We are thrilled to announce the release of the first issue of our new ANCB magazine 'The Metropolitan Laboratory', edited by Lukas Feireiss.
This first issue entitled 'Education: Trial and Error' looks at the topic of artistic and architectural education. As a survey of highly progressive pedagogical approaches, it questions the role of education in past, present, and future. The broad spectrum of articles and essays ranges from Black Mountain College, Joseph Beuys, Paul Thek, Cedric Price, and Oswald Ungers all the way to Beatriz Colomina, Olafur Eliasson, Ai Wei Wei, Thom Mayne, Odile Decq, Peter Cook, and Joan Ockmann, to mention but a few. Inherent to all approaches is a profound apprehension of the positive surplus of unsolicited changes, uninvited irritants, un-anticipated setbacks, and failures as the future seeds of human achievement and progress.
With this magazine, we wish to broaden ANCB's experimental journey as an independent public platform and further explore our deliberate goal of providing an alternative urban discourse. The magazine serves as an additional medium and tool for the documentation and discussion of ANCB's educational and cultural programme, and allows us to deepen our understanding of core issues of today's global realities by connecting the academic field, policymaking, applied technologies, and human behavior. Moreover, it gives us the opportunity to thank our numerous partners, collaborators and friends from around the world and have them participate in and contribute to the ongoing discourse at ANCB.
Histoshi Abe, Ai Weiwei, Cristobal Amunategui, Ricardo Abuauad, Pedro Aparicio, Archipreneur, Matias Bechtold, Luis Berrios-Negrón, Kate Cahill, Beatriz Colomina, Hans-Jürgen Commerell, Peter Cook, Kate Davies, Odile Decq, Iñaki Echeverría, Olafur Eliasson, Eric Ellingsen, Ludwig Engel, David Erixon, Emily Fahlén, Kristin Feireiss, Lukas Feireiss, Andreas Gehrke, Christoph Geisler, Rainer Hehl, David Helbich, Will Hunter, Erik Kessels, Mathias Klotz, Anna Kostreva, Annette Jael Lehmann, Fabrizio Leoni, Jan Liesegang, Winy Maas, Namik Mackic, Bruce Mau, Thom Mayne, Corinna Morandi, Joan Ockmann, OMA × AMO, Manuel Osterholt, Henk Ovink, Constantin Petcou, Diona Petrescu, Dagmar Richter, Andrea Rolando, Matthias Sauerbruch, Tatjana Schneider, Julia Schulz-Dornburg, Anastassia Smirnova, Paul Thek, Katya Tylevich, Urban-Think Tank, German Valenzuela, Xavier Vendrell, Jan Verwoert, Anna-Lena Werner, and Liam Young.


text:
The Age of Elegance
Since 1972,hundreds of women from across the Garden State, who have reached the age of 60, have entered the fabulous Ms New Jersey Senior America Pageant. Like their predecessors decades younger, they have graced the stages of Atlantic City Casinos,in glitzy evening gowns, in the hope of winning the coveted title, that would enable them to compete in the nationals. Join us now, as we unfold the wonderful story of this long standing organization and their beautiful women.
THERE SHE IS! .... MS NEW JERSEY SENIOR AMERICA 2010
Introducing Mrs. Rebecca Orsatti, MS NEW JERSEY SENIOR AMERICA 2010, crowned on Thursday, June 3rd, at Harrah's in Atlantic City. Rebecca Orsatti, MS NEW JERSEY SENIOR AMERICA 2010, and the QUEEN'S COURT. Pictured from right to left are: Betty Pruitt, 4th runner up, Patricia Genovese, 1st runner up, Queen Rebecca Orsatti, Marti Noel-Stier, 2nd runner up, and Leah J. Whelan, 3rd runner up. The search to find that "gracious lady who best exemplifies the dignity, maturity and inner beauty of all senior Americans" has ended. On Thursday June 3rd, the MS NEW JERSEY SENIOR AMERICA PAGEANT 2010 was held at Harrah's in Atlantic City. The Class of 2010 was made up of thirteen elegant ladies, all very impressive, as each contestant dazzled both judges and audience with her unique display of charm, witt, intelligence, and beauty. The crowd kept their own scores, and cheered along for their personal favorites, but in the end, everyone knew that the fate of these women rest
Theme images by tillsonburg
Ms New Jersey Senior America
Brick, NJ, United States
Whereas, New Jersey Senior America shares the same philosophy, mission statement, purpose and goals as its parent organization, Senior America, Inc. and, Whereas, its founder, Dr. Al Mott is the same, and Whereas, the New Jersey Cameo Club shares the same philosophy, mission statement, purpose and goals, and, Whereas, its founder is also Dr. Al Mott, Therefore, it is determined that New Jersey Senior America and New Jersey Cameo Club are one and the same. Anyone wishing to learn about NJSA and NJCC can either read herein this blogspot, or, by logging onto its parent organization, www.senioramerica.org. Our blogspot allows the reader to write a comment at the end of each article, but does not let the reader to email us directly. Therefore, please feel free to contact us personally,for pageant information and application form, by calling/emailing the following persons: Mrs. Terry Meade, Director of Pageants. 908-216-8534. Email: tbm5201@aol.com. Mrs. Josephine Araniti, Ms New Jersey Senior America 2007, Blogmaster. 732-202-1494. Email: tomori8@aol.com.

