LQR Algorithm Simulation and MATLAB Source Code for Double Inverted Pendulum

Regarding the LQR algorithm simulation and MATLAB source code for Googol Technology's double inverted pendulum system, we can delve into its implementation methodology. The inverted pendulum control problem represents a classic control challenge that has garnered significant attention in recent years. The primary objective is to maintain a pendulum rod in an upright vertical position, where it remains in equilibrium. However, due to physical constraints, the rod cannot sustain this vertical position indefinitely. Therefore, a control system must be designed to stabilize the pendulum in its upright position. The Linear Quadratic Regulator (LQR) algorithm serves as a widely adopted control method capable of achieving excellent control performance. Through simulation and MATLAB source code analysis, we can better understand both the control problem and the implementation process of the LQR algorithm. Key implementation aspects include: - Mathematical modeling of the double inverted pendulum system dynamics - State-space representation formulation for controller design - LQR weight matrix selection (Q and R matrices) for optimal performance - Implementation of real-time control algorithms using MATLAB's control system toolbox - Simulation of system response under various initial conditions The MATLAB source code typically involves functions like lqr() for gain calculation, ode45 for system simulation, and custom functions for pendulum dynamics implementation.