## SOLUTION OF THE OPTIMAL PROGRAM TRAJECTORY AND CONTROL OF THE DISCRETIZED EQUATION OF MOTION OF SUCKER-ROD PUMPING UNIT IN A NEWTONIAN FLUID

## SOLUTION OF THE OPTIMAL PROGRAM TRAJECTORY AND CONTROL OF THE DISCRETIZED EQUATION OF MOTION OF SUCKER-ROD PUMPING UNIT IN A NEWTONIAN FLUID

*F. A. Aliev, N. A. Aliev, A. F. Rasulzade, N. S. Hajiyeva*

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## Abstract

In this paper, the problem of construction of the optimal trajectory and control for oscillatory systems with liquid dampers in the movement of the sucker-rod pumping unit is considered. Firstly, the equation of motion is reduced to the second order Volterra integral equation, this equation is discretized, odd and even indices are generated for the solution. These indexes is collected in one solution. Then, the quadratic functional is constructed and by means of extended functional the Euler-Lagrange equations are obtained to construct the optimal program trajectory and control. The solution of the problem is found from the obtained system of equations. An algorithm for its calculation process is proposed. The obtained results are realized through an example.

## Keywords

sucker-rod pumping unit, optimal program trajectory, control, fractional order derivative, second order Volterra integral equation, Euler-Lagrange equations.