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Adaptive Neural Network Control of Underactuated System
Andrzej Burghardt and Zenon Hendzel
Department of Applied Mechanics and Robotics, Rzeszow University of Technology, W.Pola 2, 35-959 Rzeszow, Poland
Keywords:
Neural Network, Underactuated Systems, Adaptive Control.
Abstract:
The article presents a synthesis of the control system of an underactuated object of ball-beam type. Based on a
mathematical description of the object, we proposed an adaptational control algorithm, ensuring stabilization
of the ball position on the beam. The synthesis of the control system was conducted on the basis of Lyapunov’s
stability theory, using artificial neural networks in the adaptation process. The proposed solution was simulated
with Matlab/Simulink software and verified on the real object.
1 INTRODUCTION
Control and modelling of non-linear mechanical sys-
tems, where the number of independent control
signals is smaller than the number of degrees of
freedom (underactuated systems, US) is often an-
alyzed, among others, in these works (Blajer and
Kolodziejczyk, 2007), (Leonard and Marsden, 2000),
(Spong, 1997). The most popular systems of US type
include: a ball rolling along a beam, a ball rolling
across a plane, inverted pendulum system (Leonard
and Marsden, 2000), two-dimensional gantry cranes
and systems of masses connected with springs (Bla-
jer and Kolodziejczyk, 2007), submarines (Leonard,
1997), helicopters, and rotor flying machines.
Analysis of the literature in the field emphasized
the fact that mathematical models used in control al-
gorithms are simplified; for example, gravitation and
friction phenomena are neglected (Levine and Mull-
haupt, 1999), (Lewis and Murray, 1995) which be-
came the impulse for research in control and mod-
elling of US type systems.
The article presents a synthesis of the control sys-
tem of the underactuated object of the non-linear ball-
beam type. The neural control of non-linear systems
relays on using neural networks to compensate sys-
tem nonlinearities and its unknown properties. The
neural control systems generally consists of the neu-
ral compensator and the classical control element like
e.g. PD controller, which generates the control sig-
nal at the beginning of the NN’s weights adaptation
process. In a case of disturbances, weights of NNs
are adapted to reduce a change of controlled system
dynamics. This approach ensure high control quality
in a case of disturbances. In the proposed control sys-
tems, based on a mathematical description of the ob-
ject, a neural control algorithm, ensuring stabilization
of the ball position on the beam, was proposed. The
synthesis of the control system was conducted on the
basis of Lyapunov’s stability theory, using artificial
neural networks in the adaptation process. The ob-
tained solution was simulated with Matlab/Simulink
software and correctness of stabilization of the ball
position on the beam was verified using rapid proto-
typing environment with a dSpace control-measuring
card and ControlDesk software.
2 LINEAR IN THE PARAMETER
NEURAL NETS
It is commonlyknown that neural networks have good
properties with regard to static mapping. The use
of neural networks for real time control may require
reproducing the full dynamics of the controlled ob-
ject, which might result in a large size of dynamic
networks. Application of linear neural networks be-
cause of their weight, such as, for example, radial
networks, B-spline type networks, and networks with
functional extensions, prevents the problem of explo-
sion of the solutions. Considering the non-linearity of
the controlled object, a linear neural network whose
first weight layer is randomly generated was used in
this work to compensate for its non-linearity.
The structure of NNs used in the control system
is very universal, where can be used many different
activation functions. In the presented control systems
505
Burghardt A. and Hendzel Z..
Adaptive Neural Network Control of Underactuated System.
DOI: 10.5220/0004113505050509
In Proceedings of the 4th International Joint Conference on Computational Intelligence (NCTA-2012), pages 505-509
ISBN: 978-989-8565-33-4
Copyright
c
2012 SCITEPRESS (Science and Technology Publications, Lda.)