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Nordic Ware Microware Quick Popper Microwave Popcorn Popper No Bpa
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Sales tax:
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Shipping & Handling
Shipping (note: We can only ship to the address provided by the customer during checkout)
Your order will be shipped out through Ups, Usps, FedEx, among others. At this time, we only ship to physical addresses that are located within the 48 contiguous states of the United States of America. We are unable to ship to P. O. Boxes, Apo or Fpo addresses, or international addresses. We do utilize EBay's Global Shipping Program to ship to an international buyer in an eligible country.
Global Shipping
Available through eBay's Global Shipping program Only. Shopping cart will estimate eBay's additional time & costs. All Electrical Products including kitchen appliances, audio systems, power tools, etc. Are Usa standard Plug ins and operate at 100-200v Voltage. If the voltage in your country is not within the 100-200v range, pls make sure that you have a power transformer ready before you use the product. Returns are accepted w/n 30 days, Global return shipping costs will be the responsibility of the buyer. If the item arrives damaged thru shipping transit Ebay global shipping needs to be contacted through eBay for reinbursement. For your protection and to ensure consistency in the Marketplace, all orders are shipped to your PayPal address provide at time of sale. So pls ensure it is up to date prior to finalizing your purchase. We are not responsible for undeliverable/incorrect addresses.
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Microwave Cooking Gadgets
Make single serving popcorn in minutes
Doubles as a serving bowl
Add oil or butter after cooking is optional
Healthy alternative to bagged popcorn
BPA- and melamine-free
Nordic Ware Microware Quick Popper Microwave Popcorn Popper No BPA
Product Details:
Fun and easy to use microwave popcorn popper. This popcorn popper makes single servings of popcorn in minutes. Popper doubles as a serving bowl. No oil or butter needed but may be added after cooking. Create a healthy alternative to bagged popcorn. Bpa- and melamine-free. 8-Cup capacity. Made in the Usa.
Microwave Cooking Gadgets
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text:
San Jose, CA (PressExposure) September 02, 2009 -- Learning management system provider and courseware syndicator Coggno, Inc. provides companies with simple tools to create and deliver online sales training.
Sales skills are especially crucial during a time when potential and existing clients are buttoning up their wallets on the grounds of economic difficulty. Sales representatives must be able to cancel out any economy or budget objections before they arise.
For this reason, more organizations are finding ways to create and deliver sales training in a more cost-effective and efficient fashion. Such programs include training in sales management, sales skills, and telemarketing skills programs.
Workshops and seminars on how to prospect and sell effectively, build solid customer relationships, master cold calls and closing sales, create effective sales teams, set performance goals and expectations, and prevent sales resistance are increasingly taking place online. Using online tools, workshop leaders are able to discuss and demonstrate sales principles effectively and at a fraction of the cost of traditional training methods.
One major benefit of online sales training is the interaction that can take place. Learners can contribute to discussions begun by workshop leaders, role-playing and receiving coaching on telemarketing programs and skills. Online interactions are often a more robust and effective means of practicing skills than the in-person ones, since learners are provided with the self-paced convenience inherent to online learning.
Using online sales training platforms like Coggno, companies are finding they are able to increase a company's sales, productivity, and profits. They also serve to enhance professional and personal self-confidence of participants, and enhance professionalism in a company's selling processes.
Courses range from more involved programs to quick workshops that are able to be completed in 30 or 40 minutes, making them easy to work into learners' schedules.
Sales training for a company's sales professionals and managers can be organized and performed internationally, linking a company learning management system to its various human resources departments and ERP systems, to perform multi-locational, cost-effective and efficient training.
Coggno may serve an important role in keeping track of tasks, goals, and learners' training processes. Organization is crucial in any training initiative, and in order to avoid problems due to confusion, an LMS can be implemented to keep track of member achievements and team objectives.
Nowadays companies are often composed of a small or large network of team members to meet all the goals and functions an organization has. Service teams, for example, are an increasingly international group. They support customers or the internal organization, normally with a service or technical support role, 24/7. LMSs like Coggno are proving that if so many sales and customer services can take place across great distances, so can sales training itself.
The Coggno LMS provides robust tools such as text editor, SCORM, question banking, video and audio tool, screen recording, Flash-based video creation, an Apple podcast creator, assessment, and quiz tools. LMSs like Coggno offer a variety of ways courses can deliver practice situations dealing with customers.
But sales training courses have a shelf life, which is why a pay per use LMS model such as Coggno's works well for many companies.
"Many organizations sign on for monthly contracts, but find they never create and push out as much content as they originally thought," says Coggno VP Tod Browndorf. "Time goes by and their net costs are much higher. With Coggno, you can create your own training and deploy it as you need to."
Coggno's pay per use learning management system requires no up front costs to create and deploy training, so that sales training created, acquired, and/or delivered by an organization is always fresh and relevant. In difficult economic times, such business models are increasingly being called for.

subset: commoncrawl


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We discuss politics, computer science, philosophy, economics, gardening, and sex.
Thursday, November 21, 2013
Madison: Who should vote?
NOTE: when I dictated this passage, Siri wrote: "Elaborating on this insight in a Characteristically Gloomy Way..."
I guess she thought that "Characteristically Gloomy Way" was a street address. It is probably right next to "Morose Circle" and "Suicidal Depression Boulevard."
8 comments:
"In future times a great majority of the people will not only be without landed, but without any sort of, property."ReplyDelete
He was glaringly wrong there. I wonder what being without "any sort of property" would even look like.Replies
"He was glaringly wrong there."Delete
Nope. If he were alive today, he would be saying, "Yes, just as I predicted."
If you can't try to sympathetically imagine what a writer is talking about, you will continually grossly misinterpret what they are saying.
I would say that Madison is ultimately talking about rights, not property per se.Delete
"Nope. If he were alive today, he would be saying, 'Yes, just as I predicted.'"ReplyDelete
How so? Would he mean the corporations?Replies
You have to realize he is a classical republican. In classical republicanism, the key to being a solid citizen is independence. So property means property that supports you: a farm, a shop, a merchant vessel, or workshop. This made one independent, not beholden to a "master" (or employer) and capable of exercising citizenship.Delete
Madison knew everyone who have a shirt and a pair of trousers.
Scineram, *I* I'm not saying that an Exxon employee could or couldn't. But Madison, as a classical republican, would not think he would do so well, as he lacks economic independence.ReplyDelete
You say that James Madison was a classical republican. Was he also a classical liberal?ReplyDelete
An orgy
"The advancement of science and the rationality of politics are interwoven in a social process that, in the perspective of a more distant f...
Declares LewRockwell.com : "All of this means that while the government has been artificially propping up the economy and 'stimu...
Is shaping up nicely .
The language won't die, but that doesn't mean the programmers won't ! Funny quote: '"Just because a language is 50...


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Higher education has always had a high price tag but there are ways you can gain the knowledge you need along with an official credential from the institution and signed by the instructor. The certificate verifies your achievement and can be used to highlight skills on your resume or LinkedIn profile.
You can do this from the comfort of your own home with a computer and internet connection. Check out edX.org and find the courses you want to take!
Founded by Harvard University and MIT in 2012, edX is an online learning destination and MOOC provider, offering high-quality courses from the world's best universities and institutions to learners everywhere.
I've enrolled in HarvardX's CS50x course – Introduction to Computer Science. I'll keep you updated on my review of the course as I take it.


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Friday, December 14, 7:00 PM (EST) at Bankers Life Fieldhouse, Indianapolis, IN
12-10 (4th Atlantic, 8th East)
11-11 (3rd Central, 9th East)
TV: Comcast SportsNet Radio: 97.5 The Fanatic FM | Live Stats
NOTE: The Comcast Network HD is now on XFinity® Channel 856
by Warren Croxton and Max Rappaport
Guard Jrue Holiday sat out the Sixers' Thursday morning's practice session with soreness of the longitudinal arch in his left foot. X-rays were taken and came back negative for a fracture. An MRI taken in the afternoon revealed a sprain.
The injury will cause Holiday to wear a walking boot, as the team travels to Indianapolis Thursday afternoon in advance of their Friday night meeting with the Pacers. He is a game-time decision for that game.
