Control theory

Fractional-order control

Fractional-order control (FOC) is a field of control theory that uses the fractional-order integrator as part of the control system design toolkit. The use of fractional calculus (FC) can improve and generalize well-established control methods and strategies. The fundamental advantage of FOC is that the fractional-order integrator weights history using a function that decays with a power-law tail. The effect is that the effects of all time are computed for each iteration of the control algorithm. This creates a 'distribution of time constants,' the upshot of which is there is no particular time constant, or resonance frequency, for the system. In fact, the fractional integral operator is different from any integer-order rational transfer function , in the sense that it is a non-local operator that possesses an infinite memory and takes into account the whole history of its input signal. Fractional-order control shows promise in many controlled environments that suffer from the classical problems of overshoot and resonance, as well as time diffuse applications such as thermal dissipation and chemical mixing. Fractional-order control has also been demonstrated to be capable of suppressing chaotic behaviors in mathematical models of, for example, muscular blood vessels. Initiated from the 80's by the Pr. Oustaloup's group, the CRONE approach is one of the most developed control-system design methodologies that uses fractional-order operator properties. (Wikipedia).

Video thumbnail

Order of Operations Involving Fractions

This video shows how to simplify an expression involving fractions using the order of operations. http://mathispower4u.yolasite.com/

From playlist Order of Operations with Fractions

Video thumbnail

Simplify an Expression in Fraction Form with Absolute Values

This video explains how to simplify an expression using the order of operations. mathispower4u.com

From playlist Order of Operations with Fractions

Video thumbnail

Describing the Meaning of a Fraction

This video reviews the meaning of a fraction and introduces the meaning of a simplified fraction.

From playlist Introduction to Fractions

Video thumbnail

Introduction to Fractional Calculus

Fractional calculus develops the theory of differentiation and integration of any real or complex order. It extends the basic operations of classical calculus to fractional orders and studies the methods of solving differential equations involving these fractional-order derivatives and int

From playlist Wolfram Technology Conference 2022

Video thumbnail

Simplify an Expression in Fraction Form

This video explains how to simplify an expression using the order of operations. mathispower4u.com

From playlist Order of Operations with Fractions

Video thumbnail

Using Clocks to Solve Fractions String 2

Another introductory video using clocks to understand fractions

From playlist Arithmetic and Pre-Algebra: Fractions, Decimals and Percents

Video thumbnail

Fraction Operations on the Desmos Scientific Calculator

The video explains how to perform fraction operations on the Desmos scientific calculator.

From playlist Fractions on the Desmos and Graphing Calculator

Video thumbnail

Using Clocks to Solve Fractions String 6

Here we use the clock model to deal with 3/18 and 3/9

From playlist Arithmetic and Pre-Algebra: Fractions, Decimals and Percents

Video thumbnail

What are the Different Types of Fractions? | Don't Memorise

To learn more about Fractions, enroll in our full course now: https://infinitylearn.com/microcourses?utm_source=youtube&utm_medium=Soical&utm_campaign=DM&utm_content=RNt8CKGnPko&utm_term=%7Bkeyword%7D In this video, we will learn: 0:00 improper fractions 1:12 types of fractions 1:32 like

From playlist Fraction Class 06

Video thumbnail

Pablo Ochoa: Capacity based cond for existence of sol. to f / e problems with 1st-order terms

In this talk, we will discuss the existence of distributional solutions to fractional elliptic problems with non-linear first-order terms and measure data ! in RN. It is well-known in the literature that solutions to elliptic problems with superlinear growth in the gradient exist if the so

From playlist Hausdorff School: Trending Tools

Video thumbnail

Seminar In the Analysis and Methods of PDE (SIAM PDE): Alexander Kiselev

Title: The Flow of Polynomial Roots Under Differentiation Date: Thursday, June 2, 2022, 11:30 am EDT Speaker: Alexander Kiselev, Duke University Abstract: The question of how roots of polynomials move under differentiation is classical. Contributions to this subject have been made by Gaus

From playlist Seminar In the Analysis and Methods of PDE (SIAM PDE)

Video thumbnail

GRCon19 - Enabling Precise Timing Control in SDRs by Srikanth Pagadarai

Enabling Precise Timing Control in SDRs by Srikanth Pagadarai The necessity to estimate loopback timing delay of a waveform arises as a pre-requisite in a variety of signal processing applications namely, power amplifier digital predistortion, radar and radio frequency identification (RFI

From playlist GRCon 2019

Video thumbnail

François Golse: Linear Boltzmann equation and fractional diffusion

Abstract: (Work in collaboration with C. Bardos and I. Moyano). Consider the linear Boltzmann equation of radiative transfer in a half-space, with constant scattering coefficient σ. Assume that, on the boundary of the half-space, the radiation intensity satisfies the Lambert (i.e. diffuse)

From playlist Partial Differential Equations

Video thumbnail

Some solvable Stochastic Control Problems

At the 2013 SIAM Annual Meeting, Tyrone Duncan of the University of Kansas described stochastic control problems for continuous time systems where optimal controls and optimal costs can be explicitly determined by a direct method. The applicability of this method is demonstrated by example

From playlist Complete lectures and talks: slides and audio

Video thumbnail

"RM Models for Online Advertising and On-Demand Platforms" by Florin Ciocan - Session II

This mini-course focuses on revenue management applications in online advertising and on-demand platforms with time-sensitive customers that give rise to novel matching and queueing models. For example, online advertising platforms match impressions supply to advertiser demand, whereas on-

From playlist Thematic Program on Stochastic Modeling: A Focus on Pricing & Revenue Management​

Video thumbnail

Excel & Business Math 13: Mixed Number to Improper Fraction, Improper Fraction to Mixed Number

Download Start Excel File: https://people.highline.edu/mgirvin/AllClasses/135NoTextBook/Content/03FractionsDecimalsPercentages/ExcelBusinessMathVideo13MixedToFraction.xlsx Download pdf Notes: https://people.highline.edu/mgirvin/AllClasses/135NoTextBook/Content/03FractionsDecimalsPercentage

From playlist Excel & Business Math Class: % Change Formulas, Invoicing, Payroll, Finance & More (45 Videos)

Video thumbnail

DDPS | Applications of Fractional Operators from Optimal Control to Machine Learning

In this talk from June 3, 2021, Professor Harbir Antil of George Mason University discusses fractional operators and their applications to optimal control and Deep Neural Networks (DNNs). Fractional calculus and its application to anomalous diffusion has recently received a tremendous amo

From playlist Data-driven Physical Simulations (DDPS) Seminar Series

Video thumbnail

Ex 7: Simplify Expressions Involving Integers Using the Order of Operations

This provides an example of how to simplify or evaluate an expression involving integer operations in fraction form using the order of operations. Search All Videos at http://www.mathispower4u.wordpress.com

From playlist Order of Operations

Related pages

Fractional-order integrator | Control theory | Differintegral | Fractional calculus | Fractional-order system | Transfer function | Control system