What is the Cart-Pole Control Design multi-solver?

Cart-Pole Control Design is a guided workflow that chains 2 individual PolySim solvers into one end-to-end analysis, piping each result into the next step.

Yes. Every step runs entirely in your browser using real numerics — no install, no account, no cloud cost. Custom or private solver packs are available as a paid service.

Controls & Robotics Pack · Multi-Solver

Cart-Pole Control Design

Balance & robustness. This multi-solver chains 2 solvers into a single guided workflow — run each step in order and carry the result forward.

Workflow steps

cart-pole
→pid-control

or unlock everything with Pro →

Cart Pole

open full solver →

Cart-Pole BalanceLive

inverted pendulum control

Controls

Speed1×

Presets

Controller gain

Disturbance

Controller on

Balancing a pole on a moving cart is the classic control benchmark. A state-feedback controller senses the pole angle and cart position and pushes the cart to keep the pole upright. Turn the controller off and it topples instantly; add disturbance to test how hard it can fight back.

▶ Run in Python

Data Inspector

Pole angle8.6°

Cart position0.00

Statusbalanced

Governing equation

F = - K x = 1.0 (55 θ + 12 \dot{θ} + 1.5 x + 3 \overset{x}{˙})

Reading this result: The state-feedback law F = -K·state pushes the cart under the falling pole; with gain above the disturbance it recovers from each nudge.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

↓

PID Control

open full solver →

PID ControllerLive

step response tuning

Controls

Presets

Proportional Kp

Integral Ki

Derivative Kd

A PID controller drives a system to its setpoint using three terms: proportional reacts to the current error, integral eliminates steady-state offset, and derivative damps overshoot. Tuning the three gains trades off speed, overshoot, and stability — the workhorse of industrial control.

▶ Run in Python

Data Inspector

Overshoot0%

Settling time0.00 s

Steady-state error0.000

Governing equation

u (t) = 4.0 e (t) + 1.00 \int e d t + 0.5 \frac{d e}{d t}

Reading this result: Balanced gains — proportional for speed, integral to remove offset, derivative to damp overshoot: the textbook well-tuned response.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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More in the Controls & Robotics pack

Robot Arm Controller Drone Autopilot Mobile Robot Navigation Servo Tuning Kit DSP Pipeline State Estimator Motion Profile Generator Vibration Control

Frequently asked questions

What is the Cart-Pole Control Design multi-solver?: Cart-Pole Control Design is a guided workflow that chains 2 individual PolySim solvers into one end-to-end analysis, piping each result into the next step.
Is it free to use?: Yes. Every step runs entirely in your browser using real numerics — no install, no account, no cloud cost. Custom or private solver packs are available as a paid service.