Closed-Loop Dynamic Analysis of a Rotary Inverted Pendulum for Control Design

Ashrafiuon, Hashem; Whitman, Alan M.

doi:10.1115/1.4005358

Cited by 8 publications

(6 citation statements)

References 12 publications

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“…Park et al [29] presented a swing-up and stabilization control with coupled sliding mode control. Some other robust designs can be found in the recent papers by Iraj et al [21], Muske et al [24], Ashrafiuon and Whitman [4], and Uchiyama et al [33]. A common assumption to these robust designs is that the variation bounds of the uncertainties and disturbances have to be available; otherwise, the design is not feasible.…”

mentioning

confidence: 99%

Adaptive control of rotary inverted pendulum system with time-varying uncertainties

Chen

Huang

2013

Nonlinear Dyn

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In this paper, an adaptive controller is proposed to balance a rotary inverted pendulum with time-varying uncertainties. The goal of the control is to bring the pendulum close to the upright position regardless of the various uncertainties and disturbances. Its underactuated dynamics is first decoupled by Olfati's transformation into a cascade form, and then an adaptive controller is designed to deal with the uncertainties in the new space. Based on the Lyapunov-like theory, the closed loop stability and boundedness of all internal signals can be proved. The simulation results show that the proposed scheme is capable of giving good performance, as desired.

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confidence: 99%

Adaptive control of rotary inverted pendulum system with time-varying uncertainties

Chen

Huang

2013

Nonlinear Dyn

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“…En marzo de 2012, Ashrafiuon Hashem y Whitman Alan [23], presentan un artículo donde se obtiene una solución analítica aproximada para la dinámica en lazo cerrado para la fase de deslizamiento de un péndulo invertido rotacional controlado por modos deslizantes basado en el método de escala múltiple; la expresión analítica se obtiene de la solución no lineal de la dinámica en lazo cerrado de orden reducido y esta provee los parámetros que garantizan la estabilización y mejora del desempeño del controlador.…”

Section: Control De Péndulos Invertidosunclassified

Control De Un Péndulo De Furuta. Una Revisión Del Estado Del Arte.

García¹,

Buitrago²,

Ramírez³

2015

Sci. tech

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“…The dynamical response of an open-loop 3-DoF pendulum that is harmonically excited has been studied, and the analytical solution implementing the multiple scale method has been carried out [34]. Employing perturbative techniques, Ashra uon et al [35] have presented an approximate analytical solution for the rotary inverted pendulum based on which the step response of the system using the sliding mode controller has been investigated. However, no investigation in the frequency domain has been done yet.…”

Section: Introductionmentioning

confidence: 99%

Analytical and experimental analyses of nonlinear vibrations in a rotary inverted pendulum

2022

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Gaining insight into possible vibratory responses of dynamical systems around their stable equilibria is an essential step, which must be taken before their design and application. The results of such a study can signi cantly help prevent instability in closed-loop stabilized systems through avoiding the excitation of the system in the neighborhood of its resonance. This paper investigates nonlinear oscillations of a Rotary Inverted Pendulum (RIP) with a full-state feedback controller. Lagrange's equations are employed to derive an accurate 2-DoF mathematical model, whose parameter values are extracted by both the measurement and 3D modeling of the real system components. Although the governing equations of a 2-DoF nonlinear system are di cult to solve, performing an analytical solution is of great importance, mostly because, compared to the numerical solution, the analytical solution can function as an accurate pattern. Additionally, the analytical solution is generally more appealing to engineers because their computational costs are less than those of the numerical solution. In this study, the perturbative method of multiple scales is used to obtain an analytical solution to the coupled nonlinear motion equations of the closed-loop system. Moreover, the parameters of the controller are determined, using the results of this solution. The ndings reveal the existence of hardening-and softening-type resonances at the rst and second vibrational modes, respectively. This led to a wide frequency range with moderately large-amplitude vibrations, which must be avoided when adjusting a time-varying set-point for the system. The analytical results of the nonlinear vibration of the RIP are veri ed by experimental measurements, and a very good agreement is observed between the results of both approaches.

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Closed-Loop Dynamic Analysis of a Rotary Inverted Pendulum for Control Design

Cited by 8 publications

References 12 publications

Adaptive control of rotary inverted pendulum system with time-varying uncertainties

Adaptive control of rotary inverted pendulum system with time-varying uncertainties

Control De Un Péndulo De Furuta. Una Revisión Del Estado Del Arte.

Analytical and experimental analyses of nonlinear vibrations in a rotary inverted pendulum

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