Controlling the Double Rotary Inverted Pendulum with Multiple Feedback Delays

Casanova, Vicente; Salt, J.; Pizá, Ricardo; Cuenca, Ángel

doi:10.15837/ijccc.2012.1.1420

Cited by 16 publications

(4 citation statements)

References 34 publications

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“…The double inverted pendulum is often referred to as the most simple nonlinear multibody system featuring all the properties of higher degree-of-freedom nonlinear systems, such as complexity or chaos. As such, it is often used to demonstrate control concepts of complex systems (Casanova et al, 2012;He et al, 2018;Lukowska et al, 2018). The corresponding full state feedback involves the angular position and angular velocity of both pendulum segments, which implies that the number of control gains is four.…”

Section: Double Inverted Pendulummentioning

confidence: 99%

Calculation of the critical delay for the double inverted pendulum

Molnar

Balogh

Boussaada

et al. 2020

Journal of Vibration and Control

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Single and double inverted pendulum systems subjected to delayed state feedback are analyzed in terms of stabilizability. The maximum (critical) delay that allows a stable closed-loop system is determined via the multiplicity-induced-dominancy property of the characteristic roots, that is the dominant (rightmost) roots are associated with higher multiplicity under certain conditions of the system parameters. Other methods such as tracking the changes of the D-curves with increasing delay and the Walton–Marshall method are also demonstrated for the example of the single pendulum. For the double inverted pendulum subjected to full state feedback, the number of control gains is four, and application of numerical methods requires therefore high computational effort (i.e. optimization in a four-dimensional space). It is shown that, with the multiplicity-induced-dominancy–based approach, the critical delay and the associated control gains can be determined directly using the characteristic equation and its derivatives.

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Section: Double Inverted Pendulummentioning

confidence: 99%

Calculation of the critical delay for the double inverted pendulum

Molnar

Balogh

Boussaada

et al. 2020

Journal of Vibration and Control

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“…Driver and Thorpe [9] designed control of rotary single/double inverted pendulum. Casanova et al [10] worked on the development and control structure of DRIP by using multiple feedback delay. Li [11] worked on a rotational double inverted pendulum system by developing a mathematical model using the Euler Lagrange align and used the DAFC (direct adaptive fuzzy control) method to increase LQR (linear quadratic regulator) performance to stabilize the system.…”

Section: Introductionmentioning

confidence: 99%

Stabilization of Double Inverted Pendulum Systems Based on Hierarchical Sliding Mode Control Techniques

Idrees,

Ullah,

Younis

et al. 2023

Mathematical Problems in Engineering

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The double rotary inverted pendulum (DRIP) system belongs to the class of under-actuated mechanical systems, and it is a highly nonlinear, unstable, and benchmark system to test the different control techniques. This paper successfully designed the nonlinear hierarchical sliding mode control (HSMC) techniques to stabilize the DRIP system. We compare the performance of these techniques numerically with each other and with the previously designed control technique. We propose an aggregated HSMC technique as it has a much shorter stabilization time than other designed techniques.

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“…The pole assignment method was proposed for periodic rotation of the outer pendulum while stabilizing the inner pendulum by Komine et al 10 An RDIP developed by Pan et al 11 was controlled by using the conventional linear quadratic regulator (LQR). Casanova et al 12 used an RDIP system to evaluate a multi-loop control structure for a multivariable plant with different delays in the signals between controller and plant.…”

Section: Introductionmentioning

confidence: 99%

Control of rotary double inverted pendulum system using mixed sensitivity H∞ controller

Sanjeewa

Parnichkun

2019

International Journal of Advanced Robotic Systems

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Balancing control of a rotary double inverted pendulum system is a challenging research topic for researchers in dynamics control field because of its nonlinear, high degree-of-freedom, under actuated and unstable characteristics. The system always works under uncertainties and disturbances. Many control algorithms fail or ineffectively control the rotary double inverted pendulum system. In this article, mixed sensitivity H1 control is proposed to balance the rotary double inverted pendulum system. The controller is proposed to ensure the robust stability and enhance the time domain performance of the system under uncertainties and disturbances. Structure of the system, dynamics model and controller synthesis are presented. For performance evaluation, the proposed mixed sensitivity H1 controller is compared with linear quadratic regulator from both simulation and experiment on the rotary double inverted pendulum system. The results show high performance of the proposed controller on the rotary double inverted pendulum system with model uncertainties and external disturbances.

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Controlling the Double Rotary Inverted Pendulum with Multiple Feedback Delays

Cited by 16 publications

References 34 publications

Calculation of the critical delay for the double inverted pendulum

Calculation of the critical delay for the double inverted pendulum

Stabilization of Double Inverted Pendulum Systems Based on Hierarchical Sliding Mode Control Techniques

Control of rotary double inverted pendulum system using mixed sensitivity H∞ controller

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