Should Holiday miss any time as a result of the injury, Collins said that he would likely start guard-forward Evan Turner at the point guard position, with guard Nick Young taking Turner's place on the wing.
Veteran Royal Ivey did not make the trip to Indianapolis, due to strep throat, leaving rookie Maalik Wayns as the team's only reserve point guard, should Holiday not play.
F David West vs. F Thaddeus Young
Last season, David West's first in Indiana, the 6-9 forward averaged just 12.8 points and 6.6 rebounds per game, his lowest totals since the 2004-05 season; his 48.7% field-goal percentage was his lowest in three seasons. Still, West provided veteran leadership to a young Pacers team that won its first round series with the Orlando Magic and gave the eventual-champion Heat in the Conference Semifinals, stealing a game in South Beach and going up 2-1 before losing three straight. This season, the former Hornet has bounced back in a big way, averaging 17.5 points and 8.6 rebounds a night, while shooting 50.3% from the floor. Part of the reason why the 10-year veteran has had a successful season is his shooting from inside ten feet. He's shooting an impressive 61.7% from that distance, a vast improvement from the 52.2% he shot in last year's lockout-shortened season. His 73.4% shooting efficiency
Thaddeus Young has scored double-digit points in each of his last 12 games. During that streak, he's averaged 17.5 points (56.1 FG%), 7.3 rebounds, 1.6 steals, and 1.3 blocks per game. The six-year veteran is four 10+ point games away from tying his career high of consecutive games with double-digit points. Part of the impetus for Young's impressive play has been his ability to play off of the playmaking ability of Jrue Holiday and Evan Turner. The NBA average for %Ast (a stat that measures the percentage of a player's field goals that are the result of assists) on shots from within ten feet of the rim is just under 50 percent. Young's %Ast from those distances is 74.5% and is 88.2% from 3-9 feet, the latter of which ranks third among all players who play at least 25 minutes.
The Key
In four meetings with the Sixers last season, David West shot just 4-of-18 from 3-9 feet, with just one of those baskets coming off of an assist. Still, he averaged 19.5 points and 7.3 rebounds in games against Philly last season. He scored all but 18 of his 66 points off of field goals from inside three feet and outside 15 feet; he was assisted on 73.9% of those baskets.
Six-sentence Scouting Report
After beginning the season 2-6, the Frank Vogel-led Pacers have rebounded and now hold a .500 record (11-11). The Pacers are 6-3 at home and won their most-recent game at Bankers Life Fieldhouse, a 96-81 rout of the Cleveland Cavaliers 96-81 on Wednesday. The Pacers rank 29th in the NBA in points scored, scoring just 91.0 a night. They have only scored 100 points three times, and in two of those games, the century mark was hit in overtime. Indiana ranks 21st in free-throw percentage (73.8%), 24th in three-point shooting (33.3%), and 28th in field-goal percentage (41.7%). Their second-ranked defense (91.3 points allowed per game) has kept them afloat, though.
The Vogel Effect
Frank Vogel took over the reins as head coach after Jim O'Brien was let go 44 games into the 2010-2011 season. In the final 28 games of that season, the Wildwood, NJ native went 20-18 and led the team to a playoff berth. During the Jim O'Brien era, the Pacers played a more up-tempo offensive style; one that put less emphasis on the defensive side of the ball and allowed opponents to average over 100 points a game from 2007-11. Vogel, a former Sixers assistant coach, guided last year's Pacers team to a 42-24 record and held opponents to 94.4 points per game (10th in the league). This season, Vogel's Pacers rank second in the league in points allowed (91.3 per game). Indiana's defensive rating (a statistic that is an estimate of the ammount of points a team allows per 100 possessions) this season is 100.2, which is the second-best in franchise history.
Missing Granger
The Pacers' top scorer last season, Danny Granger, has yet to play this season, as he deals with patellar tendinosis in his left knee. The 6-8 swingman has led the team in scoring every year since 2007-08 season and ranks ninth all-time in points for the franchise. He is expected to return to action to return in February. Third-year man Paul George, who started at shooting guard last season, slid over to to Granger's spot at small forward and is averaging 16.0 points, 6.7 rebounds, and 3.5 assists per game this season, all of which are career highs.
4/21/2012 – Sixers 109, Pacers 106 OT
Guard Jrue Holiday's jumper with 31 seconds to go in overtime won the game for the Sixers, who moved within one game of securing a playoff berth. Holiday scored 17 points on 7-of-14 shooting, while dishing out seven assists. The Sixers had five players reach double figures in scoring, led by forward Elton Brand's 20 points. The Sixers' bench scored 45 points and grabbed 22 rebounds, as a unit. David West led all scorers with 32 points and 12 rebounds.


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Mark Brooks brightens junior's day at Insperity Invitational pro-am
April 30, 2014
By Chris Dornan, Special to Together.PGATOUR.com
HOUSTON- When Brayden Ingebrigtsen headed to The Woodlands Country Club Tournament Course on Tuesday he was a little more nervous than usual to hit the first tee.
One can forgive him.
Afterall, the 12-year-old was ducking under the ropes at the Insperity Invitational with seven-time PGA TOUR winner, Mark Brooks.
Brooks was one of nine Champions Tour professionals to participate in The Woodlands Development Company Junior Pro-Am that included 36 junior golfers (18 girls and 18 boys).
The talented young players ranging from the ages of seven-to-17 formed nine groups with one Champions Tour professional each for the nine-hole Pro-Am.
Dressed in his finest fluorescent-coloured Puma golf duds, the day was a dream come true for young Brayden – a talented south paw from up the road in Woodforest, TX.
"The first couple of holes I was pretty nervous, but now I'm just having so much fun. The whole experience has been so awesome and really cool," said Ingebrigtsen while sporting a 1,000-watt smile alongside the 13th green.
And why wouldn't he? The Woodforest resident just won his first golf bet against a Tour professional while making birdie on the par 4, 12th hole.
"I hit it to about one foot on 12 and I gave Mark my (left handed) gap wedge. I told him if he could hit it inside me, I'd give him a dollar. Good thing he didn't because I didn't have any money with me."
Fun and games is what this day is all about for the Champions Tour pros while playing with many of the top juniors in the area who earned a pass under the ropes to stroll the Tournament Course fairways based on points gained at competitions in the Southern Texas PGA section.
"I'm around a lot juniors so to see how great they play doesn't surprise me," said Brooks. "Many are working with coaches so I'm very careful to give them too much instruction, but I definitely like to answer any questions they have. For me though, it is important for them to have fun, but also try to learn how to play good golf with all of the proper etiquette."
Lessons Brayden will take with him for life.
"Mark is very steady out here and he really helped me with my short game and how to play with these hard and fast greens," said Ingebrigtsen. "But the one thing I'll remember about playing with him, and being out here, is just how much fun it is!"
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B2B Penton sold by PE owners to Informa plc in $1.56 billion deal
The present ownership of the company was established when MidOcean Partners and Wasserstein & Co. combined Prism Business Media with Penton Media in 2006
There is a basic rule of private equity owned media companies: at some point the PE will want to sell. The standard time is around five years. Maybe like the old line about guests and fish – maybe B2Bs, like fish, begin to smell after five years.
But MidOcean Partners and Wasserstein & Co. have been co-owners of the B2B media company Penton for a decade now. But that is about to change.
Today it was announced that the UK media company Informa plc has bought Penton for $1.56 billion (£1.18 billion). The deal is expected to be closed by November.
Penton has moved from a mainly B2B print magazine company into an events and information company, similarly positioned as its new owner.
As those with long memories might know, the last time a UK company bought a leading US B2B company it didn't turn out so well. But times are certainly different, and with the emphasis on events the results may be different.
Informa Exhibitions has several recognizable event brands including World Of Concrete. If you are not familiar with the show don't laugh, it's a big show, one I used to attend annually in my construction publishing days.
"I think we've been very consistent that we want to grow in exhibitions and trade shows, business intelligence and information services … we see the natural next rotation step for growth as being the United States of America," Informa CEO Stephen Carter told Reuters.
Penton's markets include agriculture, transportation,natural products and food, design and manufacturing and infrastructure. Its products include magazines and events in those area, with the Natural Products East/West Expo being one of the shows I used to regularly attend, and Supermarket News and Aviation Week (which it bought from McGraw-Hill in 2013) being some of its more familiar magazine titles.
