Stability and stabilization of motion of a uniaxial wheel transport platform |
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Authors: | G P Sachkov S V Feshchenko A I Chernomorskii |
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Institution: | 1.Moscow Aviation Institute (State University of Aerospace Technologies),Moscow,Russia |
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Abstract: | We consider a uniaxial wheel transport platform with a single-degree-of-freedom gyroscope moving without slipping either on
a plane nonrotating horizontal surface or on the spherical rotating Earth surface. We obtain a general mathematical model
which, in a special case, coincides with the model in the form of Chaplygin equations, which permits obtaining a physical
interpretation of the Chaplygin equations. In the case of stationary motion where only the balance weight is controlled, we
find the minimum value of the gyro angular momentum that ensures the system stability. An example with parameters of the breadboard
model is used to consider the problem of the stationary motion stability and stabilization without gyro; the control matrix
minimizing the quadratic performance functional is obtained. The characteristic curves of the transient process in the system
are given. |
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Keywords: | |
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