Performance Analysis and Implementation of Fractional Order 2-DOF Control on Cart–Inverted Pendulum System

Abstract

Analysis of a typical cart-inverted pendulum system is very effective to evaluate and perceive the significant control strategies including various aspects of control engineering with vast application in industrial robots. The system is nonminimum-phase highly unstable nonlinear with a single input voltage to the dc motor providing two outputs, i.e., cart position and pendulum angle. Based on its mathematical model comprising of two loops dispensing two outputs following a single reference input, the control method is proposed. Here, the inner primary loop is regulating the pendulum angle, while the outer secondary loop is steering the position of the cart on the rail. A robust control is achieved by the fractional-order (FO)-PI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</sup> D <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</sup> controller, which allows one to have auxiliary tuning parameters compared with the classical one. Furthermore, this is extended to FO two degrees of freedom allowing improvement in the transient response with this additional flexibility in design while maintaining adequate loop robustness. The simulation and experimental results are demonstrated to quantify the performance improvement attained. This verifies the effectiveness of the approach made minimizing significantly the oscillations in the output response.