European Journal of Control (2010)4:341–342 © 2010 EUCA Discussion on: “Stabilization of the Experimental Cart-Pendulum System with Proven Domain of Attraction”g (original) (raw)

A control strategy for the cart-pendulum system

2004

In this paper, a new control law for the pendulum on a cart is presented. The law has two parts: first, an energy-shaping law is able to swing the pendulum and to maintain in. The second part introduces additional control to stop the cart and it is based on control with bounded inputs.

On the Stabilization of the Inverted-Cart Pendulum Using the Saturation Function Approach

Mathematical Problems in Engineering, 2011

A simple stabilizing controller for the cart-pendulum system is designed in this paper. Our control strategy describes the underactuated system as a chain of integrators with a high-order smooth nonlinear perturbation and assumes initialization of the system in the upper half plane. The design procedure involves two sequentially associated control actions: one linear and one bounded quasilinear. The first control action brings the nonactuated coordinate near to the upright position and keeps it inside of a well-characterized small vicinity, whereas the second control action asymptotically brings the whole state of the system to the origin. The corresponding closed-loop stability analysis uses standard linear stability arguments as well as the traditional Lyapunov method and the LaSalle's theorem. Our proposed control law ensures global stability of the system in the upper half plane. We illustrate the effectiveness of the proposed control strategy via numerical simulations.

A new controller for the inverted pendulum on a cart

International Journal of Robust and Nonlinear Control, 2008

This paper presents a complete solution to the problem of swinging-up and stabilization of the inverted pendulum on a cart, with a single control law. The resulting law has two parts: first, an energy-shaping law is able to swing and maintain the pendulum up. Then, the second part introduces additional control to stop the cart and it is based on forwarding control with bounded input. The resulting control law is the sum of both parts and does not commute between different laws although there exist switches inside the controller.

Robust stabilization of a triple inverted pendulum cart

Design of a robust computer control system for balancing a triple pendulum mounted on a moving cart is considered. The controller is based on Discrete-time linear regulator theory implemented via a 'robust' reduced order observer. The use of integral action eliminates effects of small constant sensor offsets and rail inclinations. Relative stability and disturbance attenuation properties are investigated using frequency response methods. Experimental results are included.

Implementation of a Controller to Eliminate the Limit Cycle in the Inverted Pendulum on a Cart

Complexity, 2019

A frequency response-based linear controller is implemented to regulate the inverted pendulum on a cart at the inverted position. The objective is to improve the performance of the control system by eliminating the limit cycle generated by the dead-zone, induced by static friction, at the actuator of the mechanism. This control strategy has been recently introduced and applied by the authors to eliminate the limit cycle in the Furuta pendulum and the pendubot systems. Hence, the main aim of the present paper is to study the applicability of the control strategy to eliminate the limit cycle in the inverted pendulum on a cart. The successful results that are obtained in experiments corroborate that the approach introduced by the authors to eliminate the limit cycle in the Furuta pendulum and pendubot is also valid for the inverted pendulum on a cart.

Control of the Double Inverted Pendulum on a Cart Using the Natural Motion

Acta Polytechnica, 2013

This paper deals with controlling the swing-up motion of the double pendulum on a cart using a novel control. The system control is based on finding a feasible trajectory connecting the equilibrium positions from which the eigenfrequencies of the system are determined. Then the system is controlled during the motion between the equilibrium positions by the special harmonic excitation at the system resonances. Around the two equilibrium positions, the trajectory is stabilized by the nonlinear quadratic regulator NQR (also known as SDRE-the State Dependent Riccati Equation). These together form the control between the equilibrium positions demonstrated on the double pendulum on a cart.

Tracking trajectories of the cart-pendulum system

Automatica, 2003

The problem of tracking a periodic trajectory of the well-known cart-pendulum system is solved. After a change of coordinates and a change of feedback, the equations of this system are nonlinear but feedforward. This property is extensively used to carry out for this system the design of uniformly asymptotically stabilizing time-varying state feedbacks by using the forwarding approach.

Lyapunov-Based Controller for the Inverted Pendulum Cart System

Nonlinear Dynamics, 2005

Abstract. A nonlinear control force is presented to stabilize the under-actuated inverted pendulum mounted on a cart. The control strategy is based on partial feedback linearization, in a first stage, to linearize only the actuated coordinate of the inverted pendulum, and then, a ...

Global stabilization of an inverted pendulum–Control strategy and experimental verification

Automatica, 2009

The problem of swinging up an inverted pendulum on a cart and controlling it around the upright position has traditionally been treated as two separate problems. This paper proposes a control strategy that is globally asymptotically stable under actuator saturation and, in addition, locally exponentially stable. The proposed methodology, which performs swing up and control simultaneously, uses elements from input-output linearization, energy control, and singular perturbation theory. Experimental results on a laboratory-scale setup are presented to illustrate the approach and its implementation.

Analyzing and Designing Control System for an Inverted Pendulum on a Cart

It is a collection of MATLAB functions and scripts, and SIMULINK models, useful for analyzing Inverted Pendulum System and designing Control System for it. Automatic control is a growing field of study in the field of Mechanical Engineering. This covers the proportional, integral and derivative (PID). The principal reason for its popularity is its nonlinear and unstable control. The reports begin with an outline of research into inverted pendulum design system and along with mathematical model formation. This will present introduction and review of the system. Here one dimensional inverted pendulum is analyzed for simulating in MATLAB environment. Control of Inverted Pendulum is a Control Engineering project based on the flight simulation of rocket or missile during the initial stages of flight. The aim of this study is to stabilize the Inverted Pendulum such that the position of the carriage on the track is controlled quickly and accurately so that the pendulum is always erected in its inverted position during such movements. Introduction An inverted pendulum is a pendulum which has its center of mass above its pivot point (Said,L., Latifa, B.,, 2012). It is often implemented with the pivot point mounted on a cart that can move horizontally and may be called a cart and pole. Most applications limit the pendulum to 1 degree of freedom by affixing the pole to an axis of rotation. Whereas a normal pendulum is stable when hanging downwards, an inverted pendulum is inherently unstable, and must be actively balanced in order to remain upright; this can be done either by applying a torque at the pivot point, by moving the pivot point horizontally as part of a feedback system, changing the rate of rotation of a mass mounted on the pendulum on an axis parallel to the pivot axis and thereby generating a net torque on the pendulum, or by oscillating the pivot