redpajama_set_name: RedPajamaCommonCrawl


This photo was taken at the location of Berner Oberland - Niesen (Bern, Switzerland) on Friday 12 April 2019 at 22:45:02.
This timelapse movie was taken on Friday 12 April 2019.
Friday 12 April 2019, 22:45:02 (GMT+01).
Page generated in 0.536 seconds.


NorthShore University HealthSystem Medical Group, the principal teaching affiliate of the University of Chicago Pritzker School of Medicine, seeks an outstanding Pediatric Dermatologist to join the Division of Dermatology. The Dermatology Division at NorthShore is one of the largest academic dermatology practices in the Chicago area with 9 general dermatologists and 2 full time surgical dermatologists, who work in close collaboration with 2 board certified dermatopathologists in the Department of Pathology.
The division has full access to a wide variety of lasers and contains a comprehensive clinical trials program. The successful candidate for this position will have completed a Pediatric Dermatology fellowship and is certified or eligible for certification by the American Board of Dermatology. Clinical responsibilities will include seeing patients in clinic, teaching and research. Academic appointment to the University of Chicago is available to qualified candidates. This will be a full-time, non-tenured position with salary and academic rank to be determined by candidates qualifications.
NorthShore was recently named one of the nation's Top 100 hospitals by Thomson Reuters. Located in Chicago's north suburbs, NorthShore is a physician-led, multi-specialty group with over 600 physicians and growing. You'll benefit from being part of a fully integrated organization of healthcare providers at Evanston, Glenbrook, Highland Park and Skokie Hospitals, along with more than 75 Medical Group offices.
NorthShore has been named one of the 'Most Wired' healthcare organizations in the country by Hospitals & Health Networks Magazine, and our EMR system, EPIC, is the gold standard in the industry.' Based on NIH awards, the Research Institute ranked #1 in the State of Illinois and #9 in the United States among multi-specialty independent research hospitals. Affirmative Action/Equal Opportunity Employer. NorthShore is committed to hiring a diverse workforce.
Chicago's north suburbs are situated along and near Lake Michigan, just minutes from downtown Chicago. These communities boast outstanding schools, low crime rates, beautiful homes, award-winning cycling and walking paths, numerous recreational activities for the whole family, charming shops and terrific restaurants.


text:
Q: TypeScript equivalent of JavaScript includes() Getting a TypeScript error using includes on an array element. Of course once compiled down to js it works fine but I still get the following TypeScript error:

Property 'includes' does not exist on type 'boolean[]'

Code:
validAttrs() {
  let valid: boolean[] = this.required.map((value, index) => {
    if(this.elm.nativeElement.getAttribute(value) === null) {
      return false;
    };
    return true;
  });
  return valid.includes(false) ? false : true;
}

A: As far as fixing the compilation error goes, fixed the compilation issue was adding es2016 to the lib option in my tsconfig.json. This adds the necessary declaration of includes on arrays.
I tried with TypeScript 2.1.4 the suggested fix of replacing boolean[] with Array<boolean>. It made no difference whatsoever. Logically, it shouldn't make a difference because boolean[] and Array<boolean> are the same thing.

This being said, I concur with torazaburo that the OP's code should be implemented as:
validAttrs() {
  return this.required.every(value => this.elm.nativeElement.getAttribute(value) !== null);
}

Besides removing unnecessary logic, this also has the advantage that every stops inspecting the array as soon as the callback returns a falsy value. There's no point inspecting the rest because the return value will necessarily be false as soon as the callback returns a falsy value. On the other hand, the implementation in the question will always perform the test on all elements the of array. If the very first element fails the test, then it will inspect the rest of the array needlessly!!

