Abstract
The control of an inverted pendulum is a classical benchmark control problem. Its dynamics resemble that of many real-world systems of interest like pendulous, missile launchers, segways, and many more. The control of this system is challenging as it is a highly unstable, highly non-linear, non-minimum phase system, and underactuated. Furthermore, the physical constraints on the track position also pose complexity in its control design. A great deal of nonlinearity is present inherently and as well as affected by the surrounding external disturbances. The paper presents an approach for analysis of a cart-inverted pendulum system with harmonic disturbances. The approach is based on the index of the criterion matrix of the system named a degeneration factor. The degeneration factor is constructed with the singular values of the criterion matrix of the system and allows us to find frequency range, where the system operates as a whole. A linear-quadratic regulator is used to control the cart-inverted pendulum system. The results are supported with an example.
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