AFC @ MESA LAB ME280: Fractional Order Mechanics General Motivations on Fractional Calculus and Fractional Order Thinking (FOT) –Part-1 YangQuan Chen, Ph.D., Director, MESA (Mechatronics, Embedded Systems and Automation)LAB ME/EECS/SNRI/UCSolar, School of Engineering, University of California, Merced E: [email protected]; or, [email protected]T: (209)228-4672; O: SE1-254; Lab: Castle #22 (T: 228-4398) 09/03/2013. Thursday 09:00-10:15, KL217
58
Embed
AFC @ MESA LAB ME280: Fractional Order Mechanics General Motivations on Fractional Calculus and Fractional Order Thinking (FOT) –Part-1 YangQuan Chen,
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
AFC @ MESA LABME280: Fractional Order Mechanics
General Motivations on Fractional Calculus and Fractional Order Thinking (FOT) –Part-1
YangQuan Chen, Ph.D., Director, MESA (Mechatronics, Embedded Systems and Automation)LAB
ME/EECS/SNRI/UCSolar, School of Engineering,University of California, Merced
What is “Fractional Calculus”?• Calculus: integration and differentiation.• “Fractional Calculus”: integration and
differentiation of non-integer orders.– Orders can be real number (and even complex
numbers!)– Orders are not constrained to be “integers” or even
“fractionals”
How this is possible?
Why should I care?
Any (good) consequences (to me)?09/03/2013 ME280 "Fractional Order Mechanics" @ UC Merced
Slide-2/1024
AFC @ MESA LAB
09/03/2013 ME280 "Fractional Order Mechanics" @ UC Merced
Slide-3 of 1024
Slide credit: Igor Podlubny
AFC @ MESA LAB
09/03/2013 ME280 "Fractional Order Mechanics" @ UC Merced
Slide-4 of 1024
Slide credit: Igor Podlubny
AFC @ MESA LAB
09/03/2013 ME280 "Fractional Order Mechanics" @ UC Merced
Slide-5 of 1024
Slide credit: Igor Podlubny
AFC @ MESA LAB
09/03/2013 ME280 "Fractional Order Mechanics" @ UC Merced
Slide-6 of 1024
“Fractional Order Thinking” or, “In Between Thinking”
• For example– Between integers there are non-integers;– Between logic 0 and logic 1, there is the fuzzy logic;– Between integer order splines, there are “fractional order
splines”– Between integer high order moments, there are noninteger order
moments (e.g. FLOS)– Between “integer dimensions”, there are fractal dimensions– Fractional Fourier transform (FrFT) – in-between time-n-freq.– Non-Integer order calculus (fractional order calculus – abuse of
terminology.) (FOC – fractional order control, so we use FC, or AFC: Applied Fractional Calculus)
AFC @ MESA LAB
09/03/2013 ME280 "Fractional Order Mechanics" @ UC Merced
Slide-7 of 1024
Optimal filtering in fractional order Fourier domain
Slide credit: HALDUN M. OZAKTAS
AFC @ MESA LAB
09/03/2013 ME280 "Fractional Order Mechanics" @ UC Merced
Slide-8 of 1024
Optimal filtering in fractional Fourier domain
Slide credit: HALDUN M. OZAKTAS
AFC @ MESA LABConclusion of Talk
Integer-Order Calculus Fractional-Order Calculus
Slide credit: Richard L. Magin, ICCC12
8/29/2013 ME280 "Fractional Order Mechanics" @ UC Merced
Slide-9/1024
AFC @ MESA LAB• Integer-Order Calculus • Fractional-Order Calculus
Discrete gears vs. constantly-variable transmissionhttp://spectrum.ieee.org/energywise/energy/renewables/could-mechanics-best-power-
8/29/2013 ME280 "Fractional Order Mechanics" @ UC Merced
Slide-10/1024
AFC @ MESA LAB
09/03/2013 ME280 "Fractional Order Mechanics" @ UC Merced
Slide-11 of 1024
Slide credit: Igor Podlubny
AFC @ MESA LAB
09/03/2013 ME280 "Fractional Order Mechanics" @ UC Merced
Slide-12 of 1024
Slide credit: Igor Podlubny
AFC @ MESA LAB
09/03/2013 ME280 "Fractional Order Mechanics" @ UC Merced
Slide-13 of 1024
Slide credit: Igor Podlubny
AFC @ MESA LAB
09/03/2013 ME280 "Fractional Order Mechanics" @ UC Merced
Slide-14 of 1024
Slide credit: Igor Podlubny
AFC @ MESA LAB
09/03/2013 ME280 "Fractional Order Mechanics" @ UC Merced
Slide-15 of 1024
• Fractional Order System – official keyword of IFAC
• pid12.ing.unibs.it/
Good Consequences
AFC @ MESA LAB
2001-2010 2005-2011
Slide-16/1024
ME280 "Fractional Order Mechanics" @ UC Merced
Good Consequences
09/03/2013
AFC @ MESA LAB
ME280 "Fractional Order Mechanics" @ UC Merced
Slide-17/1024
09/03/2013
Good Consequences
AFC @ MESA LAB
ME280: Fractional Order Mechanics!
09/03/2013 ME280 "Fractional Order Mechanics" @ UC Merced
Slide-18/1024
One More Good Consequence?