A: @echonax's comment worked for me.
validAttrs() {
  let valid: Array<boolean> = this.required.map((value, index) => {
    if(this.elm.nativeElement.getAttribute(value) === null) {
      return false;
    };
    return true;
  });
  return valid.includes(false) ? false : true;
}

A: You don't even need includes for what you are trying to do. Your code can simply be
validAttrs() {
  return this.required.every(value => this.elm.nativeElement.getAttribute(value) !== null);
}

This also has the advantage that it will stop checking the minute it finds the first null value.

redpajama_set_name: RedPajamaStackExchange


Pet insurance that covers pre-existing medical conditions as long as your pet hasn't received treatment or advice for them in the three months before the policy starts. Cover for pre-existing conditions increases if you do not claim and we offer £7,000 of vet fee cover for new conditions.
Bought By Many are a new-generation insurance company offering Pet Insurance cover that has been inspired by feedback from over 40,000 pet owners. Their unique insurance includes options to cover pre-existing conditions, offer fixed prices for puppies and kittens, or give money back if you don't claim. The Complete policy is the most comprehensive on the market.


Our beautiful boy Jack is 13 years old and has severe Quadriplegic cerebral palsy due to medical negligence at birth. Jacks under gone lots of surgery throughout his life but he's a strong boy with lots of potential. We are asking for your help and support to get Jack stem cell treatment that's not available in the UK. This type of treatment has no known side effects and has the possibility to help Jack increase his abilities. We want to help Jack and realise this is not a cure but feel after years of research this could be amazing for him. This cellular stemcell treatment is not available in th UK yet so we would need to travel to Panama South America for the treatment. After giving birth to our baby daughter in February 2016 we had planned to bank her umbilical cord blood with a private company called cells for life at our own cost to hopefully use as part of siblings cord blood treatment for cerebral palsy at dukes university in America which has been known to give children with cerebral palsy amazing treatments with either there own cord blood or a siblings ord blood but the hospital took to long to give the phlebotomist our baby's umbilical cord and she only managed to get 2mls of blood plus tissue so this wasn't enough blood for treatment to go ahead. Stemcell treatment requires private funding at a cost of around £18,000 for the treatment with flights, accommodation to Panama City. We have managed to raise money ourselves but we can't afford to get it all and if this is a success we plan to take Jack as an ongoing treatment so would need to keep his fundraising journey going and will need all the help and support as possible. We love our boy and won't give up on him.
All cash donations are held by BLF in restricted funds for Jack's campaign.
BLF will hold funds on behalf of Jack and pay invoices directly.


Nowadays, as the distant work became possible a new dilemma has emerged – is it better to become a free-lancer and work at home or remain a part of the office community? The best solution is to combine these two options and start the practice of co-working.
Co-working presents a model of work in which people remain independent while performing their tasks on the same space. This method is good for freelancers and different groups of people creating and launching new projects. On the one hand, you remain free from being bossed around. On the other hand, you receive an opportunity to communicate with the others and develop new useful business connections.


text:
PM Rutte interrupts Trump on EU trade deal
By Janene Pieters on July 3, 2018 - 07:56
Mark Rutte, January 2016. (Photo: EU2016 NL / Wikimedia Commons)
Prime Minister Mark Rutte met with United States president Donald Trump in Washington on Monday. During his welcome speech Trump spoke about the U.S. and the European Union meeting soon to discuss trade agreements. "If we do work it out that will be positive. And if we don't work it out, that will be positive also", Trump said. Rutte could not agree with that. "No", he interrupted. "That's not positive. We have to work something out."
https://www.youtube.com/watch?v=9_yA5oLSB4U
According to Trump, the United States' relationship with the Netherlands is "better than ever". He immediately started talking about how good the American economy is looking and how they're "very close to making some very good trade deals". "Fair trade deals. I don't want to say good, I want to say fair. Fair trade deals for our tax payers and for our workers and our farmers."
In his response, Rutte referred to the close ties between the Netherlands and the U.S. in their long relationship. Jobs and security are the most important themes in his talk with Trump. He emphasized that the two countries create many jobs in each other, and that both will benefit from intensifying that relationship.
Trump did not respond to that, instead going on to talk about a good talk he had with the newly elected president of Mexico, Lopez Obrador.
Warmly welcomed to the @WhiteHouse by president Trump. We reaffirmed the deep bond between the Netherlands and the United States that reaches back over four hundred years and committed to building together on economic growth, security and stability. pic.twitter.com/adciXlwBh8
— Mark Rutte (@MinPres) July 2, 2018
This was the first official meeting between Rutte and Trump, and it came at a politically sensitive moment. Rutte is the first European leader to meet with Trump since the start of the trade conflict between the U.S. and the EU. On Monday the EU announced that it will answer the looming American import tariff on European cars with a packet of counter measures worth 300 billion dollars.
During their meeting, Rutte called on Trump to scrap import tariffs on steel and aluminum, according to NOS. His message to the president was to de-escalate the trade conflict between the EU and the U.S.
In the meeting Trump also said that the U.S. will continue to support the Netherlands in the MH17 investigation. Rutte thanked the Americans for their support since the MH17 disaster happened in July 2014.
trade deal
U.S. import tariff


