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Suppression of Oscillation of a Certain Two-Mass System with the Help of the Generalized Gauss Principle
International Journal of Mechanical Engineering and Applications
Volume 5, Issue 3, June 2017, Pages: 129-135
Received: May 10, 2017; Published: May 10, 2017
Authors
Kamilla Maratovna Fazlyeva, Department of Theoretical and Applied Mechanics, St. Petersburg University, St. Petersburg, Russia
Timofei Sergeevich Shugailo, Department of Theoretical and Applied Mechanics, St. Petersburg University, St. Petersburg, Russia
Mikhail Petrovich Yushkov, Department of Theoretical and Applied Mechanics, St. Petersburg University, St. Petersburg, Russia
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Abstract
The paper studies the suppression of oscillation of a certain two-mass system when it is transferred from the initial state of rest to the given state of rest during a time interval prescribed. The problem is solved by the two methods: the Pontryagin maximum principle (first method) and the generalized Gauss principle (second method). Computational results are presented and the solutions are compared to each other. When the time of motion is short the both methods give practically the same results, but when the time of motion is long the results differ widely. If the time of motion is long then the second method is more preferable than the first one, since the control obtained by the second method sways the mechanical system less than the control obtained by the classical approach. This can be explained by the fact that the first method contains the control including harmonics with the natural frequency of the system, and this seeks to put the system into resonance. In contrast to this, in the second method the control is sought in the form of time polynomial that provides relatively smooth motion of the system. It is noted that the first method always finds the control with jumps at the beginning and at the end of motion. The second method also gives the same jumps when the time of motion is short, but when the time of motion is long the similar jumps vanish when one uses the generalized Gauss principle.
Keywords
Pontryagin Maximum Principle, Generalized Gauss Principle, Control Force, Suppression of Oscillation
Kamilla Maratovna Fazlyeva, Timofei Sergeevich Shugailo, Mikhail Petrovich Yushkov, Suppression of Oscillation of a Certain Two-Mass System with the Help of the Generalized Gauss Principle, International Journal of Mechanical Engineering and Applications. Vol. 5, No. 3, 2017, pp. 129-135. doi: 10.11648/j.ijmea.20170503.11
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