PID controllers
P variant

The principle of plain P controller is simple: "greater the actual error e (greater the difference between actual value y and desired value w), greater the actuated control variable u". Transient responses (responses to a step of desired value) of a system, controlled by P controller, are shown on the Figure.

As shown on the behavior, the output value y never settles exactly at the value of w (the error e remains nonzero – so called steady state error). Greater the gain, smaller the error in steady state, but at the cost of augmented overshoot and oscillations. For higher values of proportional gain, the control system can even become unstable.

Fig. 8.20: Transient response of system with proportional controller with different gains (r0)