What does Kc do?

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

Feedback Control

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

Relationship E(t) is directly related to K c because K c 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

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 K c is infinity. There is always offset.

Controller Operating Lines KcKc 1  R s RsRs Offset SSOC KAC

K CU K QD K CD

Effects of Kc Kc = 24 %/cm H 2 0 Decay Ratio=1/500

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

Kc = 67 %/cm H 2 0 Decay Ratio=1/4 Effects of Kc

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

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