text:
Steve Turner, född Steve Neil Turner 28 mars 1965 i Houston, Texas, är en amerikansk gitarrist som är mest känd som medlem i det Seattlebaserade grungebandet Mudhoney, men även som en av originalmedlemmarna i bandet Green River.

Diskografi
Album med Mudhoney
Superfuzz Bigmuff (1988)
Mudhoney (1989)
Every Good Boy Deserves Fudge (1991)
Piece of Cake (1992)
My Brother the Cow (1995)
Tomorrow Hit Today (1998)
Since We've Become Translucent (2002)
Under a Billion Suns (2006)
The Lucky Ones (2008)
Vanishing Point (2013)
Digital Garbage (2018)

Med Green River
Rehab Doll (låtskrivare på låten "Swallow My Pride") (1988)
Live At The Tropicana Olympia WA September 28th 1984 (2019)

Referenser

Externa länkar

Officiell webbplats
Mr. Epp and the Calculations på Allmusic

Födda 1965
Amerikanska rockgitarrister
Män
Levande personer

redpajama_set_name: RedPajamaWikipedia


text:
Everything About Jayda Wayda, Her Wiki, Biography, Net Worth, Age and Boyfriend
By Joanna Wilson On Nov 30, 2021
Jayda Wayda is a well-known American entrepreneur, YouTuber, model, social media sensation, and media personality. She is well recognized for being Lil Baby's girlfriend, a well-known American rapper.
Wayda is a well-known YouTuber who constantly updates her channel with daily life occurrences. Thousands of people have watched the majority of her videos. She also posted travel and makeup lesson videos.
She also owns the AmourJayda boutique, where she sells high-end clothing labels. She also founded Wayda Shop, a website where she gives hair-growing advice.
What is the Net Worth of Jayda Wayda?
Who is Jayda Wayda Boyfriend?
Jayda Wayda Professional Life
Jayda Cheaves was born in Savannah, Georgia, on September 25, 1997. Her full name is Jayda Cheaves. Another name for her is Jayda Ayanna. In addition, she is 24 in 2021, and she recently celebrated her 23rd birthday with a magnificent celebration.
She received her primary education in a local school in her hometown. In 2015, she received her high school diploma from a recognized college. In the public eye, she hasn't shared much about her academic history.
Tricia Cheaves (her mother) and David Cheaves (her father) gave birth to Jayda Cheaves (her father). She has released a photo of her mother on social media but has kept her father's identity a secret.
She has an older brother, Len, and a younger sister, Ameerah. She never showed her siblings any images of herself. Wayda is a Christian who hails from a multi-ethnic background.
Jayda Wayda has a successful career. Modeling and commercials would bring in about $300,000 to $700,000. Her YouTube page and social media profiles also help her to make money.
Full Name Jayda Cheaves
Popular as Jayda Wayda
Place of Birth Savannah, Georgia, United States.
Profession Model, YouTuber, Entrepreneur, and social media star
Age/ How Old 24years as of 2021
Height 5 ft 1 in (1.54 m)
Body Measurements __
Weight 58 kg. 127 lbs.
Boyfriend Dominique Jones
Jayda Wayda is a young model that is absolutely lovely. She dated Dominique Jones, also known as Lil Baby, in 2016. The pair had a good life together till they split up in 2018 for an undisclosed cause.
Lil found out Wayda was pregnant after the split and returned to her to look after Jayda. In February of this year, the couple welcomed a child. Loyal Armani was his moniker. Their son is co-parented by Lil and Jayda Cheaves.
Jayda Wayda is a well-known model who has collaborated with a number of well-known companies. In July 2021, she was featured in Matte's Swim Week collection. Her provocative appearance and charming personality captivated the judges. In addition, she uses her social media platforms to promote a variety of products.
Wayda debuted her self-titled YouTube account on August 5, 2018. She had 326k subscribers and 9.5 million views as of August 2021. She released her debut video, titled 'Jayda's First Vlog,' on December 17, 2018, and it has received 449k views as of 2021.
'HAPPY FATHERS DAY,' her most popular video, was uploaded on June 24, 2020. For Father's Day, she arranges a lavish party with her husband and son. This video had 1.1 million views as of the time of writing. Mukbangs, beauty lessons, quarantine routines, and fashion videos were all available on Wayda's channel.
Jayda Cheaves is the originator and owner of the AmourJayda' clothing business, according to sources. She sells high-quality items at a range of costs. She is the owner of the Wayda Shop as well. She offers hair loss advice as well as items to aid with the problem.
In January 2021, she was featured on the cover of Prema Magazine.
She has published a black image on her social media account as a supporter of the Black Lives Matter campaign.
Jayda Cheaves keeps her form in shape by going to the gym on a daily basis.
Her partner and child enjoy going shopping with her.
Her passion of tattoos has resulted in several tattoos on her body.
At home, the popular YouTuber has an adorable pet dog.
She had 5.8 million Instagram followers, 84k Facebook followers, and 376.8k Twitter followers as of August 2021.
Her Instagram is full with beautiful photographs from photoshoots.
Jayda Wayda uses her Instagram and YouTube channels to advertise a variety of businesses.
You May Also Like: Everything About Sia, Her Wiki, Biography, Net Worth, Age, Husband and Career
Everything About Sophie Fergi, Her Wiki, Biography, Net Worth, Age, Boyfriend and Career
Everything About Trisha Paytas, Her Wiki, Biography, Net Worth, Age, Husband and Career


