ISSN 1991-2927

## Author: "Denis Sergeevich Makarov"

 O. Peregudova, D. Makarov
 Control Synthesis for Three-link Manipulator A stabilization problem of the three-link manipulator program motion by providing continuous nonlinear control with direct and feedback communication is solved in this paper. The manipulator consists of three totally rigid links. The first link is fastened on a horizontal base and can pivot about a vertical axis. The second one is interconnected with the first and the third links by the ideal cylindrical hinges. Relative movements of the second and the third links are performed in a vertical place that pivots about a vertical axis due to the first link motion. Thus, the manipulator can perform three-dimensional motion. The manipulator motions are described by the system of Lagrange equations of the second kind. The problem on synthesis of the motion control of such system involves the control moment construction that allows the manipulator to carry out the .motion given by the program in real conditions of external and internal disturbances, and the inaccuracy of the model itself. A mathematical model of the manipulator controlled motion is constructed in this paper in case of control actions in the form of continuous control actions. By applying Lyapunov’s vector functions and the comparison systems the implementation of the built control laws in the stabilization task of the spectrum of the manipulator program motions was proved. The novelty of the results includes solving the stabilization problem of the non-stationary and nonlinear formulation, without using a linearized model, as well as the ability to stabilize not just one but a whole family of program motions. A numerical solution of the received system of differential equations using both continuous and discontinuous control laws is found. The corresponding graphs for the coordinates of the manipulator links proving the theoretical results are built.Three-link manipulator, stabilization, program motion, continuous control, comparison system, lyapunov’s vector function.
 2015_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 O. Peregudova, D. Makarov
 Control Synthesis for Double-link Manipulator A stabilization problem of a doubl-link manipulator program motion on a fixed base is solved in this paper. Totally rigid manipulator links are interconnected by an ideal cylindrical hinge and via the same hinge the first element is fastened to the base. Thus, the manipulator can perform motions in a vertical plane only. The manipulator motions are described by the system of Lagrange equations of the second kind. The problem on synthesis of the motion control of such system involves the construction of the laws of a control moments change that allow the manipulator to carry out the motion given by the program in real conditions of external and internal disturbances, and the inaccuracy of the model itself. A mathematical model of the manipulator controlled motion is constructed in this paper in case of control actions in the form of continuous and discontinuous functions bounded in modulus. By applying Lyapunov’s vector-functions and the comparison systems we justified the implementation of the built control laws in the stabilization task of the spectrum of the manipulator program motions. The novelty of the results includes solving the stabilization problem of the non-stationary and nonlinear formulation, without changing to a linearized model, as well as the ability to stabilize not just one but a whole family of program motions. With the help of Maple’s mathematical package a numerical solution of the received system of differential equations using both continuous and discontinuous control laws is found. The corresponding graphs for the coordinates and velocities of the manipulator links proving the theoretical results are built.Multi-link manipulator, stabilization, program motion, relay control, comparison system, lyapunov’s vector-function.
 2014_ 4

Sections: Automated control systems

Subjects: Automated control systems, Mathematical modeling.

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