It's hard to say whether this deal will work out well for the Penton folk. The acquisition makes the US division a very large part of the company, with Bloomberg reporting that Informa will generate less than 10 percent of its revenue from the UK after the Penton acquisition. Also, the deal will be financed through new debt and equity, meaning that there needs to be profits to cover the added costs.
Here is the announcement of the deal:
NEW YORK, NY – September 15, 2016 – MidOcean Partners, a premier middle market private equity firm, and Wasserstein & Co. , a leading independent private equity and investment firm, today announced that they have entered into a definitive agreement to sell Penton, an innovative professional information services company, to Informa plc for $1.56 billion. The consideration will consist of $1.46 billion of cash (plus adjustments) and $100 million of Informa stock.
Under MidOcean and Wasserstein ownership, Penton has been significantly transformed from predominantly a print business into a preeminent professional information services company. Penton has successfully completed 13 acquisitions, creating scaled positions in growth-oriented sectors—including agriculture, transportation, natural products/food, infrastructure, and industrial design/manufacturing sectors. Today, Penton has seven of the top 250 largest trade shows in the U.S., which have helped drive an event revenue CAGR of over 20% over the last four years. Additional significant investments have been made to create an industry leading team that has built a state of the art digital platform, launched numerous SaaS products and built a scaled and fast- growing digital content marketing services business.
"We are very pleased by the transformation we have helped Penton achieve. The business has successfully transitioned from a traditional business-to-business publisher into a premier professional information services business over the last few years," said Anup Bagaria, Co-Managing Partner of Wasserstein and Co-Chairman of Penton, and Michael Struble, Partner of Wasserstein and Director of Penton. "The management team has done an excellent job establishing scaled, leadership positions in Penton's core verticals. Through continuous improvement of its core offerings, new product launches and strategic M&A, Penton has grown impressively in recent years and positioned itself to accelerate growth in the years to come."
Barrett Gilmer, Managing Director of MidOcean and Co-Chairman of Penton, said, "We are incredibly proud of our partnership with Penton and the Company's success under CEO David Kieselstein. This investment exemplifies the value we bring to our portfolio companies by working closely with management teams to identify attractive areas for expansion, enhance operations and drive growth. In this case, under David's leadership, and in particular over the last four years, Penton achieved a dramatic shift in its business mix, completed a number of highly strategic acquisitions and nearly doubled EBITDA from $77 million to $140 million. The entire Penton team played a role in this transformation and we wish them continued success as part of the Informa team."
"MidOcean and Wasserstein are seasoned, hands-on investors and have been invaluable partners in supporting Penton and allowing us to execute on our strategy," said David Kieselstein, CEO of Penton. "Their strategic insight, resources, flexibility and experience in the media services sector have been essential to our transformation by enabling our organic growth through new investment initiatives and sourcing and coordinating multiple accretive acquisitions."
The transaction, which is subject to approval by Informa shareholders and customary regulatory and closing conditions, is expected to close in the fourth quarter of 2016.
Kirkland & Ellis LLP served as legal advisor to Penton and MidOcean. Jones Day served as legal advisor to Wasserstein.


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Shrinking tunnel shrink Tectron
Need maintenance technician, revision and warranty? Click here.
Tectron shrinking tunnel. Year: 2013. Model: BAN 20/35. Supply voltage: 220 V-60 Hz. current: 32 a. mouth Measures: 350 mm height x 200 mm width
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Visitation: Schedule and availability of equipment. Merely illustrative images


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Much consideration went into designing the bar, particularly the counter, which was made from handsome pecan wood. The bar area is meant to pay homage to Spain's view of it as a primary fixture. "It is the first thing you see when you walk into most restaurants," explains Jerez. "In a restaurant the idea is that you have wine or beer and then you work your way to the dining room. And then on the way out, you to do the same."
Similarly, the bar at Barlata is a lively focal point, one that encourages patrons to dine at the counter, or to wander over for a drink before and after their meals. The bar will soon be expanding its pinchos offerings and have a tv for screening futbol (soccer) games.
Barlata features exclusively Spanish wines. Olivella, who won awards for his B44 wine selections, created an affordable wine list that represents each of Spain's regions. There is an assortment of Sherry – Manzanilla, Fino, Amontillado — from Jerez de la Frontera in southwest Spain. Barlata offers six types of cava, Spanish sparkling wine, which is produced in the Penedes area of Catalonia, in the north. There is wine from Ribera del Duero, Madrid, Bilbao, and Galicia, among others. Oviella, who returns to Spain at least one a year, seeks out wines unavailable in stores and other restaurants. Because there are small vineyards throughout Spain, he often purchases wine from family wineries that make only two- or three-hundred bottles a year.
Vermouth ("vermut" in Spanish) may appear on the drink menu more than in most restaurants. However, in Spain, it is a traditional apértif, flavored with various botanicals: barks, flowers, herbs, spices. "It goes well with nuts, anchovies, and anything that's pickled," says Jerez. The sweet compliments the salty. Vermouth can be drunk by itself, garnished with olives or an orange (like a martini) or enhanced with carbonated water from a siphon, a classic symbol of Spanish bars.
Barlata also offers Spanish and domestic beer, sangria, as well traditional, classic and a few signature cocktails.


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|Publication number
|Publication type
|Application number
|Publication date
|Mar 13, 2007
|Filing date
|Sep 24, 1999
|Priority date
|Sep 24, 1999
|Fee status
|Publication number
|Andrew A. Berlin, Tad H. Hogg, Oliver Guenther, Warren B. Jackson
|Original Assignee
|Xerox Corporation
|Export Citation
|BiBTeX, EndNote, RefMan
|Patent Citations (25), Non-Patent Citations (1), Referenced by (2), Classifications (4), Legal Events (6)
|External Links: USPTO, USPTO Assignment, Espacenet
The present invention relates to control and operation of structure movement, including both substantially unitary and linked structures. More particularly, the present invention relates to analog circuits implementing market allocation for control and coordination of actuators inducing structural movement.
Market based control requires allocating a task (e.g. physical actuation) among a large number of producers, with each producer bidding for part of the task. The task is determined by consumer agents in the system (higher level controllers or external requirements). Each producer has a supply curve reflecting the actuation or control produced as a function of price and each consumer has a demand curve indicating the actuation needed as a function of price. The equilibrium price is determined by the price at which aggregate demand and aggregate supply are equal. The price in turn determines what each individual actuator produces and individual consumer uses such that the total actuation equals the demanded actuation. As the task changes, different combinations of producers combine to collectively accomplish the task. Such a market is robust against failure of individual agents and changes in tasks, while requiring communication of only one quantity, namely the price, in order to coordinate the actions of an arbitrary and even time varying number of producers. Advantageously, such a price based market system naturally provides a Pareto optimal solution that is near optimal allocation within a degenerate array, even though the full optimization problem is NP-complete. Furthermore, reconciling conflicting goals is readily accomplished by having each individual actuator or consumer individually weight the conflicting goals. The market produces a group resolution between conflicting goals.
Unfortunately, presently available implementation schemes for market based control are impractical and scale poorly for large numbers of producers or consumers, especially when systems requiring real time actuation are considered. One could imagine, for example, connecting the producers and consumers using a bus (e.g. CAN bus, SPI, I2C or Ethernet bus) to communicate pricing information. For example, a 10 Mbit Ethernet system could be used to control 103 nodes of producers and consumers. Even using readily available off-the-shelf hardware, such a market control system is quite expensive, with per connection node costs of about $10 US dollars, for a total cost on the order of $10,000 US dollars. Moreover, due to the long packet header required, the bus would take on the order of 1–10 μsec to transmit a 10 bit number to each node, and then the same time to transmit the results back to each agent for one cycle of the market equilibration loop. If there are such 103 nodes, this would take on the order 2–20 msecs in the best case without packet collisions. Other widely available buses (e.g. CAN or SPI) would take at least an order of magnitude longer. The problem is even worse if multiple markets for competing allocations are required. For example, in object motion control both torques and forces must be allocated even though the requirements for each may conflict. If one had 10 markets to compute the supply and demand curves of competing allocations, either one would require 10 buses or the process would take on the order of seconds. There also is the issue of synchronizing the processors if a synchronous communication scheme is used.
