Passivity-Based Control of Stewart Platform for trajectory tracking
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Date
2015-03
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Addis Ababa University
Abstract
Passivity based control, as one of the tools available to design robust controllers, is introduced
for trajectory tracking of the Stewart platform. Since Passivity is a fundamental property of many
physical systems which may be roughly defined in terms of energy dissipation and
transformation, its inherent input output property quantifies and qualifies the energy balance of a
system when simulated by external inputs to generate some outputs. PD+ controller is designed
based on passivation principle so that the closed loop system becomes globally uniform and
asymptotically stable.
The mathematical model of the Stewart platform, derived from Euler Lagrange equations of
motion, is simulated on MALAB/Simulink with the designed controller. So as to get the desired
leg-length trajectory, the inverse kinematics formulation is investigated. The mathematical model
is verified using “automatic dynamic analysis of mechanical systems” (ADAMS) software.
In the absence of disturbances, the maximum trajectory tracking error is recorded as ( 0.006m) in
the time interval between 0sec and 0.8sec . Applying unit step disturbance makes the error
0.006m after 0.8sec , which never be seen in undisturbed system.. The maximum speed of all
the six legs trajectory have been found to be 0.43m/ s , 0.49m/ s , 0.48m/ s , 0.5m/ s , 0.5m/ s and
0.49m/ s respectively. More realistic results are observed from ADAMS simulation results.
Key words: passivity based control, PD+, global uniform asymptotically stable, Euler Lagrange
equation, ADAMS software, inverse kinematics, MATLAB/Simulink.
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Keywords
passivity based control; PD+; global uniform asymptotically stable; Euler Lagrange equation;ADAMS software;inverse kinematics; MATLAB/Simulink