Control theory

H-infinity loop-shaping

H-infinity loop-shaping is a design methodology in modern control theory. It combines the traditional intuition of classical control methods, such as Bode's sensitivity integral, with H-infinity optimization techniques to achieve controllers whose stability and performance properties hold despite bounded differences between the nominal plant assumed in design and the true plant encountered in practice. Essentially, the control system designer describes the desired responsiveness and noise-suppression properties by weighting the plant transfer function in the frequency domain; the resulting 'loop-shape' is then 'robustified' through optimization. Robustification usually has little effect at high and low frequencies, but the response around unity-gain crossover is adjusted to maximise the system's stability margins. H-infinity loop-shaping can be applied to multiple-input multiple-output (MIMO) systems. H-infinity loop-shaping can be carried out using commercially available software. H-infinity loop-shaping has been successfully deployed in industry. In 1995, R. Hyde, K. Glover and G. T. Shanks published a paper describing the successful application of the technique to a VTOL aircraft. In 2008, D. J. Auger, S. Crawshaw and S. L. Hall published another paper describing a successful application to a steerable marine radar tracker, noting that the technique had the following benefits: * Easy to apply – commercial software handles the hard math. * Easy to implement – standard transfer functions and state-space methods can be used. * Plug and play – no need for re-tuning on an installation-by-installation basis. A closely related design methodology, developed at about the same time, was based on the theory of the gap metric. It was applied in 1993 for designing controllers to dampen vibrations in large flexible structures at Wright-Patterson Air Force Base and Jet Propulsion Laboratory (Wikipedia).

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Infinity Kinetic Sculpture

http://www.woodthatworks.com/kinetic-sculptures/infinity Infinity Kinetic sculpture by David C. Roy with actual sounds The video segments of the full sculpture have been endited to keep the total length of the video short. For a longer sequence https://youtu.be/nPUcQpyLBh0

From playlist Kinetic Sculpture

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Epsilon delta limit (Example 3): Infinite limit at a point

This is the continuation of the epsilon-delta series! You can find Examples 1 and 2 on blackpenredpen's channel. Here I use an epsilon-delta argument to calculate an infinite limit, and at the same time I'm showing you how to calculate a right-hand-side limit. Enjoy!

From playlist Calculus

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Epsilon delta limit (Example 4): Limits at infinity

This part of the epsilon-delta series covers limits at infinity. You can find Examples 1 and 2 on blackpenredpen's channel, and Example 3 on my channel. Enjoy! Note: I realized after the fact that this limit may be a bit too simple, but if you want to prove that the limit of f at infinity

From playlist Calculus

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Hugging Face Infinity Launch - 09/28

On this live event, we shared for the first time in public details about our new inference product: 🤗 Infinity It achieves 1ms latency on Transformer models 🏎 and you can deploy it in your own infrastructure 🚀 If you'd like to see what 🤗 Infinity can do for your business, you can reques

From playlist Infinity

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limit x to infinity ln(sqrt(x))/x = answer by L'Hopital's Rule LHR // #Shorts

limit ln(sqrt(x))/x = answer by L'Hopital's Rule LHR // #Shorts

From playlist Calc 2 #Shorts

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Infinity root of infinity

A classic calculus 1 limit problem, evaluating the limit of x-th root of x as x goes to infinity. This is an inf^0 indeterminate form example. We will have to convert the x-root of x to x^(1/x) and then write x as e^ln(x) and use L'Hopital's Rule. Try this next: what do you think what (inf

From playlist Calculus Limits

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Infinite Limits (Limit Example 10)

Epsilon Definition of a Limit In this video, I illustrate the epsilon-N definition of a limit by doing an example with an infinite limit. More precisely, I prove from scratch that the limit of sqrt(n-2)+3 is infinity Other examples of limits can be seen in the playlist below. Check ou

From playlist Sequences

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Finding a Limit Using L'Hopital's Rule x^(1/x) as x approaches infinity

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From playlist Calculus

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Michael Farber: Topology of large random spaces

The lecture was held within the framework of the Hausdorff Trimester Program : Applied and Computational Algebraic Topology I will discuss various models producing large random spaces (simplicial complexes and closed manifolds). The main goal is to analyse properties which hold with proba

From playlist HIM Lectures: Special Program "Applied and Computational Algebraic Topology"

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From playlist Mathematics

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Elba Garcia-Failde - Quantisation of Spectral Curves of Arbitrary Rank and Genus via (...)