In contrast to conventional digital control schemes, the present invention uses a high speed analog system minimally requiring only a single line (i.e. a "market wire") interconnecting multiple producers and consumers in a given market. Analog electronic versions of markets allocate tasks such as actuation or control in a multi-producer and consumer system using correspondences set up between current and the quantity of a commodity and between the voltage and the price. The market consists of consumers removing current from a wire and producers adding current to the wire. The price is the voltage on the wire that eventually reaches an equilibrium price. This voltage, analogous to the equilibrium price, determines the current and hence the actuation produced by each actuator. As in the case of markets, the performance of the system is robust against failures and changes in actuators or tasks.
In one version of an analog system in accordance with the present invention, each consumer has a demand curve that decreases linearly as the voltage on the market wire increases and each producer, such as an actuator or controller, draws current from the wire that serves as the 'market'. The conductances determine the slopes of the supply and demand curves as well as the market voltage. If some producers produce less, for example, actuation, less current is removed from the wire, the voltage rises causing more actuation from the remaining producers and reduces the demand by the consumers. Conversely, a decrease in demand (smaller conductances) causes less current to be added to the wire causing the market wire voltage to decrease. Production therefore decreases, and demand by the other consumers increases.
Implementation of the foregoing control schemes is of particular utility for problems requiring a large number of actuators to produce a desired actuation level. In this case there would be one consumer with a flat demand curve, i.e., a current source, for which the current (demand) does not change with voltage (price). The actuators (producer agents) would produce actuation such that all this current is removed to ground (demand balanced by supply). This high bandwidth, asynchronous coordination occurs through one wire and can be inexpensive per connection (only a few chips per node). No explicit computation is required to allocate the resources and a near optimal solution is obtained from a possibly degenerate set of equivalent solutions.
Advantageously, like traditional economic markets, analog circuit implementations of the present invention are robust against changes in actuator function or failures. As the cost per unit functionality of sensors, actuators, and computers (agents) continues to decrease, control systems comprised of many interconnected elements become increasingly practical. High speed systems having 103 processors with 10 market wires connected with multiplexed A/D's and D/A's or multiple op amp packages operating in real time are economically feasible using apparatus and methods of the present invention. Such systems could be much more responsive to events in their environment and internal states as well as exhibit robustness against component failure. Such an analog electronic implementation is distributed, flexible, easily extensible, efficiently uses wires, and reduces the communication load. Analog markets that can compute weighted sums of up to 104 spatially distributed agents and communicate the resulting sum back to agents in about 1–10 μsecs are supportable. The complexity of each such node is about 1–3 op amps per node or one embedded processor chip per node for the more flexible implementations.
In one preferred embodiment of the present invention, a distributed market based analog control system includes multiple producing units, each producing unit having an output responsive to a market price. Production levels are in part determined by needs of multiple consuming units, each consuming unit also having an input responsive to a market price. Communication of pricing information between the producing units and the consuming units is mediated by a marketwire connecting multiple producing units to multiple consuming units. Absolute or relative voltage level, current level, or frequency of voltage or current level changes can all be used to represent price information on the marketwire. For voltage level based pricing schemes, typically voltages of about 5–10 volts are used. Since noise based voltage fluctuations on the marketwire are typically less than about 1.0 mV, as much as 10 bits of precision is available for distinguishing price levels in the system. To simplify construction, reduce cost, and enhance system robustness, substantially identical adjustable circuit elements can be used for both multiple producing units and multiple consuming units, with the substantially identical voltage adjustable circuit elements being connected to the marketwire.
In a particularly preferred embodiment of the present invention, the distributed market based control system has no central controller for setting market prices. In the absence of either a central controller or a central timing mechanism, both of which can be expensive, prone to failure, or introduce substantial delays in price computation and distribution, the reliability of the system is improved. In operation, a producing unit having an output responsive to a market price, a consuming unit having an input responsive to a market price, are connected to a marketwire connecting the producing unit to the consuming unit with changes in analog electrical characteristics of the marketwire representing market price fluctuations. These analog electrical characteristics of the marketwire can be voltage level changes, current level changes, or time or frequency domain changes in electrical properties. Such a system operates asynchronously, without a central timing clock, with the marketwire immediately transmitting changes in price information on a microsecond scale, with no need for polling or n-way exchanges of information between n number of producers and consumers.
Advantageously, the present system for sharing pricing information between producers and consumers is not limited to electrical analog signals. Other analog propagating physical quantities can be used to compute the market and communicate pricing information. For example, a distributed market based analog control system including multiple producing units and multiple consuming units can be based on partitioning or distribution at least in part on non-electrical properties, including systems based singly or in combination on changes in electromechanical, mechanical, pressure, temperature, or thermal properties, chemical concentrations, light levels, or any other suitable physical property that allows for ready addition or subtraction of measurable system properties (e.g. by substitution of easily measurable fluid pressure changes in a closed pipeline system for voltage changes in wire circuits). Other physical characteristics suitable for communication of price include pressure within a cavity, magnetic flux within a superconducting loop, or optical energy within a resonant cavity.
As will be appreciated, since not all producers (consumers) are capable of providing a continuous range of actuation (demand) in response to a continuous range of received prices, some mechanism for handling stepped (or quantized) actuator response functions without introducing unwanted oscillations is needed. More generally, while it may not be possible to balance supply and demand exactly at each instance of time it can be possible to balance the time averaged supply and demand. The present invention provides such a mechanism by employment of an inventory or buffer unit to temporarily store excess output or demand and permit market equilibration. The inventory unit may be attached, along with producing units and consuming units, to a single marketwire or incorporated into individual or groups of producing and/or consuming units. In operation, for example, the inventory unit can inject additional charge, raise voltage level, or adjust vibrational amplitudes to smoothly equilibrate the market of consumers and producers.
Such inventory units are particularly useful in conjunction with on/off actuators such as valves. Most often instantaneous valve actuation cannot exact balance the instantaneous demand. For those embodiments of the invention having multiple valves, each of the multiple valves has a valve controller to control opening and closure of the multiple valves. A marketwire is connected to each valve controller to convey price information by analog fluctuations in electrical characteristics of the marketwire. Valves can be completely open and completely closed in certain embodiments, while valves controllable to partially open or close are possible in other embodiments. Valves can be used to control fluid flow (liquid or air), or even used to control radiant energy (e.g. light valves).
Multiple markets can be used to reconcile conflicting resource allocation, a problem that nearly always occurs in real systems. The present invention provides a smooth robust balance between conflicting goals. A market wire is established for each resource to be allocated. The actuators (producers) and consumers for each resource participate in a market that establishes a price for each resource. The utility curve for each agent (consumer or producer) that participates in more than one market, represents a weighted combination of each resource. The operation of the aggregate response to the various markets produces a robust, continuous, and optimal solution for conflicting resource allocation. The analogy to traditional economic markets such the allocation between apples and oranges, for example, is that each individuals utility curve expressing their preference for apples verses oranges at a given prices, determines not only how many apples and oranges an individual receives, but also how conflicting resource demands for apple and orange production are resolved.
In other embodiments of the invention, a distributed market based control assembly can be used in conjunction with fixed or movable structures. Typically multiple actuators are attached to the structure, with each of the multiple actuators having an actuator controller to control actuator applied force. Sensors are used for measuring structure movement, and a marketwire is connected to each actuator controller to convey price information to the actuator controllers by analog fluctuations in electrical characteristics of the marketwire. Actuators can be used to stabilize a fixed structure against movement, or alternatively can be used to control movement of movable structures from defined first positions to second positions (e.g. moving a robotic arm so its tip moves from point A to point B).
More generally, the present invention encompasses a control method for non-linear coupled systems of producing units having a single consumer output. The method of the invention includes the steps of setting each producing unit to have an output responsive to an analog signal representative of a market price, and connecting each producing unit to a marketwire, with the changes in the analog signal on the marketwire representing changes in the market price and output response of each producing unit.
Additional functions, objects, advantages, and features of the present invention will become apparent from consideration of the following description and drawings of preferred embodiments.
