PID Controller Balance Lab

[Pt] PID Controller Balance Lab lets students experience closed-loop feedback control first-hand. A metallic ball rolls along a tilting beam driven by twin end thrusters while a real-time scrolling chart plots the target setpoint r(t) (green) against the actual ball position x(t) (gold). The controller continuously measures position error e(t) = r − x(t) and computes thruster command u(t) = Kp·e + Ki∫e dt + Kd(de/dt). By dragging the setpoint ring along the beam or kicking the ball, learners discover why pure Proportional control oscillates endlessly, how Derivative gain Kd acts as a predictive brake to damp overshoot, and how Integral gain Ki eliminates steady-state trim offset.

• [Pt] Set Ki = 0 and Kd = 0 while keeping Kp = 6, then drag the green setpoint ring and watch the ball oscillate back and forth without damping.
• [Pt] Raise Derivative gain Kd to 4.0 and observe how the controller brakes the beam tilt before the ball crosses the setpoint, eliminating overshoot.
• [Pt] Set Ki = 0 with Kp = 4 and Kd = 3.5 and notice the small Steady-State Offset readout caused by gravity trim bias, then raise Ki to 1.0 to pull the error to 0.00 m.
• [Pt] Click the ball or press Disturbance kick to apply a sudden velocity impulse and test how quickly your tuned PID loop recovers.
• [Pt] Drag the green target ring rapidly between the left and right ends of the beam to test step-response rise time and peak overshoot.

1. 1[Pt] Define position error e(t) = r(t) − x(t) in a closed-loop feedback control system.
2. 2[Pt] Explain the physical role of each PID term: Proportional stiffness (Kp), Integral bias elimination (Ki), and Derivative damping (Kd).
3. 3[Pt] Analyze step-response metrics including rise time, peak overshoot percentage, settling time, and steady-state error.
4. 4[Pt] Tune a three-term PID controller to achieve fast, critically damped stabilization after an external disturbance.

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