Stabilizing Control of the Coupled Inverted Pendulums

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  • 結合倒立振子の安定化制御
  • ケツゴウ トウリツ フリコ ノ アンテイカ セイギョ

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Abstract

In this paper, modern control theory is applied to the stabilization of the inherently unstable system of “coupled inverted pendulums”. The system consists of two carts and two pendulums. Each cart, on which one pendulum is mounted, is driven by a motor controlled independently. The two pendulums are coupled mechanically by a spring in order to make, the system multivariable. The system has two control inputs, given as the, voltages to the two servo motors driving the carts. The most remarkable distinction between our system and those inverted pendulum investigated so far is that the former is multivariable. This makes one unable to apply the classical control theory directly.<br>A linear quadratic optimal regulator is used to derive a stabilizing feedback gain matrix. The obtained control law is implemented via the“function observer” that makes it possible to reduce the order of the controller significantly. Actually, we constructed it by the second order system.<br>First, a single inverted pendulum system is stabilized and the stabilized region with respect to the initial conditions is obtained. Next, the system of coupled inverted pendulums is stabilized. For each experiment the actual response of the system is shown.

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