PID Controller Tuner

Real-time Proportional-Integral-Derivative simulation for control systems analysis.

Proportional (Kp)1.50

Adjusts current error response. High values may cause instability.

Integral (Ki)0.50

Eliminates steady-state error. Too high causes oscillation.

Derivative (Kd)0.10

Predicts future error. Dampens the system response.

Setpoint50

Current State

0.00

Error

50.00

Engineering Insight: The PID Algorithm

A PID controller continuously calculates an error value $e(t)$ as the difference between a desired setpoint (SP) and a measured process variable (PV). It applies a correction based on proportional, integral, and derivative terms:

$u(t) = K_p e(t) + K_i \int_0^t e(\tau) d\tau + K_d \frac{de(t)}{dt}$

Proportional (Kp): Corrects based on current error. High gain reduces rise time but can cause overshoot.
Integral (Ki): Corrects based on past errors. Accumulates error over time to eliminate offset.
Derivative (Kd): Corrects based on error rate. Acts as a damper to prevent overshoot and improve stability.

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