A self-erecting single inverted pendulum (SESIP) is one of typical nonlinear systems. The control scheme running the SESIP consists of two main control loops. Namely, these control loops are swing-up controller and stabilization controller. A swing-up controller of an inverted pendulum system must actuate the pendulum from the stable position. While a stabilization controller must stand the pen...

Inverted pendulum system is a complicated, unstable and multivariable nonlinear system. In order to control the angle and displacement of inverted pendulum system effectively, a novel double-loop digital PID control strategy is presented in this paper. Based on impulse transfer function, the model of the single linear inverted pendulum system is divided into two parts according to the controlle...

The balancing of an inverted pendulum by moving a cart along a horizontal track is a classic problem in the area of control. This paper describes two Neural Network controllers to swing a pendulum attached to a cart from an initial downwards position to an upright position and maintain that state. Both controllers are able to learn the demonstrated behavior which was swinging up and balancing t...

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...

In this paper, the feasibility of a Control Moment Gyroscope (CMG) as balance assistance device is investigated. An inverted pendulum is used as experimental set-up. Our initial results show that it is possible to maintain balance within a 4 degrees range from vertical.

State-space methods are well adapted for solving stabilization problems. In the linear multivariable case, when the poles are placed, some degrees of freedom are left which can be used to place some zeros in the transfer functions from the perturbations to the outputs, called regulation zeros, to reject some perturbations. It is therefore interesting to use a suitable representation to compute ...

This paper analyzes the comfort of wheelchair users when a sliding-mode trajectory-tracking controller is used. The transmission of the horizontal (fore-and-aft) vibration to the head-neck complex (HNC) in the seated human body may cause unacceptable discomfort and motion sickness. A double-inverted pendulum model with two degrees of freedom is considered as a model for the HNC. The user comfor...

This note describes two problems related to the digital implementation of control laws in the infinite dimensional family of matching control laws, namely state estimation and sampled data induced error. The entire family of control laws is written for an inverted pendulum cart. Numerical simulations which include sampled data and a state estimator are presented for one of the control laws in t...