text:
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Mediterranean & West Europe, Transatlantic
Barcelona is Spain's second largest city, with a population of nearly two million people, and the capital of Catalonia.
A major port located on the northeastern Mediterranean coast of Spain, Barcelona has a wide variety of attractions that bring in tourists from across the globe. The many faces of Barcelona include the medieval Old Town, the unique street grid resulting from 19th-century urban planning. The city has both long sandy beaches and green parks on the hills, pretty much side-by-side. Barcelona is also famous for some prominent buildings, of which perhaps the most-known are by the architect Antonio Gaudi, including his
, which became Barcelona's symbol to many.
Founded more than 2,000 years ago as the ancient Roman town Barcino, Barcelona is thus as historic as it is modern, with a constant flow of projects changing the face of the city and long-standing penchant for design and innovation. Thanks to the wealth of attractions, a very well-developed accommodation base, a lively nightlife and a robust transportation system, Barcelona has become one of Europe's, and pretty much the world's, most popular tourist destinations.
August is probably the busiest time for tourists in Barcelona. That said, a very large percentage of the shops and restaurants can be found closed from early-August to early September. During this time, you will find the most expensive hotel rates (outside of conference times such as the World Mobile Congress) and the city is devoid of locals as the vast majority of residents go on vacation in August and leave the heat and humidity to the hordes of tourists who come. This also happens to be one of the highest periods of home break-ins as criminals know that many places are unoccupied for an entire month.
It is important to note that, while Barcelona has decent, albeit crowded beaches, the locals will be very appreciative if visitors do not consider Barcelona a beach resort and do not wear beachwear when visiting churches, restaurants, etc. If you only want a beach, and a good beach at that, head south to Costa Daurada, north to Costa Brava or out to sea for the Balearic Islands.
Barcelona is great off-season and is a lovely city even in the winter months of January and February, as long as the possibility of rain is low. Given the high humidity, 19–23 °C (66–73 °F) is considered comfortable weather, which is usually the temperature between April and June and between late September–November. This is the best time to visit the city. Anything warmer than this can feel too hot.
Toddler happiness is considered a public responsibility in Spain. In any public place, people around you will make every effort possible to make your toddler happy: whenever he or she looks bored or is crying, everyone does their best to entertain or to calm them.
Tourist office at
Plaça de Catalunya
, Plaça de Catalunya, 17-S (Metro: L1, L3. Bus: 9, 22, 28, 42, 47, 58, 66, 67, 68. Train: R4). 8:30am-8:30pm. This is the main tourist office in the city.
The other tourist offices can be found at Plaça de Sant Jaume, Ciutat, 2 Ajuntament de Barcelona. (City Hall.) Opening time: Monday to Friday: 8.30am-8.30pm. Saturday: 9am-7pm. Sunday and public holidays: 9am-2pm.; Estació de Sants, Plaça dels Països Catalans. How to get there: Metro: L5,L3. Bus: 63,68. Opening time: daily, 8am-8pm. And Aeroport del Prat. Terminal 1 and 2. Opening time: Daily, 9am-9pm. All are closed on 1st January and 25th December. For a full list of tourist information points check the link above.
The department store El Corte Ingles publishes a free street map for tourists. You can pick a copy at the store, or at one of the many hotels in the city.
Barcelona Card. This card gives an opportunity to visit more than 25 museums and other sites in Barcelona without an extra charge. For another 70 plus sites, it offers various kinds of discounts during a validity period of the card. It also includes a travel pass for public transport in Barcelona (for details see Hola BCN! card below). The card is available for purchase for periods of between 2 and five days. Bear in mind that if you don't plan to see lots of museums every day, then it may be cheaper to buy transport-only tickets (see below). They cannot be used on the cable cars or funiculars (except for Montjuïc).
