Stabilization of the Furuta Pendulum Based on a Lyapunov Function

Ibáñez, Carlos Aguilar; Azuela, Juan Humberto Sossa

doi:10.1007/s11071-006-9099-8

Cited by 22 publications

(8 citation statements)

References 20 publications

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“…Åström [12] considers the swing-up of a one-mass pendulum using energy considerations providing a novel physically based approach to its control. AguilarIbáñez and Azuela [13] have worked on stabilizing the underactuated Furuta pendulum, and they obtain local asymptotic stability around the vertical position of the pendulum using a suitable Lyapunov function in combination with partial feedback linearization. More recently, Aguilar-Ibáñez et al [14] have considered the underactuated control of an inverted (planar) pendulum mounted on a cart that moves along a straight line.…”

Section: Introductionmentioning

confidence: 99%

“…[12][13][14], it is this control approach that is developed and used in this paper. It does not use conventional methods of control design and comes from recent developments of the theory of constrained motion of mechanical systems.…”

Section: Introductionmentioning

confidence: 99%

“…The current literature (see Refs. [12][13][14]) has been limited to the validation of control methods for much simpler types of motion control such as the swing-up of a pendulum system from its static, stable, equilibrium position directly to its vertically inverted position. In fact, such studies have been reported for pendulum systems made up of just two or three bodies.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics and control of a multi-body planar pendulum

Udwadia

Koganti

2015

Nonlinear Dyn

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The explicit equations of motion for a general n-body planar pendulum are derived in a simple and concise manner. A new and novel approach for obtaining these equations using mathematical induction on the number bodies in the pendulum system is used. Assuming that the parameters of the system are precisely known, a simple method for its control that is inspired by analytical dynamics is developed. The control methodology provides closed-form nonlinear control and makes no approximations/linearizations of the nonlinear system. No a priori structure is imposed on the controller. Globally, asymptotic Lyapunov stability is achieved along with the minimization of a userprovided control cost at each instant of time. This control methodology is then extended to include uncertainties in the parameters of the system through the use of an additional continuous controller. Simulations showing the simplicity and efficacy of the approach are provided for a 10-body pendulum system whose model is only known imprecisely. The ease with which the uncertain system can be controlled to move from any initial

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamics and control of a multi-body planar pendulum

Udwadia

Koganti

2015

Nonlinear Dyn

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“…It enables the semiglobal stabilization of Furuta pendulum to be achieved. In [6], the local stabilization of Furuta pendulum around the unstable vertical equilibrium was realized by a Lyapunov-function-based control method. To achieve the stabilization of Furuta pendulum in the whole motion space, a common used control strategy is firstly to divide the motion space into two subspaces: swing-up area and balancing area, and then to design swing-up controller and balancing controller for each subspace, respectively.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear stabilization control of Furuta pendulum only using angle position measurements

Zhao¹,

Gong²,

Zhang³

et al. 2016

J. Math. Computer Sci.

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In this paper, we discuss the stabilization control problem for a nonlinear mechanical system called Furuta pendulum. A new stabilizing control method that only uses the measurements of angle position is developed. This method has three successive steps. First, we present the dynamic equation of Furuta pendulum and change it into an affine nonlinear system by appropriately choosing state variables. Second, we linearize the nonlinear system around the origin and consider the nonlinear higher order term to be system's fictitious disturbance. After that, an idea of equivalent input disturbance is used to design the stabilizing controller for the nonlinear system. The effectiveness of our proposed control strategy is illustrated via a numerical example.

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“…A stabilizing controller is then obtained following an energy-based Lyapunov approach, which exploits the physical properties of the mechanical system. Intuitively speaking, the energybased Lyapunov control shapes, using a feedback loop, the potential, and kinetic energies of the controlled system to ensure a motion guaranteeing the control objective see, e.g., 8,12,13 . Moreover, this approach requires the total energy of the system to be a nonincreasing function.…”

Section: Introductionmentioning

confidence: 99%

PD Control for Vibration Attenuation in a Physical Pendulum with Moving Mass

Gutiérrez-Frías

Martínez-García

Moctezuma

2009

Mathematical Problems in Engineering

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This paper proposes a Proportional Derivative controller plus gravity compensation to damp out the oscillations of a frictionless physical pendulum with moving mass. A mass slides along the pendulum main axis and operates as an active vibration-damping element. The Lyapunov method together with the LaSalle's theorem allows concluding closed-loop asymptotic stability. The proposed approach only uses measurements of the moving mass position and velocity and it does not require synchronization of the pendulum and moving mass movements. Numerical simulations assess the performance of the closed-loop system.

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Stabilization of the Furuta Pendulum Based on a Lyapunov Function

Cited by 22 publications

References 20 publications

Dynamics and control of a multi-body planar pendulum

Dynamics and control of a multi-body planar pendulum

Nonlinear stabilization control of Furuta pendulum only using angle position measurements

PD Control for Vibration Attenuation in a Physical Pendulum with Moving Mass

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