Modeling and Control of a Double Inverted Pendulum on a Cart With PSO-Based Parameter Optimization

The inverted pendulum system, known for its applications across various domains, continues to inspire innovative research owing to its underactuated, nonlinear, inherently un-stable, and multivariable nature. Typically modeled using Euler-Lagrange or Newtonian dynamics, this study focuses on control-ling a Double Inverted Pendulum (DIP) through pole placement, Linear Quadratic Regulator (LQR), and Lyapunov-based control methods. To optimize the LQR control parameters, Particle Swarm Optimization (PSO) is employed. The proposed control approach involves the application of linear control design to a nonlinear system. To illustrate the efficacy of the proposed control strategy, many simulations under diverse condition (comparing the performance of each control technique based on the system rise time, settling time, peak amplitude, and steady-state error) with an 2D animation using Matplotlib© in Python are given.