The interpolation synthesis of automatic control systems’ regulators based on zeros of the Chebyshev polynomials

Authors: Goncharov V. I., Nguen F. D.

Annotation: The application of the real interpolation method (RIM) for solving problems of synthesis of automatic control systems’ regulators of objects with distributed parameters is considered. The approach peculiarity is in creating a grid of interpolating nodes based on zeros of the Chebyshev polynomials of the first kind. The positive expectation for the decision accuracy improvement related to the unique property of these polynomials of least deviation from zero. The produced example of calculation showed that this way of synthesis, based on numerical methods, the procedure of the synthesis of the regulators without the stage of approximation and the use of the nodes distribution law, leads to quite simple computational scheme and guarantees the increased accuracy in the problem solution.

Keywords: objects with distributed parameters, synthesis of regulators, real interpolation method, che- byshev polynomials