Transient Response Oscilloscope (Target vs Physical vs Filtered)
● Target Angle ● Real Arm ● Sensor/Filtered
System Telemetry Proof
Settling Time
1.12 s
Peak Overshoot
2.4 %
Steady-State Err
0.14°
Stability State
STABLE
Feedback Control Theory vs Intuition
Mathematical Feedback Control (PID)
Unlike linear heuristic guesswork, dynamic robotic actuators require precise error formulation: u(t) = Kp·e(t) + Ki·∫e(t)dt + Kd·(de/dt). Proportional gain drives the primary recovery force, Integral gain eliminates steady-state gravitational droop, and Derivative gain acts as virtual dynamic damping to quell overshoot.
Kalman Sensor Filtering
Physical joint encoders suffer from high-frequency structural vibration and electrical noise. A 1D Discrete Kalman Filter dynamically estimates the true angular state by recursively combining a physical motion model prediction with noisy Gaussian measurements, isolating target trajectory signals from environmental disturbance.