Intelligent control for swing up and balancing of an inverted pendulum system

Adaptive fuzzy control: experiments and comparative analyses

“…To do this, we use a first-order backward difference approximation of the derivative. As tested in [31], this estimation method turns out to be very reliable and accurate. Thus, for the rest of the discussion, it will be assumed that all states are directly available for the controllers without need of further estimation.…”

“…The experimental setup used in this paper was developed in [31] and [32], where a nonlinear mathematical model of the system was obtained via identification techniques, and four different control methods were applied: proportional derivative control, linear quadratic regulation, direct fuzzy control, and autotuned fuzzy control.…”

“…1 (taken from [31]). It consists of three principal parts: the pendulum itself (controlled object), interface circuits, and the controller, implemented by means of a program in a digital computer.…”

“…As detailed in [31], the rotational pendulum system presents two somewhat separate problems: first, a controller needs to be designed that is able to balance the pendulum, and second, an adequate algorithm has to be used to swing up the pendulum so that when it reaches an upright position (i.e., where ) its angular velocity ( ) is close to zero. This facilitates the job of the controller which "catches" the pendulum and tries to balance it.…”

“…In this paper, we will not be concerned with swing-up details, and will concentrate only on the balancing control of the pendulum. The so-called "simple energy pumping" swing-up algorithm developed in [31] 4 will be used without changes in all the experiments and 4 Please consult this reference for details on the swing-up algorithm.…”