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Linearization is a standard part of modeling and control design theory for a class of nonlinear dynamical systems taught in basic undergraduate courses. Although linearization is a straight-line methodology, it is not applied correctly by many students since they often forget to keep the operating point in mind. This paper explains the topic and suggests a way to improve the teaching of the methodology...
In this paper we analyze the inverted pendulum system and use variable structure theory in controlling the car position and pendulum angle. We use Lyapunov theory getting the sliding mode function and output expression of the controller. At the same time we prove the astringency of sliding mode. The simulation and inverted pendulum system experiment both prove that the nonlinear variable structure...
We study the solution properties of a family of inverted pendulum systems driven by odd periodic forcing. Using the Schauder fixed point theorem, we show that the inverted pendulum with an odd periodic driving acceleration at the pivot always possesses an odd periodic solution. Fundamental to the production of good estimates is the development of a Green's function for an unstable harmonic oscillator...
This paper considers an ldquohomotopy methodrdquo for solving the exact tracking problem for nonlinear affine nonminimum phase systems. The method is presented in a general setting and is applied to the special case of the spherical pendulum. This approach allows finding sufficient conditions for exact tracking for T-periodic curves and bounds on the internal dynamics.
In this paper, we deal with the backstepping control design of the two-wheeled inverted-pendulum-type autonomous robot, the e-nuvo-wheel, made in ZMP Inc.. First, we derive a second-order motion equation of the angle and design an adaptive integral backstepping controller to stabilize the angle in the manner of the modeling in. This controller requires the full-state measurements. In the output feedback...
The inverted pendulum is a unstable non-minimum-phase plant, Hinfin output feedback control of the system is far less robust. The difficulties of control of such a plant are analysed from the viewpoint of systempsilas bandwidth: the bandwidth for control of a non-minimum-phase plant must be narrow, and the control of an unstable plant need a rather wider bandwidth. It is pointed out that a fast feedback...
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