https://en.wikivoyage.org/wiki/
Text is available under Creative Commons Attribution-ShareAlike 3.0
Barcelona, Spain: Port Information
Being a major port located on the northeastern Mediterranean coast of Spain, Barcelona has a wide variety of attractions that bring in tourists from across the globe. The city's port is one of the busiest on the Mediterranean.
Large cruise ships dock 1-2 km to the southwest. Many of them offer bus-shuttles to locations at the south end of La Rambla. The ferries dock almost directly on the Ramblas. Anyway, you can also take a taxi to get to the city's attractions.
There are regular ferry connections with the Balearic Islands (Alcúdia, Ciutadella de Menorca, Ibiza City, Sant Antoni de Portmany, Mahón, Palma de Mallorca), Italy (Savona, Genoa, Livorno, Porto Torres and Civitavecchia for Rome) and Tangier, in Morocco. From Rome (Civitavecchia) it is cheaper to take the ferry than a bus.
Get around Barcelona, Spain
The public transport in the city and the surrounding area managed by Autoritat del Transport Metropolità (ATM) consortium. The whole area is covered by the Integrated Fare System, which is divided into 6 zones. This system includes the most of the public transport in the area: metro, city and intercity bus, tram and commuter trains.
The city limits of Barcelona are completely located inside zone 1. The public transport in the city itself is mostly managed by Transports Metropolitans de Barcelona (TMB). They have a separate site dedicated for tourists. The other two operators in Barcelona are Rodalies de Catalunya and Ferrocarrils de la Generalitat de Catalunya (FGC).
Travel cards are excellent value in comparison with a single ticket. Be sure to look after them well as bent or damaged cards will not be read by the ticket machines. Such cards can be replaced at one of TMB's customer service centres.
TMB also offers a few route planners on their website: versions for desktop, for mobile browser and mobile apps for Android and iPhone. Another route planner is available on the ATM site.
Metro. M–Th 5:00–24:00, F 5:007ndash;2:00, continuous service from Saturday at 5:00 until Sunday at midnight). Stations are marked <M> on most maps; every station has a detailed map of exits to the city. Trains are fast, often coming in two minute intervals. However, on holidays and weekends trains only run every 6-8 minutes and can get easily packed. Announcements are made only in Catalan, though signs and ticketing machines are generally trilingual in Catalan, Spanish and English.
Pay attention to the fact that to get from metro lines operated by TMB (1,2,3,4,5, 9/10 and 11) to the ones operated by FGC (6,7 and 8), or vice versa, you need to exit and then enter through a new pay-gate. In this case, if you had a one-journey ticket, you need to get a new one. If you used a multiple journey ticket you won't be charged for a second time when changing lines as long as you are within the stated travel time for a single journey. Also, you can't repeat operator, so you can't use a FGC ride to make a shortcut. For instance: changing to L9S to L1 via L8 using Fira and Espanya will charge you with two journeys, you should go via Torrassa instead although its way longer. All trains are air-conditioned.
Take also care when travelling to the airport: while the T-10 is valid for Renfe services, it is not accepted at Metro. If you get to the airport by metro using a T-10, you'll be forced to pay the full fare, and the ticket you've used will not be refunded.
Bus. The bus network in Barcelona is pretty extensive. Perhaps the best option in planning your route is to consult with one of the route planners mentioned above.
