Robotics & Control

Advanced

PID Controller

Control output from proportional, integral and derivative of the error.

Formula

u(t) = K_p e + K_i \!\int e\,dt + K_d \frac{de}{dt}

Variables

uControl output

eError

K_pProportional gain

K_iIntegral gain

K_dDerivative gain

Example

Tuning K_p, K_i, K_d balances speed, overshoot and stability.

Did You Know?

PID control dates to ship autopilots of the 1920s and still runs the vast majority of industrial systems today.

robotics pid control

Share this formula

More in Robotics & Control

Degrees of Freedom

Independent motions of a mechanism from bodies and constraints.

Gear Reduction Torque

Output torque after gear reduction, allowing for efficiency.

Encoder Resolution

Smallest angle a rotary encoder can resolve.

DC Motor Torque

Torque of a DC motor is proportional to current.

Motor Back-EMF

Voltage a spinning motor generates against its supply.

Forward Kinematics (2-Link)

End-effector position from joint angles of a two-link arm.