Control of a Nonlinear Vibratory System of the Fourth Order with Unknown Parameters
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A problem of control of a mechanical system is considered that represents two mass points connected by a spring and moving along parallel straight lines. It is assumed that masses of the points and the rigidity of the spring are unknown and the points are subject to forces of dry friction with unknown variable coefficients. A control law is built up by which a limited force applied to the first mass brings it into a prescribed position in a finite time. An algorithm is put forward that uses piecewise-linear feedback links whose gain factors tend to infinity as the system approaches a terminal set. The second Lyapunov method is used for substantiating the algorithm. The effectiveness of the suggested control law is shown with the aid of numerical modeling.
KeywordsNumerical Modeling System Theory Mechanical System Unknown Parameter Fourth Order
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