As seen in
Communication of pricing information between the producing units and the consuming units is mediated by a marketwire or groups of marketwires 16 connecting multiple producing units 14 to multiple consuming units 12. Absolute or relative voltage level, current level, or frequency of voltage or current level changes can all be used to represent price information on the marketwire. In addition, non-electrical signals, such as may be represented by vibrational modes (e.g. acoustic transmission), radio wave links with amplitude and frequency encoding, heat, pressure, or optical links (e.g. pairwise infrared diode or laser links) between producer and consumer units. For voltage level based pricing schemes, typically voltages of about 5 volts are used. Since noise based voltage fluctuations on the marketwire are typically less than about 1.0 mV and can be as low as 10 μV within typical bandwidths used in this application, 10 bits or more of precision are available for distinguishing price levels in the system.
To provide better understanding of the theoretical underpinning of the present invention,
While this simple circuit of
More generally, one can create any arbitrary supply and demand curve using an embedded microprocessors 90 for each consumer 86 and producer 88 connected via marketwire 84 as shown in circuit 80 in
Alternatively, an all analog solution for an example case of an LED producer using op amps is presented in
An alternative pure analog circuit 110 implementation where the market speed is not limited by the actuator, shown in
Using the foregoing analog circuits such as illustrated in
In other embodiments of the present invention, the marketwire function of aggregating supply and demand and communicating price can be accomplished by separate wires. For example,
There are various possible embodiments of the analog market wire as shown in
An important additional embodiment consists of replacing the market wire by a leaking transmission line 167 with distributed capacitance per unit length 164 and distributed resistance per unit length along the conductor 161, and a leakage conductance from the market wire to ground per unit length 175 as shown in the lumped circuit representation of a transmission line 167. In this embodiment, the currents I0, I1, I2 etc. (168) due to producers and consumers do not cause a uniform voltage (therefore a price) change throughout the whole market. Instead each producer and consumer current changes the price in a localized neighborhood shown in 169. The localization is a function the values of distributed capacitances 164, leakage conductances 175, and resistances 161 as is well known from transmission line formulas. This embodiment of a marketwire can be implemented using discrete resistors and capacitors or using resistance lines. The trace material 147 may be indium tin oxide rather than copper, the material 145 may be any suitable leaky dielectric, and the dimensions of 147 are such to provide the desired capacitance 164. The advantage of the leaky transmission line is that effects of each producer and capacitor are localized. Such a market would guarantee that producers and consumers active in the market are spatially distributed along the marketwire. Moreover, if a producer or consumer malfunctions and attempts to short the market out, the effects would be localized rather than destroying the entire market. One could imagine inductors and other distributed or lumped components could be added to construct a market wire with characteristics beneficial for specific applications.
In still other embodiments of the present invention, a marketwire can carry information using other partitionable physical properties or information transfer media than that based on changes in electrical characteristics. For example, as seen in
In a second example of a non-electrical embodiment of the present invention using the same chamber system of
More generally, any intensive thermodynamic quantity such as pressure, temperature, voltage, chemical potential, magnetic field etc may serve as the market price. For example, sensors distributed in the chamber system of
Whether based on changes in electrical or non-electrical physical properties, certain modifications must be made to analog circuits in accordance with the present invention when supply and demand can not be instantaneously balanced. This often occurs for example when either discrete actuators ((on/off or quantized) are producers or discrete goals are consumers. As can be seen with respect to
In addition to an inventory circuit analog circuits operating in conjunction with discrete actuators can be implemented with circuit elements imparting predefined hysteresis such as shown in
For certain applications, the foregoing behavior (producers all on/all off) is not desirable since it is sometimes necessary to insure that all actuators or consumers participate in the market so that only a few do not end up dominating the market (monopolize the market). This more equitable allocation can be implemented using a circuit 222 shown in
The practical utility of the foregoing circuit is seen in
Analog controllers operating under some type of market communication could find a useful role in many applications, but is most useful for those applications requiring many actuators or controllers, and whose collective behavior is approximately characterized by a weighted summation of the individual responses. The desirable action of a particular agent (producer, actuator) must depend on these weighted averages and location information as opposed to detailed information about the state of other particular valves. While these restrictions appear to limit the utility of the marketwire, actually many problems satisfy these constraints. For example, as seen in
In addition to heaters, illuminators, valve assemblies for air jets, or other suitable actuator systems, marketwire controllers can be used to both move and prevent movement of structures. As seen in
As those skilled in the art will appreciate, any nonlinear-coupled systems with a single output that has a response that is to first order a linear sum of the actuations for sufficiently small actuations can be reliably controlled using apparatus in accordance with the present invention. If the response R of a system is a function of the vector x of actuations given by R=f(x), by a Taylor expansion R=f(xo)+ΣiwiΔxi. where wi are the weights related to the first derivatives, xo is the previous actuation state, and Δxi are the small changes in the actuation state. Moreover, significant local non-linearity's can be captured if wi=wi (xi) depends only on the local state. Hence, the applicability of market based systems is quite general, applying, for example to control of buckling beams or arrays of inverted pendulums, as well as the previously discussed valve arrays, robotic arms, or computational resource problems.
To better understand operation of the present invention, one particular analog implementation of a market based algorithm for controlling arrays of discrete actuators is hereafter described. In this implementation, motion of a sheet of paper though the use of a very large number of actuators (open/shut valves for pressurized air jets) must be coordinated to achieve a global goal of precision motion of the sheet of paper (see, e.g.
A typical system of this sort will have a few thousand actuators, with a few hundred actuators lying under the paper at the same time. Typically all air-jets will produce the same amount of force, but will point along different direction in the plane. Assuming a system with motion (of the paper) along one axis and rotation, each actuator (valved air jet) produces not only a vertical supporting force, but also a torque force that is proportional to its perpendicular distance to the center of the paper. For air-jets distributed randomly along the paper, achieving the optimal force and torque requires solving an NP-complete problem, whose difficulty exponentially grows as the number of actuators increases.
The present implementation is based on market principles guiding local distribution of force, with minimal communication between the air-jets and the controller, and minimal communication among the air-jets themselves. The operation of such a decentralized system can easily be continuous in time because the switching time between two actuators need not be a multiple of some fixed time. Because the decentralized system can oscillate at a rate much faster than 3 ms even when the amplitude of oscillations is non-optimal, the root mean square (RMS) error of the integral will be comparable or even smaller than the equivalent error of the centralized controller.
The market principle treats the air-jets as producers and the force and torque controllers as consumers. The producers and consumers communicate through a common voltage (per market) that acts as the price. The price is determined as a function of aggregate supply and demand, which are fed into the market as currents from the actuators and controllers. When demand exceeds supply, the price increases, and either supply increases or the demand decreases, until equilibrium is reached. Thus, it becomes possible to coordinate a large number of sensors and actuators through a single market-wire.
The control of many systems often require reconciliation between a variety of constraints. The analog market system can accomplish this reconciliation through the use of multiple markets. For example, the air-jet system requires at least two markets. Because each actuator provides a different ratio of force to torque, the prices of torque and force must be kept separate. However, the allocation is done in a local fashion, with only the two prices (and their corresponding aggregate current feedback) determining the utility function of each actuator thereby determining behavior of the system. In fact, there exists no entity (e.g. a central actuator controller) that is aware of the positions and orientations of the actuators.
Each producer block 302 is the portion of the circuit that interacts with one actuator (valve). The producer block 302 must observe the market prices, evaluate using the utility function, and set the state of the actuator based on them. Additionally it must feed back its state into the force and torque market wires 280 and 281, respectively. The producer block consists of three stages: the utility computation, the decision stage and the feedback to the market. The utility computation stage is the point where each actuator combines the prices from the different markets to obtain a total utility or total price for its product. The utility function any monotonic increasing function of the prices selected to produce desirable behavior of the market. For the air-jet's, the utility beneficially can be a weighted sum of the prices of force and torque. The weighting factor, for example, may be selected to be the perpendicular distance to the center of the paper Δy corresponding to the ratio of torque to force that the air-jet produces. The factor Δy multiplies the price of torque, so that the air-jets near the center tend to ignore the price of torque, and vice-versa for the air-jets near the edge. Additionally, multiplying by Δy sets the correct relative sign between torque and force. A backwards facing air-jet should also multiply the utility by −1, since it produces the exact opposite of a forwards facing air-jet.
