Model Reference Adaptive vs. Learning Control for the Inverted Pendulum.A Comparative Case Study

Abstract

The Inverted Pendulum system (also called "cart-pole system") is a classic example of a
nonlinear and unstable control system. By controlling the force applied to the cart in the
horizontal direction, the inverted pendulum can be kept in various unstable equilibrium positions
.In this paper we develop a case study where we perform a comparative analysis between a
conventional adaptive control technique using the stability theory of Lyapunov (MRAC - Model
Reference Adaptive Control) and a fuzzy learning control technique (FMRLC - Fuzzy Model
Reference Learning Control). Both control techniques are based on reference models. The term
"learning" is used as opposed to "adaptive" to distinguish the two control structures. In
particular, the distinction is drawn since the FMRLC, which is also a direct model reference
adaptive controller, will tune and to some extent it will remember the values it had tuned in the
past, while the conventional adaptive approach will continue to tune the controller
parameters.The performances of the proposed control algorithms are evaluated and shown by
means of digital simulation.