Geodesic
Inverse Problem in the Control of Dynamic System
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 14 (2012), pp. 162-166

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We propose a synthesis of motion control for manipulation robot (MR) to the destination point of the programmed trajectory by the Lyapunov's direct method. During constructing of the model of dynamics MR is presented as a unified system, whose phase vector is determined by the data of a mechanism, as well as of the actuators. This approach to the control synthesis is based on the use of first integrals of the system motion as Lyapunov functions, therefore a considered drive must have specific physical meaning, such as DC electric drive, hydraulic drive with throttle control, etc., what will enable to take drive's energy into account in the construction of Lyapunov function. For definiteness, an MR with electric drives and the anchor control was taken as an example, which does not limit the possibility to use a different type of drive. Derivation of the MR motion equations is conducted on the basis of complete non-linear MR model using tensor analysis. The stability of movements of industrial MR with the solid of revolution as operating device is studied.
Keywords: model of dynamics, control synthesis, point of programmed trajectory, Lyapunov functions. 
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     author = {A. A. Bragina},
     title = {Inverse {Problem} in the {Control} of {Dynamic} {System}},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {162--166},
     publisher = {mathdoc},
     number = {14},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2012_14_a15/}
}
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A. A. Bragina. Inverse Problem in the Control of Dynamic System. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 14 (2012), pp. 162-166. http://geodesic.mathdoc.fr/item/VYURU_2012_14_a15/