Modeling and Control of a Double Inverted Pendulum using LQR with Parameter Optimization through GA and PSO

An inverted pendulum system has potential applications in different domains that motivate researchers for new innovative development. An inverted pendulum system is an underactuated, nonlinear, inherently unstable and a multivariable system. The system is modelled mainly through either Euler-Lagrange or Newtonian dynamic formulation. This paper aims to examine the control of a double inverted pendulum (DIP) using pole placement and linear quadratic regulator (LQR) control. To find the optimal parameters of the LQR control law, Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) are used to tune and determine the proper control parameters. Simulations are conducted using MATLAB/Simulink under different circumstances and the performance of each control technique is analyzed and compared in terms of the system rise time, settling time, peak amplitude, and steady state error.