Swing-up and stabilization control of double inverted pendulum on a cart
In this project, I derived the system dynamics for an underactuated, highly nonlinear double inverted pendulum on a cart (DIPC) using Lagrangian mechanics and utilized a two-phase control strategy to drive the system from a stable "down-down" initial state to an unstable "up-up" equilibrium. I implemented and compared two different swing-up methods: energy shaping and offline trajectory optimization then used a Linear Model Predictive Controller (MPC) to catch and stabilize the chaotic system once it entered the domain of attraction.
- Energy Shaping (Passivity-Based Control): Utilized input-output feedback linearization and passivity-based control to drive the pendulum's energy to the desired equilibrium level, achieving swing-up in 19.1 seconds.
- Trajectory Optimization (Direct Collocation): Solved a discrete-time nonlinear programming (NLP) optimization problem using trapezoidal direct collocation to generate an optimal pre-computed trajectory, significantly reducing the swing-up time to just 4.26 seconds.
- Linear MPC Regulation: Designed a Linear Model Predictive Controller (LMPC) to stabilize the chaotic dynamics and maintain the desired equilibrium point once the switching conditions were met.
- Dynamics Modeling: Derived the full Equations of Motion (EOMs) using Euler-Lagrange equations and converted them into a compact state-space model for advanced control design.
- Software: MATLAB, Simulink,
- Hardware: N/A
- Concepts: Optimal Control, Linear Model Predictive Control (LMPC), Trajectory Optimization (Direct Collocation), Passivity-Based Control, Feedback Linearization, Lagrangian Mechanics