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Optimal control of mechanical systems subjected to periodic loading via chebyshev polynomials
Author(s) -
Joseph Paul,
Pandiyan R.,
Sinha S. C.
Publication year - 1993
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.4660140202
Subject(s) - chebyshev polynomials , control theory (sociology) , mathematics , floquet theory , algebraic equation , mechanical system , chebyshev filter , inverted pendulum , differential equation , computer science , mathematical analysis , nonlinear system , control (management) , quantum mechanics , artificial intelligence , physics
Abstract Controllers using full‐state feedback and observer‐based feedback for mechanical systems subjected to periodic follower loads are designed in this paper. The designs are accomplished using an algebraic method incorporating Chebyshev polynomials coupled with principles of optimal control theory. The major advantage of this method is that it transforms differential equations with periodic coefficients to linear algebraic equations. Also, a dual‐system approach to design observers for such periodic systems turns out to be a novel technique and appears to have been employed for the first time. As an example of a mechanical system a triple inverted pendulum subjected to a periodic follower load is chosen and it is shown that both types of controllers can be successfully designed. The computational aspects and the suitability of this method for higher‐order mechanical systems are studied by applying it to one through five‐mass inverted pendulum models. The efficiency of the method is checked against the Runge–Kutta, Adams–Moulton and Gear numerical algorithms available in the IMSL software package by comparing the CPU time taken to evaluate the characteristic exponents of the Floquet transition matrix (FTM) as well as the norm of the control vector at the end of one period. It is shown that the proposed technique becomes much more efficient for higher‐order systems.