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Books on the topic 'Inverted pendulum'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 July 2024

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1

Li, Zhijun, Chenguang Yang, and Liping Fan. Advanced Control of Wheeled Inverted Pendulum Systems. London: Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-2963-9.

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2

Li, Zhijun. Advanced Control of Wheeled Inverted Pendulum Systems. London: Springer London, 2013.

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3

King, S. P. Digital control of an inverted pendulum using an H-infinity design. Manchester: UMIST, 1994.

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4

Loram, Ian David. Mechanisms for human balancing of an inverted pendulum using the ankle strategy. Birmingham: University of Birmingham, 2002.

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5

Inverted Pendulum [Working Title]. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.80106.

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6

Li, Zhijun, Chenguang Yang, and Liping Fan. Advanced Control of Wheeled Inverted Pendulum Systems. Springer, 2014.

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7

Advanced Control Of Wheeled Inverted Pendulum Systems. Springer, 2012.

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8

Holzapfel, Frank G. Fuzzy logic control of an inverted pendulum with vision feedback. 1994.

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9

Barrett, Spencer Brown. Predictive control using feedback-: A case study of an inverted pendulum. 1995.

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10

Iriarte, Rafael, and Olfa Boubaker. Inverted Pendulum in Control Theory and Robotics: From Theory to New Innovations. Institution of Engineering & Technology, 2017.

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11

Inverted Pendulum in Control Theory and Robotics: From Theory to New Innovations. Institution of Engineering & Technology, 2017.

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12

Boubaker, Olfa, and Rafael Iriarte, eds. The Inverted Pendulum in Control Theory and Robotics: From theory to new innovations. Institution of Engineering and Technology, 2017. http://dx.doi.org/10.1049/pbce111e.

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13

Zhang, Mengshi, Jian Huang, and Toshio Fukuda. Robust and Intelligent Control of a Typical Underactuated Robot: Mobile Wheeled Inverted Pendulum. Springer, 2023.

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14

Lam, Simon Sai-Ming. The real stability and stabilizability radii of the multi-link inverted pendulum system. 2005.

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15

Rajeev, S. G. Fluid Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.001.0001.

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Abstract:

Starting with a review of vector fields and their integral curves, the book presents the basic equations of the subject: Euler and Navier–Stokes. Some solutions are studied next: ideal flows using conformal transformations, viscous flows such as Couette and Stokes flow around a sphere, shocks in the Burgers equation. Prandtl’s boundary layer theory and the Blasius solution are presented. Rayleigh–Taylor instability is studied in analogy with the inverted pendulum, with a digression on Kapitza’s stabilization. The possibility of transients in a linearly stable system with a non-normal operator is studied using an example by Trefethen et al. The integrable models (KdV, Hasimoto’s vortex soliton) and their hamiltonian formalism are studied. Delving into deeper mathematics, geodesics on Lie groups are studied: first using the Lie algebra and then using Milnor’s approach to the curvature of the Lie group. Arnold’s deep idea that Euler’s equations are the geodesic equations on the diffeomorphism group is then explained and its curvature calculated. The next three chapters are an introduction to numerical methods: spectral methods based on Chebychev functions for ODEs, their application by Orszag to solve the Orr–Sommerfeld equation, finite difference methods for elementary PDEs, the Magnus formula and its application to geometric integrators for ODEs. Two appendices give an introduction to dynamical systems: Arnold’s cat map, homoclinic points, Smale’s horse shoe, Hausdorff dimension of the invariant set, Aref ’s example of chaotic advection. The last appendix introduces renormalization: Ising model on a Cayley tree and Feigenbaum’s theory of period doubling.

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