PID Controller Tuning Lab

How to Use the PID Tuning Lab

A Proportional-Integral-Derivative (PID) controller is the most common control loop algorithm used in modern automation (from cruise control in cars to drone flight stabilization and temperature management in industrial furnaces).

In this interactive lab, your goal is to make the System Output (y(t), blue line) quickly reach and lock onto the Setpoint Target (red dashed line) with minimum oscillation and zero offset.

Understanding the 3 Control Knobs

Adjust the sliders in the interface to see how each parameter changes system dynamics in real time:

1. Proportional Gain (K_p) — The Present Error Controller

• How it works: Drives the system based on current error magnitude ( Error = Setpoint − Position ).
• What to observe: Increasing K_p makes the system respond faster, but setting it too high causes severe overshoot and violent oscillations.

2. Integral Gain (K_i) — The Past Error Corrector

• How it works: Accumulates historical error over time.
• What to observe: K_p alone often leaves a small gap between the target and actual position (steady-state error). Raising K_i eliminates this residual offset, pulling the blue line directly onto the red target line. Setting K_i too high leads to "windup" and instability.

3. Derivative Gain (K_d) — The Future Trajectory Predictor

• How it works: Dampens the system by looking at the rate of change of error.
• What to observe: Acts like an electronic shock absorber. Increasing K_d reduces peak overshoot and smooths out rapid oscillations caused by high K_p.

Step-by-Step Tuning Guide (Ziegler-Nichols Manual Approach)

To tune the simulated system effectively, test this standard engineering procedure:

1. Isolate K_p: Set K_i = 0 and K_d = 0. Slowly increase K_p until the system responds quickly without bursting into sustained, violent oscillations.
2. Add K_d to Damp Oscillations: Gradually raise K_d. You will notice the overshoot shrink and the output curve smooth out.
3. Add K_i for Zero Steady-State Error: Increase K_i slightly (e.g., 0.2 − 0.5) to pull the blue line directly onto the red setpoint line, eliminating remaining offset.

Why This Interactive Lab is Valuable for Engineering Students

• Replaces Multi-Lakh Physical Hardware: Premier institutes use physical rotary inverted pendulums or motor control benches costing ₹5 Lakhs to ₹15 Lakhs to teach control theory. This web tool delivers identical mathematical behavior (100% free) using client-side differential equation solving.
• Bridges Theory and Intuition: Students often learn PID through complex Laplace transforms H(s) = Kp + (Ki / s) + Kds. By manipulating live sliders, abstract calculus transforms into immediate physical visual feedback.
• Direct Metrics Tracking: Automatically calculates key control metrics used in industry:
  • Peak Overshoot (%): Maximum percentage the system exceeds the target.
  • Rise Time (s): Time taken to go from 10% to 90% of the target.
  • Settling Time (s): Time taken to stabilize within 2% of the setpoint.
  • Steady-State Error: Final offset between position and target.

Target Engineering Streams

This lab provides practical experience for students across several engineering departments: