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.

Arun D. Mahindrakar

Department of Electrical Engineering

Feedback

Linear matrix inequalities

Lyapunov functions

CONSTRAINED STABILIZATION

INPUT-OUTPUT LINEARIZATION

INVARIANT SET

State constraints

Feedback linearization

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IIT Madras

International Journal of Robust and Nonlinear Control

The problem of asymptotic stabilization of the cart on an asymmetric-beam system (CaB) is addressed and solved. This system captures the essential features of state-constrained stabilization while being underactuated. The control problem is solved through the Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) methodology. It is noticeable that considering the asymmetry of the beam makes the system quite challenging to be solved since, the solution with a constant inertia matrix reported so far is no longer valid. The performance of the control law is demonstrated through simulations. © 2014 IEEE.

2014 IEEE Conference on Control Applications, CCA 2014

Constrained stabilization of a cart on an asymmetric-beam system through IDA-PBC

In this paper, we present a constructive method for the design of any order sliding surface using the necessary conditions for the existence of sliding surfaces for single-input affine nonlinear control systems. These conditions are a set of PDEs whose general solution will help in arriving at the sliding surfaces. The constructive design procedure is demonstrated on the cart-beam system to obtain a third-order sliding surface and on the inertia wheel pendulum system to obtain a fourth-order sliding surface. We validate the fourth-order terminal sliding mode control on inertia wheel pendulum with experimental result. © 2011 IFAC.

IFAC Proceedings Volumes (IFAC-PapersOnline)

A constructive method for designing higher order sliding surfaces for single-input nonlinear system

We propose an output feedback second-order sliding mode controller to stabilize the cart on a beam system. A second-order sliding mode controller is designed using a Lyapunov function-based switching surface and finite-time controllers, while the state estimator is designed based on the Luenberger-like observer. The proposed observer extends the applicability of Luenberger-like observer to nonlinear systems that are not input-output linearizable, but can be approximately input-output linearized. The approximation is based on the physical property of the system, wherein certain terms in the total energy are neglected. Extensive numerical simulations validate the robustness of the proposed controller to parametric uncertainties using estimated states. © 2009 John Wiley & Sons, Ltd.

Output feedback second-order sliding mode control of the cart on a beam system

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.

Journal	International Journal of Robust and Nonlinear Control
ISSN	10498923
Open Access	No