Control Synthesis for Three-link Manipulator

Olga Alekseevna Peregudova, Ulyanovsk State University, Doctor of Physics and Mathematics, Associate Professor; graduated from the Faculty of Mechanics and Mathematics at Ulyanovsk State University; Professor at the Department of Information Security and Control Theory of Ulyanovsk State University; an author of articles, textbooks, and a monograph in the field of stability theory and the motion control of mechanical systems. [e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it. ]O. Peregudova,

Denis Sergeevich Makarov, Ulyanovsk State University, a Post-Graduate Student; graduated from the Faculty of Mathematics and Information Technologies of Ulyanovsk State University; Junior Researcher at the Department of Scientific Research of Ulyanovsk State University; an author of articles in the field of the motion control of mechanical systems. [e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it. ]D. Makarov

Control Synthesis for Three-link Manipulator 000_12.pdf

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.