AFC @ MESA LAB
09/03/2013 ME280 "Fractional Order Mechanics" @ UC Merced
Slide-19 of 1024
AFC @ MESA LAB
09/03/2013 ME280 "Fractional Order Mechanics" @ UC Merced
Slide-20 of 1024
Slide credit: Igor Podlubny
AFC @ MESA LAB
09/03/2013 ME280 "Fractional Order Mechanics" @ UC Merced
Slide-21 of 1024
AFC @ MESA LAB
09/03/2013 ME280 "Fractional Order Mechanics" @ UC Merced
Slide-22 of 1024
Why and How and WhenWhy – Many reasons. Dynamic systems modeling and controls. Better characterization, better control performanceHow – Analog versus digital realization methods. Many.When – Now. Ubiquitous. Take a try since we have the new tool.
Slide credit: Igor Podlubny
AFC @ MESA LAB
End of lecture side-remarks
09/03/2013 ME280 "Fractional Order Mechanics" @ UC Merced
Slide-23/1024
AFC @ MESA LAB
On Research Excellence
YangQuan Chen, Ph.D., Director, MESA (Mechatronics, Embedded Systems and Automation)LAB
MEAM/EECS, School of Engineering,University of California, Merced
• There is no place for second place in research• “Do something significant”• Research matters!• Research is an urgent matter!•Work harder and smarter!•Work hard but not harder to
“I have to get you to drop modesty and say to yourself, ``Yes, I would like to do first-class work.'' Our society frowns on people who set out to do really good work. You're not supposed to; luck is supposed to descend on you and you do great things by chance. Well, that's a kind of dumb thing to say. I say, why shouldn't you set out to do something significant. You don't have to tell other people, but shouldn't you say to yourself, ``Yes, I would like to do something significant.”
Richard Hamming. “You and your research”http://www.youtube.com/watch?v=a1zDuOPkMSw
“If you do not work on an important problem, it's unlikely you'll do important work. It's perfectly obvious. Great scientists have thought through, in a careful way, a number of important problems in their field, and they keep an eye on wondering how to attack them.” - Richard Hamming. 08/30/2013 Robotics&Ribs@MESALAB@UCMerced Symposium
Slide-36/1024
AFC @ MESA LAB
“One of the characteristics of successful scientists is having courage. Once you get your courage up and believe that you can do important problems, then you can. If you think you can't, almost surely you are not going to. Courage is one of the things that Shannon had supremely.” - Richard Hamming. 08/30/2013 Robotics&Ribs@MESALAB@UCMerced Symposium
Slide-37/1024
AFC @ MESA LAB
“You should do your job in such a fashion that others can build on top of it, so they will indeed say, ``Yes, I've stood on so and so’s shoulders and I saw further.'' The essence of science is cumulative. By changing a problem slightly you can often do great work rather than merely good work. Instead of attacking isolated problems, I made the resolution that I would never again solve an isolated problem except as characteristic of a class.” - Richard Hamming. 08/30/2013 Robotics&Ribs@MESALAB@UCMerced Symposium
Slide-38/1024
AFC @ MESA LAB
Robotics&Ribs@MESALAB@UCMerced Symposium
Slide-39/1024
Outline• Introducing new MESA Lab members• Research Excellence
–Finding (research problems to attack)–Writing–Reading–Presenting–Networking, ethics, broad impacts …
08/30/2013
AFC @ MESA LAB
If you do not write down or write up, it did not happen!
“I have now come down to a topic which is very distasteful; it is not sufficient to do a job, you have to sell it. `Selling' to a scientist is an awkward thing to do. It's very ugly; you shouldn't have to do it. The world is supposed to be waiting, and when you do something great, they should rush out and welcome it. But the fact is everyone is busy with their own work. You must present it so well that they will set aside what they are doing, look at what you've done, read it, and come back and say, ``Yes, that was good.”” - Richard Hamming.
There are three things you have to do in selling. You have to learn to write clearly and well so that people will read it, you must learn to give reasonably formal talks, and you also must learn to give informal talks. - Richard Hamming.
AFC @ MESA LAB“Now self-delusion in humans is very, very common. There are
enumerable ways of you changing a thing and kidding yourself and making it look some other way. When you ask, ``Why didn't you do such and such,'' the person has a thousand alibis. If you look at the history of science, usually these days there are 10 people right there ready, and we pay off for the person who is there first. The other nine fellows say, ``Well, I had the idea but I didn't do it and so on and so on.'' There are so many alibis. Why weren't you first? Why didn't you do it right? Don't try an alibi. Don't try and kid yourself. You can tell other people all the alibis you want. I don't mind. But to yourself try to be honest.” - Richard Hamming.
AFC @ MESA LAB“In summary, I claim that some of the reasons why so
many people who have greatness within their grasp don't succeed are: they don't work on important problems, they don't become emotionally involved, they don't try and change what is difficult to some other situation which is easily done but is still important, and they keep giving themselves alibis why they don't. They keep saying that it is a matter of luck. I've told you how easy it is; furthermore I've told you how to reform. Therefore, go forth and become great scientists!” - Richard Hamming.
• Teachers can no longer only throw information, and facts at students and expect 'education' to occur!– Rob Reilly Ed.D. http://www.media.mit.edu/~reilly
• When you forgot everything, what’s left is “higher education” – YangQuan Chen (??)
• Google or wikipedia etc. can make you “informed” but not “educated”.– YangQuan Chen
• http://www.youtube.com/watch?v=a1zDuOPkMSw• Dr. Charles (Chuck) Swenson of Utah State
University for first bringing “You and Your Research” to my attention during our ECE Faculty Retreat in circa 2007(?) and his USU ECE 2011 Talk slides: http://www.neng.usu.edu/classes/ece/6800/fall11_resources/Swenson%20Fa11%20Presentation.pdf