The topological recursion is a ubiquitous procedure that associates to some initial data called spectral curve, consisting of a Riemann surface and some extra data, a doubly indexed family of differentials on the curve, which often encode some enumerative geometric information, such as vol

From playlist Workshop on Quantum Geometry

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Eyal Lubetzky - Entropic repulsion in 3D Ising

Fifty years ago, Dobrushin famously showed that the 3D Ising interface on a cylinder with plus/minus boundary condition is rigid. By now there is detailed understanding of the (2+1)D Solid-On-Solid model that approximates said interface, and notably, its entropic repulsion phenomenon above

From playlist 100…(102!) Years of the Ising Model

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Poincare duality for loop spaces - Kai Cieliebak

Joint IAS/Princeton University Symplectic Geometry Seminar Topic: Poincare duality for loop spaces Speaker: Kai Cieliebak Affiliation: Augsburg University; Member, School of Mathematics Date: February 07, 2022

From playlist Mathematics

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5: Hodgkin-Huxley Model Part 2 - Intro to Neural Computation

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From playlist MIT 9.40 Introduction to Neural Computation, Spring 2018

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COLLOQUIUM IN SEARCH OF QUANTUM GEOMETRY SPEAKER: Pranav Pandit (ICTS - TIFR, Bengaluru) DATE: Mon, 29 November 2021, 15:30 to 17:00 VENUE: Online and Ramanujan Lecture Hall RESOURCES ABSTRACT Notions of geometry have evolved throughout the history of mathematics, often in parallel

From playlist ICTS Colloquia

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The Real Physics of Roller Coaster Loops

A look at the physics principles and calculations that engineers use to design roller coaster loops. Support Art of Engineering on Patreon: https://www.patreon.com/ArtofEngineering Shop Art of Engineering Merchandise: https://teespring.com/stores/ArtofEngineering Twitter: https://twitte

From playlist Theme Park Engineering

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DON'T use logarithms (Limit Example 9)

Epsilon Definition of a Limit In this video, I illustrate the epsilon-N definition of a limit by showing directly, without using ln or l'Hopital's rule, that n^1/n goes to 1 as n goes to infinity. Enjoy this beautiful analysis example :) Other examples of limits can be seen in the playli

From playlist Sequences

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Mark Pollicott - Dynamical Zeta functions (Part 3)

Dynamical Zeta functions (Part 1) Licence: CC BY NC-ND 4.0

From playlist École d’été 2013 - Théorie des nombres et dynamique

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Alexander Hock: From noncommutative quantum field theory to blobbed topological recursion

Talk at the conference "Noncommutative geometry meets topological recursion", August 2021, University of Münster. Abstract: Scalar quantum field theory on noncommutative Moyal space can be approximated by matrix models with non-trivial covariance. One example is the Kontsevich model, which

From playlist Noncommutative geometry meets topological recursion 2021

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Calculus 1: Limits & Derivatives (22 of 27) Finding the Limits of a Function - Example 9

Visit http://ilectureonline.com for more math and science lectures! In this video I will calculate the limit(x approaches infinity) of sqrt[(x^2-1)-x]. Next video in the series can be seen at: https://youtu.be/_tsA1MVkB9w

From playlist CALCULUS 1 CH 1 LIMITS & DERIVATIVES

Related pages

Control theory | Transfer function | Frequency domain | Bode's sensitivity integral