn how to effectively manipulate system variables to optimize control performance. The document simplifies complex concepts while providing valuable insights for engineers and students alike.
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Feedback loop (CV changes input) + - E Controller Gc PlantGp SP MV (Manipulated Variable S SensorGs CV Controlled Variable
The input of each block determines the output • CV = Gp(s)*MV PlantGp MV (Manipulated Variable CV Controlled Variable
MV = Gc E E Controller Gc MV (Manipulated Variable
Combine blocks • CV = Gp*Gc*E E Controller Gc PlantGp MV (Manipulated Variable CV Controlled Variable
E = SP – S • S = Gs*CV or E = SP – Gs*CV + - E SP S SensorGs 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