PID Joint Control

Proportional Kp 6.0

Integral Ki 1.0

Derivative Kd 1.2

Setpoint angle 45°

Error e(t)

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Output u(t)

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Overshoot

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Settled

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How it works

A robot joint is driven toward a commanded setpoint by comparing its current angle to the target and feeding the error through a PID controller. The proportional term reacts to the error right now, the integral term accumulates past error to erase steady-state offset, and the derivative term reacts to how fast the error is changing to damp overshoot before it happens.

e(t) = setpoint − θ(t)
u(t) = Kp·e(t) + Ki·∫e(t)dt + Kd·de/dt
α = (u − b·ω) / I,  ω += α·dt,  θ += ω·dt

Kp — proportional gain; higher values snap toward the setpoint faster but ring more.
Ki — integral gain; eliminates any lingering steady-state error, but too much causes slow oscillation ("integral windup").
Kd — derivative gain; anticipates the rate of change and damps overshoot, but amplifies sensor noise if pushed too high.
Disturbance kick — injects a sudden external torque (like a bumped arm) so you can see how the controller rejects a real-world upset.

Real-world relevance: this is the same feedback loop that runs on the motor controller of every joint in an industrial or service robot arm, tuned per-joint against its own inertia and load.

Setpoint Joint angle θ(t) Control output u(t)