This simulator closes a control loop around a simple process, a first-order lag with a 15 second time constant, and lets you be the tuner. A live trend plots the process variable against the setpoint while a diagram shows the PID controller, the process and the feedback path. Change Kp, Ti and Td and watch for overshoot, oscillation or sluggish response.
• A trend of PV (green) and SP (amber) covering the last two minutes, with a live PV label. • A loop diagram: SP to PID controller to process (tank level) to PV, with a dashed feedback path and the current CO value. • Sliders for setpoint (10-90 percent), Kp (0.1-10), Ti (5-120 s) and Td (0-20 s), a 1×/5× speed toggle and a Reset loop button. • Readout tiles for SP, PV, error and CO, with expandable notes, formulas and a worked example.
Error is the setpoint minus the process variable. The proportional term multiplies error by Kp; the integral term accumulates error at a rate of Kp/Ti and is clamped between 0 and 100 percent to prevent windup; the derivative term reacts to the rate of change of the measurement, filtered to limit noise. Their sum, clamped to 0-100 percent, is the controller output. The process responds with a first-order lag of 15 seconds and a gain of 0.8, with a little measurement noise.
With only proportional action the loop settles with an offset; adding integral action removes it, at the cost of overshoot if Ti is too short. A high Kp speeds the response until it starts to oscillate. Derivative action adds damping but magnifies noise. Because the process is slow, use the 5× speed button while exploring, then return to real time to judge the feel. The lab is a teaching model, so tuned values do not transfer directly to a real plant.
Kp is the proportional gain that scales the present error. Ti is the integral time, where a shorter value means stronger integral action that removes steady-state error. Td is the derivative time, which reacts to how quickly the process variable is changing and adds damping.
Proportional action alone needs a non-zero error to hold a non-zero output. The integral term is what slowly drives that error to zero, so very long integral times leave the offset in place for longer.
A simulated tank level modeled as a first-order lag with a 15 second time constant and gain of 0.8, plus small measurement noise. It is a teaching model and does not include dead time, valve nonlinearity or disturbances.
The PID Control Loop Tuning web app is a separate tool. This lab is a compact, fixed loop simulator focused on the relationships between setpoint, PV, error and controller output.