This paper deals with the stabilization of an under-actuated circular ball-and-beam system with constraints on the beam angle, ball traverse and the torque input. The constraints are formulated as a set of LMI's and a feedback control law is synthesized to maximize the basin of attraction of the unstable equilibrium. Simulation results are used to validate the proposed control strategy. © 2008 IEEE.

Arun D. Mahindrakar

Department of Electrical Engineering

BALL AND BEAM SYSTEMS

BASIN OF ATTRACTION

BEAM ANGLE

Control strategies

Feedback control law

Simulation result

State constraints

Underactuated

Control theory

Cybernetics

Feedback

Linear control systems

Stabilization

Linear matrix inequalities

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IIT Madras

Stabilization of a circular ball-and-beam system with input and state constraints using linear matrix inequalities

Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics

The ball on a circular beam system is an under-actuated mechanical system that is challenging control problem compared to its variant: the ball on a horizontal beam. The control challenge stems out from the fact that the ball on a circular beam system has two unstable eigenvalues unlike its variant which has one. A stabilizing controller synthesized using backstepping methodology is presented. In doing so, a series of nonlinear coordinate transformations is applied on the equations of motion to arrive at a state-space representation which is in the so called quadratic non-triangular normal form. Simulation results are presented to demonstrate the effectiveness of the proposed controller in stabilizing the system while respecting the physical constraints on the system. ©2010 IEEE.

11th International Conference on Control, Automation, Robotics and Vision, ICARCV 2010

Stabilization of a circular ball-and-beam system

We present nonlinear control techniques to stabilize a beam-balance system with state constraints. We consider two different actuator configurations: the first one is actuated by a cart moving on the beam, while in the second case, the actuation is by a single electromagnet. In the first case, the constrained stabilization problem is solved via an output feedback controller designed using feedback linearization, Luenberger-like observer and linear matrix inequality based optimization. In the second case, a Lyapunov-based controller is proposed that takes care of both the input and state constraints. Copyright © 2007 John Wiley & Sons, Ltd.

International Journal of Robust and Nonlinear Control

State-constrained stabilization of beam-balance systems

2007 European Control Conference (ECC)

An original circular ball-and-beam system: Stabilization strategy under saturating control with large basin of attraction

Journal of Dynamic Systems, Measurement, and Control

Constrained Control Design for Magnetic Bearing Systems

Systems & Control Letters

On enlarging the basin of attraction for linear systems under saturated linear feedback

Automatica

Set invariance in control

Journal	Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics
ISSN	1062922X
Open Access	No