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Understanding Kc: The Role of Controller Gain in Control Systems

Kc, or controller gain, is a critical parameter in feedback control systems. It adjusts the system's input to reduce error E(t), defined as the difference between the set point R(t) and the output C(t). As Kc increases, it affects various system characteristics such as decay ratio, frequency, settling time, and offset. Higher values can lead to increased oscillation amplitude and frequency, emphasizing the need to find an optimal Kc value to balance offset minimization with controlled oscillation.

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Understanding Kc: The Role of Controller Gain in Control Systems

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  1. What does Kc do?

  2. What is Kc? • Kc is the Controller Gain of a control system. • It can be adjusted to obtain a variety of system responses.

  3. Feedback Control

  4. E(t): Input to the Controller E(t)=R(t)-C(t) • E(t) = Error of system • R(t) = Set Point • C(t) = Output of System (Controlled Variable)

  5. Relationship • E(t) is directly related to Kc because Kc adjusts the system’s input to reduce E(t). • In a proportional controller by the equation • The controlled output will always have an offset from the set point after a change of set point. • The offset is the difference between the output and the setpoint

  6. Offset • E(s) = R(s)-C(s) • By Block diagram algebra: By FVT for R(s) = 1/s (step response) E(s) is never zero unless Kc is infinity. There is always offset.

  7. Controller Operating Lines KAC 4-9-04 Offset 1 Kc D Rs Rs SSOC

  8. KQD KCU KCD

  9. Effects of Kc Kc = 24 %/cm H20 Decay Ratio=1/500

  10. Effects of Kc Kc = 48 %/cm H20 Decay Ratio=1/10

  11. Effects of Kc Kc = 67 %/cm H20 Decay Ratio=1/4

  12. As Kc Increases • The Decay Ratio increases • The frequency increases • The offset decreases • The settling time increases

  13. What does Kc Do? • Kc effects the Decay Ratio, Frequency, Settling time, Offset. • As the Kc of a system increases so does the oscillation amplitude and frequency of the system output. • There is an optimum value of Kc that minimizes offset while minimizing oscillation.

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