This paper concerns active vibration damping of a frictionless physical inverted pendulum with a radially moving mass. The motion of the inverted pendulum is restricted to an admissible set. The proposed Proportional Derivative linear controller damps the inverted pendulum (which is anchored by a torsion spring to keep it in a stable upright position), excerting a force on the radially moving m...

In this paper, we will propose a nonlinear passivity based controller fur a double inverted pendulum system, consisting of a two-link pendulum mounted on a pad which is moved by a linear induction motor so that the double pendulum points straight-up The proposed controller nut only can drive the double pendulum from its “natural stable hanging position” tu its “unstable upright inverted positio...

The Furuta pendulum, or rotational inverted pendulum, is a system found in many control labs. It provides a compact yet impressive platform for control demonstrations and draws the attention of the control community as a platform for the development of non-linear control laws. Despite the popularity of the platform there are very few papers which employ the correct dynamics and only one that de...

The inverted pendulum is a simple system in which both stable and unstable configurations are easily observed. The upward inverted state is unstable, though it has long been known that a simple rigid pendulum can be stabilized against small disturbances in its inverted state by oscillating its pivot in an up-and-down motion. Numerical simulations of the inverted pendulum are employed to investi...

This paper proposes a method of robust optimal stabilization for balance systems such as rocket and missile systems, Segway human transportation systems, and inverted pendulum systems. Constant-gain controllers such as linear-quadratic regulators may not guarantee stability let alone optimality for balance systems affected by parametric variations. The robust stability and robust performance ac...

Forwarding is a tool for constructing stabilizers for nonlinear systems. A key step in this design technique is to find an explicit solution to a partial differential equation (PDE), which may be hard to find—actually, the PDE may even not be solvable at all. In this brief note we show that it is possible to provide an additional degree of freedom for the solution of the aforementioned PDE, hen...

For 3D walking control of a biped robot we analyze the dynamics of a three-dimensional inverted pendulum in which motion i s constrained to move along an arbitrarily defined plane. This analysis leads us a simple linear dynamics, the Three-Dimensional Linear Inverted Pendulum Mode (SD-LIPM). Geometric nature of trajectories under the 3D-LIPM and a method for walking pattern genemtion are discus...

A novel approach to design fuzzy controllers using fuzzy-arithmetic-based Lyapunov function that gives a linguistic description on the plant and the control objective is presented in this paper. An inverted pendulum system is used as a benchmark dynamic nonlinear plant for evaluating the proposed method. It is shown that a set of stable fuzzy control rules can be derived from perception-based i...