Swinging up a pendulum by energy control

Abstract

Properties of simple strategies for swinging up an inverted pendulum are discussed. It is shown that the behavior critically depends on the ratio of the maximum acceleration of the pivot to the acceleration of gravity. A comparison of energy-based strategies with minimum time strategy gives interesting insights into the robustness of minimum time solutions.

Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping

“…Our potential shaping approach is inspired by [12] and [28]. Other relevant work involving energy methods in control and stabilization includes [1], [3], [18], [26], [33], [34], [37], [38], and [41]. In [6], we relate the potential shaping approach here to that of [24], [25], and [40].…”

“…The essence of the modification of involves changing the metric tensor that defines the kinetic energy . The tangent bundle can be split into a sum of horizontal and vertical parts defined as follows: for each tangent vector to at a point , we can write a unique decomposition (1) such that the vertical part is tangent to the orbits of the -action and where the horizontal part is the metric orthogonal to the vertical space; that is, it is uniquely defined by requiring the identity (2) where and are arbitrary tangent vectors to at the point . This choice of horizontal space coincides with that given by the mechanical connection (see [30]).…”

“…Otherwise, it will leave , contradicting the invariance of . 1 Note that is an iso-energy trajectory since and so is constant. Since is an isolated maximum of , no iso-energy flows except the equilibrium at can converge to .…”

Grey-box modeling of an inverted pendulum system via identification of a PD-LTI system

“…The family of inverted pendulum systems has been widely used for a benchmark for testing control algorithms, and has been a classic tool in the control laboratories since the 1950s (See [2] and references therein for the history of the pendulum system). Because of nonlinear nature, the pendulum systems have been used for illustrating the idea in nonlinear control and in mechanical systems; see e.g.…”

“…Because of nonlinear nature, the pendulum systems have been used for illustrating the idea in nonlinear control and in mechanical systems; see e.g. [3,4] for global stabilization, andÅström and Furuta [2,5] for swing-up control.…”