Question 1

Why is the inverted pendulum unstable and how does LQR control stabilize it?

Accepted Answer

The inverted pendulum is unstable because the linearized system has a positive eigenvalue meaning any small disturbance grows exponentially. The LQR controller applies a horizontal force F on the cart that is proportional to the state vector F equals negative K times theta theta dot x x dot. The gain vector K is chosen to minimize a quadratic cost balancing control effort against state deviation making all closed loop eigenvalues negative and the system stable.

Question 2

What are the equations of motion for the cart-pole system?

Accepted Answer

The cart-pole equations come from Newton second law applied to the coupled system. The mass matrix form is M plus m times x double dot minus m l cosine theta times theta double dot equals F minus b x dot minus m l sine theta times theta dot squared. The second equation is negative m l cosine theta times x double dot plus I plus m l squared times theta double dot equals m g l sine theta. Inverting the mass matrix gives explicit formulas for x double dot and theta double dot.

Menu

⭐ Popular Tools

🕒 Recently Used

📁 All Categories

Quick Links

Support

Cart-Pole (Inverted Pendulum with LQR Control)