See how proportional gain changes speed, offset, damping and actuator demand in a feedback loop.
P(t)=Kp(βr(t)−y(t))
Proportional action scales the current error. Increasing proportional gain usually makes the initial response stronger, but the plant dynamics decide when that extra authority becomes overshoot or oscillation.
01
What Kp changes
A larger proportional gain increases the immediate command for the same error. It can reduce rise time and improve disturbance rejection, while also reducing stability margin and increasing sensitivity to delay.
GAIN VIEW 01
More Kp makes the first move stronger
Higher proportional gain shortens rise time and reduces offset until the plant loses enough damping to overshoot.
SetpointKp = 0.5Kp = 1.0Kp = 2.0
READ THE PLOTIncrease authority only while damping remains acceptable
02
Why offset remains
On many self-regulating processes, a non-zero error is required to maintain a non-zero controller output. Proportional-only control therefore settles with offset when a constant load must be balanced.
OFFSET VIEW 02
Proportional-only control needs some error
When a constant load arrives, the loop recovers quickly but settles below the setpoint because error is needed to hold controller output.
SetpointLow KpMedium KpHigh Kp
READ THE PLOTA remaining gap is proportional offset—not slow settling
03
Setpoint weighting
A two-degree-of-freedom controller can apply a weight to the setpoint inside the proportional term. This softens setpoint response without weakening the controller's reaction to disturbances in the measured process.
DELAY VIEW 03
Dead time converts gain into oscillation
With more delay, the controller keeps correcting an error before it can see the result of its previous action.
SetpointShort delayModerate delayLong delay
READ THE PLOTDelay limits safe Kp even when the plant itself is simple