For correct scaling between the force and torque terms there must be an additional constant scaling factor. If the force and torque prices are in the same units of value, the scaling factor should be proportional to the inverse of the radius of gyration, named R−2. For a rectangular sheet,
R−2=12/(L2+W2) where L is the length and W is the width. Hence, R is about five inches for an 8.5�11 inch sheet of paper. Summarizing, the first stage of the producer block, will compute a utility
that characterizes an appropriate tradeoff between the various markets for each producer.
The second stage of the producer block consists of the decision stage in which each actuator must determine, based on its current utility function, whether it should turn on or off. A first constraint that might, beneficially, be taken into account for the air-jets is that there must be a delay time, here at least 3 ms, between changes of state. Not only does the constraint mean that the decision stage must ignore the utility for 3 ms after a transition, but that in general there is a cost to transition between states. Hence the air-jet should not turn on as soon as the utility is positive, or turn off as soon as it is negative, rather it must have some hysteretic threshold. Crossing above the positive threshold or below the negative threshold, once the first 3 ms have passed, should cause the air-jet to change state.
In certain cases there will be actuators with identical utility functions, for example, rows of air-jets at constant Δy. In this case it is desirable to vary slightly the threshold between actuators so that the market will react more nearly continuously so that large numbers of air-jets are not turned on simultaneously. Such collective behavior can lead to excessive oscillation The thresholds can be set to independently oscillate in time to avoid having one actuator doing all the work. In practice though, many of the air-jets will be waiting for their 3 ms to expire, so most actuators will get a chance to fire, even if they have a high static threshold. The decision stage also controls the actuation of the real actuators. Finally, a third stage of a producer, feeds back the state of the actuator to the market. This is accomplished by applying a force proportional current to the main force market-wire, 280, and a torque proportional current to the torque market-wire, 281. These of these currents are then added by the wire to produce the aggregate supply for force and torque. In a dynamic setting, each producer must have an extra sensor that determines if the paper is located above it. As the paper moves, different sets of actuators will be located under the paper, while the rest produce no force if the jets do not lie under the sheet of paper. The actuators that are not under the paper must remove themselves from the market (i.e. not feedback any current) until after they are under the paper.
In one preferred implementation of the producer circuit, the market-wire can be split into two wires: one wire having the market price as voltage, and another wire with zero voltage that accepts the market feedback as current. While this increases the wire count from two to three within the system (note that any voltage wire requires a ground reference as a implicit or explicitly second required wire), it advantageously allows market feedback with voltage sources connected through a resistor to the feedback wire, instead of current sources (one of which needed to be a bipolar voltage controlled current source). Even more important is the fact that the utility computation stage, which normally requires a voltage multiplier at each site, can be built from a single resistor ladder.
To implement the utility computation stage of the producer block 302, each actuator is connected to a ladder of resistors such that the resistance between any two actuators is proportional to their perpendicular distance Δy. The resistor ladder can also be substituted with a continuous resistive strip, and each actuator is connected to the nearest part of the strip. All that is required to compute the local utility is to apply voltages at the ends of the strip given by
where r is the distance from the each of the ends of the ladder to the center of the paper (note that in one case r will be negative). This resistive ladder, acting as a voltage divider, substitutes for the utility computation stage at each location and the parts of the market-wire that carry the price information for both force and torque.
The utility voltage is directly connected to the decision stage consisting of a voltage comparator with hysteresis. The decision stage can be built out of an op-amp with circuit 320 as seen in
Choosing RT in the range of 8 KΩ to 10 KΩ, provides a threshold value near half a volt. However, right after a transition, the capacitor sends this threshold voltage to 12 V preventing further transitions until the capacitor has charged. The value of the capacitor is chosen so that the threshold approaches 2 V after 3 ms, after which time the actuator is allowed to change state. Because the threshold voltage slowly converges to its final value even after the 3 ms, recently flipped actuators are less likely to flip again, preventing one actuator from doing all the work.
The last stage of the producer block 302 is the market feedback, which must output a current to the market-wire when the actuator is turned on. Supplying the current is simple straightforward when the market-wire is split into two, since the feedback component is connected to ground (actually, a virtual ground created by an op-amp). A resistor between the power supply and the market-wire provides the necessary current. The resistor is chosen so that 0.1 mA equals one unit of force, with a sign dependent on the direction of the air-jet. The current can be turned on and off by inserting a FET or analog switch between the resistor and the market-wire.
Minor adjustments must be made in the torque market, since current must be proportional to Δy. In a system where the paper can move in the transverse direction (or when we generalize this method for 2D), each actuator must be able to calculate Δy. To supply paper position information, a second resistive ladder can be built with a voltage gradient such that zero corresponds to the center of the paper. Each actuator can use this voltage, with voltage buffer and a suitably chosen resistor to feedback the produced torque into the market.
The demand side of the market in the control loop is particularly simple given the existence of a global controller that can determine the desired force and torque for the paper. The output of the global controller takes on continuous values and is independent of the price (constant demand curve). The consumer block 304 functions by dumping a force proportional current on the force market-wire, and a torque proportional current on the torque market-wire where the scale of the current must be the same as the one used by the actuators. The sign of the consumer current must be opposite to that of the producers so that when supply equals demand the net current on the wire is zero. Accordingly, the consumer block 304 of the market can be constructed exactly as the feedback circuit for the producer block, with a current determined by the controller.
One final component is required to match the discrepancies between the instantaneous values of the consumer and actuation supplied by the actuators: a warehouse 306. Functioning as an "inventory unit", the warehouse 306 is needed to match the discrete supply with a continuous demand. One warehouse (capacitor) per market acts as a deposit for the excess force or torque allowing the time average supply and demand to balance. Alternatively, each agent could have a capacitor in order to smooth its individual supply or demand. For voltage based pricing markets, the typical warehouse component is a capacitor, whose voltage (price) will be the integral of the difference of demand and supply.
The warehouse block consists simply of a capacitor connected between the virtual ground of an op-amp, and the output of the op-amp, forming an integrator. The two prices are fed back into the utility ladder to complete the circuit. Since the capacitor voltage should swing between the positive and negative threshold once for every actuator that is not needed to produce the base force and that has a counterpart in the opposite direction. If the individual thresholds are separated by 1 V, the typical error current is 0.05 mA, and the system has N actuators in each direction, then a reasonable value for the capacitance would be:
As will be appreciated, anything having an effective capacitance within the same order of magnitude can also be used, including for example, the distributed capacitance of the market wire itself.
In operation, when demand exceeds supply, the price will begin to rise, and more actuators will turn on, and vice versa. The capacitor will also keep track of the net excess of force so that they it be corrected at a latter time. Note that in this market the price can be both positive and negative. The dual signed price occurs because the market offers both positive and negative force. The consumer does not distinguish between getting an additional unit of forward force, or one less unit of backwards force. A backwards air-jet must behave like a forward air-jet, but based on the negative of the price.
In the simplest case with only one actuator (valve) and one market, the market will work as a sigma-delta converter. The market will pulse width modulate the actuator so that the average supply equals the average demand. A more complicated scenario would have still only a force market but many actuators. As an example of operation of such a force market, assume that half of the actuators can produce one unit of positive force, and the other half can produce one unit of negative force. Of course, they must all have slightly different thresholds, which happens in the real market through their distribution along Δy.
When the one market system is faced with a constant force demand of 2.5 units of force, the price will rapidly rise until the forward actuator with the lowest threshold is turned on, then slightly slower until the second one is turned on. At this point we have the best constant output that can be produced. However, the market can do even better by rapidly pulsating between 2 and 3 actuators. With only 2 actuators turned on, the price will continue to rise until the actuator with the third lowest threshold turns on. After the third actuator turns on, supply will exceed demand and the price will begin to drop. If the price drops rapidly enough, it will turn on an actuator that produces negative force. Once again the force will be 2 units and the price will begin to rise, turning on the forth forward actuator. Later the second backwards actuator will turn on, followed by the fifth forward actuator, and so on. Eventually 3 ms will have passed and actuators will be ready to turn off. When the price turns negative again, instead of turning on another backwards actuator, it will turn off the first forward actuator, followed eventually by the first backwards actuator. The result will be rapid oscillations around the desired force, with a period much smaller than 3 ms.
