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.

Arun D. Mahindrakar

Department of Electrical Engineering

Design

Nonlinear control systems

Sliding mode control

Wheels

CART-BEAM

CONSTRUCTIVE DESIGN

CONSTRUCTIVE METHODS

Fourth order

General solutions

INERTIA WHEEL PENDULUM

Sliding surface

TERMINAL SLIDING MODE CONTROL

Pendulums

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IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

A Constructive Method for Designing Higher Order Sliding Surfaces for Single-input Nonlinear System

IFAC Proceedings Volumes (IFAC-PapersOnline)

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.

International Journal of Robust and Nonlinear Control

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

In this paper, we present a sliding mode control algorithm to robustly stabilize a class of underactuated mechanical systems that are not linearly controllable and violate Brockett's necessary condition for smooth asymptotic stabilization of the equilibrium, with parametric uncertainties. In defining the class of systems, a few simplifying assumptions are made on the structure of the dynamics; in particular, the damping forces are assumed to be linear in velocities. We first propose a switching surface design for this class of systems, and subsequently, a switched algorithm to reach this surface in finite time using conventional and higher order sliding mode controllers. The stability of the closed-loop system is investigated with an undefined relative degree of the sliding functions. The controller gains are designed such that the controller stabilizes the actual system with parametric uncertainty. The proposed control algorithm is applied to two benchmark problems: a mobile robot and an underactuated underwater vehicle. Simulation results are presented to validate the proposed scheme. © 2009 IEEE.

IEEE Transactions on Robotics

Control of a class of underactuated mechanical systems using sliding modes

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.

State-constrained stabilization of beam-balance systems

Proceedings of the 18th IFAC World Congress

Second-order sliding mode control of underactuated mechanical systems I: Local stabilization with application to an inverted pendulum

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

Journal	IFAC Proceedings Volumes (IFAC-PapersOnline)
Publisher	IFAC Secretariat
ISSN	14746670
Open Access	No