Pendulum Lab

PallaS

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About this app

Pendulum Lab is an interactive, visual simulation engine designed for engineering students, educators, and control systems enthusiasts. Explore the fundamentals of classical and modern control theory by stabilizing an inverted pendulum on a cart in real time.
Bridge the gap between differential equations and real-world engineering through tactile, hands-on visual feedback.
🔑 Key Features
🕹️Direct Touch & Interactive Physics
• Flick to Disturb: Tap or swipe directly on the pendulum canvas to apply user-defined impulse forces and test controller disturbance rejection.
• Real-time ODE Integration: High-precision physics solver running continuous nonlinear equations of motion at 60 FPS.
• Adjustable Plant Parameters: Modify cart mass ($M$), pendulum length ($l$), rod mass ($m$), and friction coefficients on the fly.
🎛️ Classical & Modern Control Algorithms
• PID & Cascaded PID: Tune Proportional, Integral, and Derivative gains. Learn why simple PID fails and how cascaded angle-position loops solve cart drift.
• State-Space & LQR: Design Linear Quadratic Regulators by adjusting state weighting ($Q$) and control effort ($R$) matrices.
• Advanced Control Strategies: Experiment with robust, sliding mode, and adaptive control algorithms to handle unmodeled system dynamics.
📊Dynamic Real-Time Visualization
• Live Oscilloscope Graphs: Track angle error ($\theta$), cart displacement ($x$), and control effort output ($u$) simultaneously.
• Phase Portraits: Plot angular velocity ($\dot{\theta}$) against angle ($\theta$) to visual stability regions, limit cycles, and system attractors.
• Impulse Markers: Visual force vector arrows and chart event flags trigger the instant you touch the screen.
⚠️ Real-World Hardware Imperfections
Switch on practical engineering constraints to see how real controllers react outside ideal math:
• Actuator Saturation & Integral Windup: Set maximum motor torque limits.
• Sensor Noise: Inject Gaussian noise into state measurements to test derivative filter performance.
• Sampling Latency: Lower loop update rates (10 Hz – 100 Hz) to analyze discretization effects.
🎓Who Is Pendulum Lab For?
• Electrical, Mechanical, & Mechatronics Engineers learning feedback control theory.
• Professors & Educators looking for an intuitive visual aid for lectures and lab demonstrations.
• Robotics Enthusiasts & Developers experimenting with control algorithm design on mobile.
Download Pendulum Lab today and turn complex control system mathematics into an interactive, visual playground!

What’s new

Update 23 October 2026