Eventually there will be cases when actuators turn on or off at the same time. Primarily this occurs when the magnitude of the price grows large triggering an actuator with large threshold, and in the meantime an actuator with low threshold ends its 3 ms waiting period and also flips. This problem can be corrected by forbidding actuator flips when the slope of the utility function is negative. However, the larger the error in force is, the faster the price changes, so states with excessive error are rapidly corrected.
The analysis of a system with both force and torque markets, is somewhat more complicated but the results are similar. The only caveat is that, given the choice of utility function, the first actuators to turn on to correct the torque market are those that provide the highest torque. This is necessary to ensure the stability of the markets, but has the effect that the torque oscillations will be greater than in other systems.
A sample system was built with 3 actuators in each direction. The output of the physical system 352 is compared against an equivalent simulation 350 in
Systems built in accordance with the foregoing instructions are known to be overall stable in the sense that the price, which is the integral of the error in force, will always be finite even as time goes to infinity. For one market this is a trivial statement, since no later than 3 ms after crossing the last highest threshold, every actuator will have changed state to reduce the price. Even if the market overshoots in the other direction, the same condition will apply: the price cannot increase 3 ms after having crossed the highest threshold. Since the total force is bounded, the maximum price, and hence the maximum error integrated over all time, is bounded by approximately 3 times the number of actuators.
With two markets, when the prices of force and torque are high enough, the center actuators will tend to respond to the force market, while the edge actuators will only respond to the torque market. Each group of actuators cause its market to tend towards time averaged equilibrium, in the same way described above with a bounded integral of the error.
Another stability criterion that can be asked is whether the market can get trapped in a state of oscillation where all the actuators are on at the same time, and then all off at the same time. In this undesirable case, the system is only stable because there are a finite number of. This state can occur in highly symmetrical systems, where actuators have the same thresholds and the maximum positive torque is equal to the maximum negative torque. In most systems though, a rail to rail oscillation will decay to smaller oscillations near the average. The mechanism for this desirable decay that in a non-symmetrical system, there is a torque imbalance that will eventually break the symmetry between actuators, preventing them all from turning on at the same time. While one cannot prove that all systems are unconditionally stable from a theoretical standpoint, stimulation has shown that this decay generally happens for a wide range of systems.
Implementations according to the present invention also exhibit good scalability properties. From a theoretical standpoint, as the number of actuators grows, the system oscillates faster, and the RMS of the integral of the error decreases. Hence, as the number of actuators increases, the system can only perform better. From a practical standpoint there are certain issues that must be considered carefully. For example, as the number of actuators increases either the current per actuator decreases, or the total average current in the market wire must increase. The high current will require special hardware and consume a lot of power, whereas the low current per actuator could result in the signals from individual actuators being lost in the noise. One way to avoid these problems is to have sub-markets, with a reduced number of actuators in each, that will produce a fraction of the goal force. The sub-markets can allocate the force between themselves though another greater market. However, for systems of up to a few thousand actuators, a single market should be sufficient to coordinate all the actuators.
Robustness is the greatest advantage achieved by building the system as a decentralized market model. Because there is no central controller that must be aware of the positions of each actuator, a single actuator can remove itself from the market, without affecting the force allocation. Robustness is also important because as the paper moves, actuators will slowly enter and exit the market. Thus it is important that the system be able to handle these changes gracefully.
So far we have only considered a system with 2 degrees of freedom: torque and force. However, many times it is desirable to move the paper along the y axis as well. This motion in 2D corresponds to 3 degrees of freedom, and hence 3 independent markets: force along x, force along y, and torque. In a full 2D system, air-jets that push along x will operate as before computing their utility from the prices of force in x, and torque. Similarly air-jets that push along y will observe the price of force in y, and the torque. In fact, an actuator that points along an angle θ, can take its force price to be P=PxForce*sin(θ)+PyForce*cos(θ) (which is a simple calculation that can be done with suitably chosen resistors for each actuator), and then proceed as normal.
The physical implementation of the 2D system requires 3 wires for current feedback into each of the markets. Additionally, there must be two resistive strips, one along x and one along y, that will compute the utility function. Finally, there must be another two strips that will compute Δx and Δy so that the actuators can produce the correct torque feedback. The stability of the system can be guaranteed in the same way as with the two market loop. When the prices become too high, the system uncouples into actuators fixing the x force, actuators fixing the y force, and actuators fixing the torque. Otherwise the system should work as desired.
As those skilled in the art will appreciate, the error in position can still diverge. For example, let the desired force be 0.5 units of force, and let the produced force switch between 0 and 1 units of force with a period T. Then
where ΔF is the error in force, ΔX(t) is the error in position of the paper and could be unbounded with time, and ΔV(t) and M is the mass of the paper
While the position error diverges as time goes to infinity, the error can be reduced by decreasing the period, thus our emphasis on rapid oscillations. However, to eliminate the possibility of divergence completely, the market must compensate for the cumulative error in position. This is accomplished by adding a double integral term to the price:
where C is some suitably chosen constant.
In practice though, for a system with enough actuators, this error in position is generally small relative to the physical errors that affect the paper such as differences in air-jets, unwanted air-currents, and so on. The position error produced by the market can usually be fixed by the paper controller, along with all the other errors.
As those skilled in the art will appreciate, other various modifications, extensions, and changes to the foregoing disclosed embodiments of the present invention are contemplated to be within the scope and spirit of the invention as defined in the following claims.
|Cited Patent
|Filing date
|Publication date
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|Mar 9, 1976
|Veeder Industries, Inc.
|Computer auxiliary gear box
|Mar 10, 1977
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|Phillips Petroleum Company
|Control system for plurality of gas supplies
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|Phillips Petroleum Company
|Pressure regulator for a chromatograph
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|Veeder Industries Inc.
|Fuel delivery control and registration system
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|Story James R
|Apparatus and method for an electronic identification, actuation and recording system
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|Matsushita Electric Industrial Co., Ltd.
|Refueling system adapted to gasoline service station
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|Monitronix Systems Limited
|Monitored delivery systems
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|Intelli-Tech Corporation
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|Intellectual Property Development Associates Of Connecticut, Inc.
|Methods and apparatus for dispensing a consumable energy source to a vehicle
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|Orlando; Vincent
|Wireless remote fuel gauge
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|M&Fc Holding Company, Inc.
|Pressure measuring system for gas flow meter
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|Dec 7, 1999
|Abelow; Daniel H.
|Customer-based product design module
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|Apr 25, 2000
|Jtw Operations
|Unattended automated system for selling and dispensing fluids, with change-dispensing capability
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|Xerox Corporation
|Market-based control system for controlling object motion with smart matter
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|Motorola, Inc.
|Device for electrical source sharing
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|Aug 21, 2001
|Lava Trading Inc.
|Securities trading system for consolidation of trading on multiple ECNS and electronic exchanges
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|Autogas Systems, Inc.
|System and method of providing multiple level discounts on cross-marketed products and discounting a price-per-unit-volume of gasoline
|Jun 16, 1999
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|Marconi Commerce Systems Inc.
|Internet asset management system for a fuel dispensing environment
|Feb 26, 1999
|May 6, 2003
|Massachusetts Institute Of Technology
|Architecture for distributed control of actuator and sensor arrays
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|May 27, 2003
|Xerox Corporation
|Distribution of partitionable physical properties for market based control of actuators and sensors
|Sep 24, 1999
|Jul 5, 2005
|Xerox Corporation
|Distributed control of non-linear coupled systems with a single output
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|Nicholson G. Randy
|System and method of maintaining a posted street price for fuel while offering different prices to identified customers
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|Cornell Research Foundation, Inc.
