Plenary
Lecture
Chaotic Dynamics of a Triple Pendulum: Numercial vs.
Experimental Investigations
Professor Jan Awrejcewicz
Technical University of Lodz
Department of Automatics and Biomechanics
1/15 Stefanowski St.
90-924 Lodz, Poland
E-mail:
awrejcew@p.lodz.pl
Abstract: The triple physical pendulum is
designed as a system of two symmetrically joint
pendulums to eliminate stress caused by torques and/or
forces out of the pendulum's plane dynamics ((see [1],
[2], [3]). It possesses a module-like structure and a
stand being symmetrical steel welded construction. The
pendulum-driving subsystem consists of two engines of
slow alternating currents and optoelectronic
commutation. The engine stator has been designed in such
a way that the current intensity in the windings is
linearly dependent on the engine torque owing to the
removal of the ferromagnetic cores. The LabView software
environment is applied. Namely, blocks are linked by
lines of various colors and patterns in the environment
and represent some predefined application procedures
(reading and writing to channel inputs and outputs,
numerical analysis, etc.) A series of measured data is
stored in the text files and shown in various wave form
graphs. In addition, a mathematical model of the
experimental rig is derived as a system of three second
order strongly nonlinear ODEs. Mathematical modeling
includes details, taking into account some
characteristic features (for example, real
characteristics of joints built by the use of roller
bearings) as well as some imperfections (asymmetry of
the forcing) of the real system. Parameters of the model
are obtained by a combination of the estimation from
experimental data and direct measurements of the
system's geometric and physical parameters. A few
versions of the model of resistance in the joints are
tested in the identification process. Good agreement
between both numerical simulation results and
experimental measurements have been obtained and
presented. Some novel features of our real system
chaotic dynamics have been reported.
|