Proportional-Integral-Derivative Control

A classic feedback controller that combines the current error, its accumulated history, and its rate of change into one output.

PID control is the most widely used feedback control method; Minorsky gave it a formal control law in 1922 while studying automatic steering for U.S. Navy ships. The control output is u = Kp·e + Ki·∫e dt + Kd·de/dt, where e is the target value minus the measured value (the error), and Kp, Ki, Kd are three gains to be tuned. The proportional term responds to the current error; the integral term accumulates past error, eliminating the steady-state error that proportional action alone would leave behind; the derivative term looks at how fast the error is changing, providing damping that reduces overshoot but can also amplify measurement noise. Dropping the integral term gives PD control, and dropping the derivative term gives PI control. PID shows up in joint motors, camera gimbals, and drone attitude loops; reinforcement-learning locomotion policies typically output only target joint angles, which a lower-level PD controller converts into torque. When the motor's output is already saturated at its limit but the integral term keeps accumulating anyway, the result is pronounced overshoot — a problem called integral windup, which needs anti-windup handling.

ExampleA robot arm joint needs to reach 30° and is currently at 25°: the P term pushes based on the 5° error; if gravity keeps it stuck at 29.5° short of the target, the I term keeps accumulating that 0.5° gap until it's closed; as the joint nears the target, the D term sees the error shrinking fast and eases off early, preventing overshoot past 30°.

Also called

PID, PID Control, PID Controller

Related

Proportional-Derivative Control · Cascade Control · Stiffness and Damping Gains · Integral Windup / Anti-windup · Step Response Metrics (Overshoot / Settling Time / Steady-State Error) · Position Control

Sources

Wikipedia: Proportional–integral–derivative controller
legged_gym legged_robot_config.py（PD 刚度/阻尼与 action_scale 配置） (Chinese)