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|Method for determining the provision value of electrical energy and means for carrying out the method
|Title not available
|Guenther et al., "Controls for Unstable Structures", Proc. SPIE vol. 3039, p. 754-763, Smart Structures and Materials 1997: Mathematics and Control in Smart Structures.
|Citing Patent
|Filing date
|Publication date
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|Mar 16, 2010
|Fujitsu Limited
|IT resource management system, IT resource management method, and IT resource management program
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|IT resource management system, IT resource management method, and IT resource management program
|U.S. Classification
|International Classification
|Cooperative Classification
|European Classification
|Nov 15, 1999
Owner name: XEROX CORPORATION, CONNECTICUT
Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNORS:BERLIN, ANDREW A.;HOGG, TAD H.;GUENTHER, OLIVER;AND OTHERS;REEL/FRAME:010401/0813;SIGNING DATES FROM 19991026 TO 19991029
|Jul 30, 2002
Owner name: BANK ONE, NA, AS ADMINISTRATIVE AGENT, ILLINOIS
Free format text: SECURITY AGREEMENT;ASSIGNOR:XEROX CORPORATION;REEL/FRAME:013111/0001
Effective date: 20020621
Owner name: BANK ONE, NA, AS ADMINISTRATIVE AGENT,ILLINOIS
Free format text: SECURITY AGREEMENT;ASSIGNOR:XEROX CORPORATION;REEL/FRAME:013111/0001
Effective date: 20020621
|Oct 31, 2003
Owner name: JPMORGAN CHASE BANK, AS COLLATERAL AGENT, TEXAS
Free format text: SECURITY AGREEMENT;ASSIGNOR:XEROX CORPORATION;REEL/FRAME:015134/0476
Effective date: 20030625
Owner name: JPMORGAN CHASE BANK, AS COLLATERAL AGENT,TEXAS
Free format text: SECURITY AGREEMENT;ASSIGNOR:XEROX CORPORATION;REEL/FRAME:015134/0476
Effective date: 20030625
|Jul 20, 2010
|Fee payment
Year of fee payment: 4
|Aug 18, 2014
|Fee payment
Year of fee payment: 8
|Feb 5, 2015
Owner name: XEROX CORPORATION, NEW YORK
Free format text: RELEASE BY SECURED PARTY;ASSIGNOR:BANK ONE, NA;REEL/FRAME:034911/0383
Effective date: 20030625
Owner name: XEROX CORPORATION, NEW YORK
Free format text: RELEASE BY SECURED PARTY;ASSIGNOR:JPMORGAN CHASE BANK, N.A.;REEL/FRAME:034915/0220
Effective date: 20061204


text:
The Heart of the Matter with Manchán Magan
Autumn 2015 - this course has now passed.
Participants will be encouraged to write what really matters with personal essays or words that define a moment of confession, revelation or emergence in an elegant, engaging way. Capture your readers by laying bare what it is that lies hidden inside; those cloaked, secret issues, memories, feelings that occupy so much of our inner thought, but never get expressed. Manchán Magan will show participants how to adopt a balanced voice and a critical perspective, so that the writing does not come across as a rant or self-absorbed, but has the pleasing trait of being self-aware and reasoned, in addition to the initial display of untrammelled honesty and passion.
Manchán Magan is a travel documentary-maker. He has written books on his travels in Africa, India and South America (known for their searing, uncompromising honesty), and wrote the 'Magan's World' travel column for the Irish Times.
Starts: Sat 03 Oct
Time: 10.30am – 4.30pm
Duration: 1 Day
Cost: €80/€70 Members
Booking Terms and Conditions >>>
Praise for Manchán Magan's courses:
'All round a very pleasant experience, Manchán showed tremendous enthusiasm, and fellow participants were interested and participated fully....highly recommend it.'


text:
People Are Thirsty For Pokémon Sun and Moon's Hot New Professor
Move over, Professor Sycamore. There's a new daddy in town. (NSFW warning!)
Move over, Professor Sycamore. There's a new daddy in town. (NSFW warning!)
We loved the finale of The Legend of Korra, but there was one tiny thing that didn't happen in the episode's final moments that we were really hoping would happen. Fortunately, a fan animation has given us the moment we were missing. Spoilers ahead.
Check out these [actual creator approved!] fan-arts of Hey Arnold and Rugrats characters in their 20's, all done by the talented Celeste Pille. According to the accompanying blurbs she writes, it seems like these kids have some good heads on their shoulders and are doing the kinds of things most of us non-fictional…
And here is some wonderful artwork of DC's female superheroes as Zooey Deschanel-worshipping, Modcloth-clicking, free range organic hipster girls. (I basically own Wonder Woman's shorts.)
With an Entertainment Weekly cover story hitting stands this week, The Hunger Games frenzy is reaching a mainstream fever pitch. Though the filming of the movie is just beginning, the internet is already obsessed with the the books, the characters, and the lore. The Hunger Games Fandom is intense, with fansites, …
In this music video Snoop Dogg raps about his favorite show, True Blood, inviting Sookie Stackhouse to "Come and play on my team / we'll do it in the daytime / Bill won't know a thing." Click to watch. [People]


text:
Online Freebies. If you like stuff for free, then you have come to the right website. If you find other freebies email us with details.
Free Horse Racing Tips
Get your free horse racing tips online here:
Free Horse Racing Tips, Click Here!
Free Samples and Other Free Items
Get your details listed in our Directory
Drop us an email providing the details you would like entered into the directory or alternatively write using the contact details above.
You do not need to have a website to get listed.


text:
If you are the owner of a small business, you may be intimately aware of the problem of keeping track of all your customers and leads. Customer insight and intelligence, especially in relation to their locations, is something that will help you immensely. It really helps if you can visualise where each and every lead or customer is located on an interactive map.
Thankfully, there's a remarkable solution that works really well. It's called Badger Maps. You don't have to guess where everyone is located in relation to one another. What's more, it works seamlessly with Google Maps. All you have to do is enter their names and addresses, and they would appear "magically" on your interactive map. You may also choose to select only a subset of your customers and leads, and you could even display them in color.
Give your small business the edge you need with intelligent location mapping software. With Badger Maps on your mobile device, you can be assured that you will always know the way to your most important leads and customers. So what are you waiting for? Sign up for a free trial today!
- Route Software Small Business
- Small Business Delivery Software
- Small Business Router
- Small Business Routing Software
- Software for Small Business
- Small Business Sales Map App
- Business Routing Software
- Small Business Routing Software
- Small Business Route Planner
- Small Business Route Scheduler
- Small Business Mapping Software
- Small Business Rep App
- Small Business Rep Software


text:
The Palestinian Cause is Just?!
Or so says the President of the Arab League on TeleSur [SouthTV] TV.
Well, TeleSur is the brainchild of Hugo Chavez, hardly a neutral observer.
From the October 2012 Latin-Arab Summit in Peru
You really could not imagine this stuff on Network American TV, but TeleSur broadcasts all over Latin America.
This is naked Palestinian propaganda.
However, remember that this came out of Hugo Chavez's Venezuela. Venezuela has a majority control over TeleSur.
Nabil El Araby [Nibal the Arab] is an Egyptian with a law degree from both New York and Cairo. He is now president of the Arab League. The Arab League's first – and obviously continuing action – was to fight the state of Israel in 1948.


text:
Eiffel Tower Summit Tour w. skip the line
Skip the line to the Eiffel Tower! Visit both the 1st and 2nd floor of the Eiffel Tower together with your tour guide and get tickets to the highest point, the Summit!
- Skip the line to the Eiffel Tower
- Admire the view from the very top of the tower
- Get access to all three levels, including the Summit
- Learn about the tower from your English speaking guide
Special Christmas Offer - Save 10%
Book and visit between now and December 26, 2017 and save 10% on your tickets.
Visit the Highest Point of the Eiffel Tower
Our guide will take you straight to the second level while discussing the history, architecture, and fascinating stories about the iconic landmark.
You will learn about monuments along the Paris skyline, historical events including its place in two World Wars, and its role as a playground for countless daredevils.
We offer small tour groups, so you are assured a great personal experience.
The tour includes tickets to the Summit, so after your tour you are free to go right to the top of the tower to explore the summit at your leisure.
How do I get my tickets?
Shortly after your booking is complete your e-ticket will be sent directly to your email, just print it out and bring it with you to the Eiffel Tower.
Where does the tour start?
The tour starts at the Eiffel Tower. The address will be on your e-ticket. Please be there 15 minutes before your tour starts.
How long does the tour last?
The tour lasts 2 hours, plus however long you wish you spend at the Summit on your own after the tour.
Are there children's tickets?
No, but children under age 4 are free when accompanied by a paying adult.