Inverted pendulum stabilization by means of fractional order PID controllers

摘要

A simulated study of three different control strategies to stabilize an inverted pendulum on a cart is presented in this paper. Linear Quadratic Regulator (LQR), Integer order PID (IOPID) and Fractional order PID (FOPID) are designed, applied and compared. A nonlinear model of the cart-pendulum system is first derived and used later in the simulation of the control strategies aforementioned. The tuning parameters of all three controllers are obtained using Particle Swarm Optimization (PSO) technique, using the Integral of the Squared Error (ISE) index as fitting function, when a sequence of step reference inputs is applied. The simulation results, when applying a sequence of step references, show a better performance for the LQR, when using the cost function of the LQR as performance index. However, in the more general case of a sinusoidal references, the FOPID is the one that exhibits the best behavior.