How to Ride a Swinging Pendulum

Swinging up a pendulum by energy control

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.

When to start antiretroviral therapy: a swinging pendulum?

Although early initiation of antiretroviral treatment has long been associated with some benefit over later initiation, the magnitude of the benefit is becoming better defined with longer follow-up of large numbers of patients in cohort studies. These benefits have become more evident in part because of improvements in efficacy, tolerability, and convenience of antiretroviral treatment regimens...

Asymptomatic hyperparathyroidism: is the pendulum swinging back?

Treatment of the menopause: the swinging pendulum

Facts and views on the treatment of the menopause underwent dramatic swings during the last fifty years, from a non-issue fifty years ago to a must for the well-being of all postmenopausal women at the end of the 20 century. the enthusiasm for hormone replacement therapy (hRt) was smashed in 2002, after the publication of a large-scale prospective randomised study, the Whi trial, on health cost...

A family of smooth controllers for swinging up a pendulum

The paper presents a new family of controllers for swinging up a pendulum. The swinging up of the pendulum is derived from physical arguments based on two ideas: shaping the Hamiltonian for a system without damping; and providing damping or energy pumping in relevant regions of the state space. A family of simple smooth controllers without switches with nice properties is obtained. The main res...