📖 How to Use
🎯 Getting Started
This simulator helps you understand how Proportional (P), Integral (I), and Derivative (D) gains affect a control system's behavior:
- Set Point: The target value your system is trying to reach
- Process Type: Choose between temperature, motor speed, liquid level, or define your own custom process
- PID Gains: Adjust P, I, and D sliders to tune the controller, or select a preset from the dropdown
- Simulation: Click "Start" to see how the system responds (or use ⚡ Instant mode for immediate results)
🧮 PID Controller Basics
A PID controller calculates an error correction using three terms:
- Proportional (P): Reacts to the current error. Higher P = faster response but may overshoot.
- Integral (I): Eliminates steady-state error by accumulating past errors. Too much causes oscillation.
- Derivative (D): Predicts future error based on rate of change. Reduces overshoot and dampens oscillations.
Output = Kp×e(t) + Ki×∫e(t)dt + Kd×de(t)/dt
📊 Performance Metrics
The simulator automatically calculates key performance indicators:
- Rise Time: Time to reach 90% of set point (faster is better)
- Overshoot: Maximum percentage above set point (lower is better)
- Settling Time: Time to stay within ±2% of set point (faster is better)
- Steady-State Error: Final error after system stabilizes (should be near zero)
🎛️ Tuning Guidelines
Start with P only: Set I and D to zero, increase P until system oscillates, then reduce by 50%.
Add I term: Gradually increase I to eliminate steady-state error. Stop if oscillations appear.
Add D term: Increase D to reduce overshoot and dampen oscillations.
💡 Each process type has different characteristics - experiment with different combinations!
🔧 Process Types
- Temperature Control: Slow response, high inertia (like an oven or heater)
- Motor Speed Control: Medium response, moderate inertia
- Liquid Level Control: Fast response, low inertia (like a tank with valve)
- Custom Process: Define your own system dynamics with custom gain (K) and time constant (τ)
⚙️ Custom Process Model
The first-order process model uses:
dPV/dt = (K × u - PV) / τ
- K (Gain): How strongly the output responds to input (0.1-5.0)
- τ (Time Constant): How quickly the system responds in seconds (0.5-20.0)
💡 Try K=1.0, τ=5.0 as a starting point, then experiment!