Fractional calculus helps control systems hit their mark

December 22, 2016

If you've ever searched for ways to curb your car's gas-guzzling appetite, you've probably heard that running on cruise control can help reduce your trips to the pump. How? Cars, it turns out, are much better than people at following what control systems experts call a setpoint--in this case, a set speed across different terrain. But they could be even better. Calling upon a branch of mathematics known as fractional calculus, a team of researchers has developed a new setpoint-tracking strategy that can improve the response time and stability of automated systems--and not just those found in your car.

One popular method for tracking setpoints is to use what's known as a setpoint filter. A setpoint filter helps solve the problem of under- or overshooting a far-away target. Blast furnaces, for example, have to go from room temperature to precisely thirteen hundred degrees to infuse iron with carbon to make steel. Some temperature controllers may overshoot as they quickly try to reach that temperature. Adding a setpoint filter smooths the path to make sure the furnace reaches the target temperature without going over. The problem, of course, is that it takes longer to get there. That's where fractional calculus comes in.

Compared with classical (or integer-order) calculus, which forms the mathematical basis of most control systems, fractional calculus is better equipped to handle the time-dependent effects observed in real-world processes. These include the memory-like behavior of electrical circuits and chemical reactions in batteries. By recasting the design of a setpoint filter as a fractional calculus problem, researchers created a filter that could not only suppress overshooting but also minimize the response time of a virtual controller.

A side-by-side comparison showed that their fractional filter outperformed an integer-order filter, tracking the complex path of a given setpoint more closely.

One drawback of this fractional design is that it's difficult to incorporate into existing automated systems, unlike integer-order filters, which are generally plug-and-play. But as the world of automation becomes increasingly complex, fractional filters may ultimately set the new standard for controlling everything from robotics and self-driving cars to medical devices.
-end-
Fulltext of the paper is available:

http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7589492
http://html.rhhz.net/ieee-jas/html/20160413.htm

Video summary:
https://youtu.be/ycD4iJME96k
https://vimeo.com/191958035
http://players.brightcove.net/4887491952001/default_default/index.html?videoId=5209849198001
http://v.youku.com/v_show/id_XMTgyMzMzMTc4NA==.html

IEEE/CAA Journal of Automatica Sinica (JAS) is a joint publication of the Institute of Electrical and Electronics Engineers, Inc (IEEE) and the Chinese Association of Automation. JAS publishes papers on original theoretical and experimental research and development in all areas of automation. The coverage of JAS includes but is not limited to: Automatic control/Artificial intelligence and intelligent control/Systems theory and engineering/Pattern recognition and intelligent systems/Automation engineering and applications/Information processing and information systems/Network based automation/Robotics/Computer-aided technologies for automation systems/Sensing and measurement/Navigation, guidance, and control.

To learn more about JAS, please visit: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6570654

http://www.ieee-jas.org

Chinese Association of Automation

Related Chemical Reactions Articles from Brightsurf:

Shedding light on how urban grime affects chemical reactions in cities
Many city surfaces are coated with a layer of soot, pollutants, metals, organic compounds and other molecules known as ''urban grime.'' Chemical reactions that occur in this complex milieu can affect air and water quality.

Seeing chemical reactions with music
Audible sound enables chemical coloring and the coexistence of different chemical reactions in a solution.

Nanocatalysts that remotely control chemical reactions inside living cells
POSTECH professor In Su Lee's research team develops a magnetic field-induced heating 'hollow nanoreactors'.

New NMR method enables monitoring of chemical reactions in metal containers
Scientists have developed a new method of observing chemical reactions in metal containers.

Levitating droplets allow scientists to perform 'touchless' chemical reactions
Levitation has long been a staple of magic tricks and movies.

Predicting unpredictable reactions
New research from the University of Pittsburgh's Swanson School of Engineering, in collaboration with the Laboratory of Catalysis and Catalytic Processes (Department of Energy) at Politecnico di Milano in Milan, Italy, advances the field of computational catalysis by paving the way for the simulation of realistic catalysts under reaction conditions.

First-time direct proof of chemical reactions in particulates
Researchers at the Paul Scherrer Institute PSI have developed a new method to analyse particulate matter more precisely than ever before.

Finding the source of chemical reactions
In a collaborative project with MIT and other universities, scientists at Argonne National Laboratory have experimentally detected the fleeting transition state that occurs at the origin of a chemical reaction.

Accelerating chemical reactions without direct contact with a catalyst
Northwestern University researchers demonstrate a chemical reaction produced through an intermediary created by a separate chemical reaction, findings that could impact environmental remediation and fuel production.

Visualizing chemical reactions, e.g. from H2 and CO2 to synthetic natural gas
Scientists at EPFL have designed a reactor that can use IR thermography to visualize dynamic surface reactions and correlate it with other rapid gas analysis methods to obtain a holistic understanding of the reaction in rapidly changing conditions.

Read More: Chemical Reactions News and Chemical Reactions Current Events
Brightsurf.com is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com.