Proportional (P) Control is a control method in which the controller output is directly proportional to the present error between the desired setpoint and the actual system output. It is expressed as u(t) = Kp e(t), where u(t) is the controller output, e(t) is the error, and Kp is the proportional gain. Increasing Kp generally makes the system respond faster and reduces the error, but an excessively high gain can cause oscillations or instability. P control is simple, fast, and widely used in systems where some steady-state error can be tolerated.
Proportional (P) Control Simulation
Explore how proportional gain affects system response. The controller continuously reacts to the present error.
Setpoint
70.0
System Output
0.0
Error
70.0
Controller Output u(t)
140.0
Real-Time P-Control Response
Setpoint
System Output
Error
P-Control Equation:
u(t) = Kp × e(t)
Error:
e(t) = Setpoint − Output
Increasing Kp makes the controller react more strongly to the present error. A low Kp produces a slower response, while a higher Kp generally produces a faster response and smaller tracking error. Excessively high gain can produce overshoot and oscillatory behavior.
u(t) = Kp × e(t)
Error:
e(t) = Setpoint − Output
Increasing Kp makes the controller react more strongly to the present error. A low Kp produces a slower response, while a higher Kp generally produces a faster response and smaller tracking error. Excessively high gain can produce overshoot and oscillatory behavior.