Inverted Pendulum Simulator

Cart-pole (inverted pendulum) with PID control. Watch the pendulum balance upright on a moving cart, tune the controller, or destabilize it with a kick to see how the controller recovers.

RK4 integrator, substepped at 0.5 ms, runs entirely in the browser.

Cart-Pole Animation

Cart position x Reference (target x) Pole Control force F

Time-Series Response

Cart x (m) Setpoint (m) Pole angle (deg) Control F (N)

0.000

theta

0.0

deg

0.00

|theta|max

0.0

peak (deg)

Cart and Pole Parameters

Cart mass M 2.0 kg

Pole mass m 0.2 kg

Half-length L 0.5 m

Cart friction b_cart 0.1

Pivot friction b_pivot 0.01

PID Gains

Kp 50

Ki 0

Kd 10

N (deriv filter) 20

Fmax (control saturation) 30 N

Equations of Motion

The cart-pole has four state variables: cart position x, cart velocity v, pole angle theta (0 = straight up), and pole angular velocity omega. The PID controller drives the cart to a setpoint x_ref = 0.

Cite this tool: Li, H. (2026). Inverted Pendulum Simulator. https://hongbinli.ca/tools/inverted-pendulum-simulator