Barcelona is a very walkable city. It takes little over an hour to walk from Port Vell at the seaside to Park Güell at the foothills of the mountain range at the northeastern end of the city, and you can see a range of attractions, including La Rambla and Sagrada Familia, on your way. There are opportunities all around to sit down and enjoy a drink or a meal everywhere. If you are fit, you can pretty much explore the city by foot alone, unless the heat beats you in the warmer months (and then you can always resort to the air-conditioned metro).
Parking around all major tourist destinations is expensive and the spaces are difficult to navigate, as there are several classes of public parking spaces, with complicated rules for each class. Barcelona is plagued with the same problems that plague other major European cities; massive traffic jams and extremely narrow streets in some areas, coupled with a very complicated road system. As such, driving yourself around is not recommended for tourists, especially those with no driving experience in large cities. Public transport will get you to all the major areas, and you should use that as your main mode of transport.
Having a driving map is essential - plan your route before you set off. Navigating with an average tourist map is frequently misleading: many streets are one-way; left turns are more rare than rights (and are unpredictable). As an example, Gran via de Les Corts Catalanes is technically two-way, but in one direction supports only minor traffic: after every crossroad you'll find the traffic light on the next crossroad turns red by the time you reach it.
Some free parking spots reported by travelers are:
Near Moll de Sant Bertran (which is south-west from Museu Maritim) - driving at B-10, exit to WTC and make a complete round at roundabout, heading to warehouses - and park next to its employee's cars.
Somewhere near Guell Park.
Near Font Màgica, in Plaça Espanya.
Getting around by car makes sense if you plan to spend much more time driving outside the city borders than inside it - and ideally if you don't plan to park overnight at all. Otherwise, for purely in-city transportation, consider renting a scooter, or using public transportation instead.
What to see in Barcelona, Spain
The old city
Walk around the winding streets and hidden squares, fountains and palaces in the Barri Gòtic (Ciutat Vella). Highlights include the Catedral, the Museu d'Història de Barcelona (formerly known as the Museu d'Història de la Ciutat), and Plaça Reial.
Modernist architecture
Since 1984 seven buildings by the architect Antoni Gaudí (1852–1926) in or near Barcelona are listed as "Works of Antoni Gaudí" on the UNESCO World Heritage List: the basilica of Sagrada Familia, Casa Mila (La Pedrera) and Casa Batlló in Eixample, Palau Güell in Ciutat Vella, Parc Güell and Casa Vicens in Gràcia, the crypt of the Church in Colònia Güell.
The works by the Catalan art nouveau architect Lluís Domènech i Montaner listed on the UNESCO World Heritage List: Palau de la Música Catalana in Ciutat Vella and Hospital de Sant Pau in Eixample.
The Ruta del Modernisme run by Modernisme Centre (Pl. de Catalunya, 17, subterráneo; phone +34 933 177 652): guidebook and discount voucher book for €12. Takes you round all the best Modernisme (art nouveau) buildings in Barcelona. The main part of the route can be walked in a couple of hours, providing you don't stray too far from the main routes. The Tourist Offices offer a pack that includes discounted tickets to many attractions such as La Pedrera and La Casa Batlló. All can be seen from the outside for free.
Museum of Natural History in the Forum - Museu Blau
CosmoCaixa: Museum of Science Amazing museum for kids from 4-5 upwards. Adults will really enjoy it also.
What to do in Barcelona, Spain
Barcelona Bus Turístic. Take a tour at Barcelona Bus Turístic which links all of the Barcelona tourist sites you could want to visit. It has three routes (map provided as you board), including a northbound and a southbound line that leaves from opposite sides of the Plaça de Catalunya. Each takes 1–2 hours. The hop-on/hop-off format lets you get-off at any interesting stop, see what interests you, then get back on any later bus at that or any other stop. One approach stays for an entire route, then continue while getting off at locations that interested you earlier. Buses are double-decked, with the open-air upper deck offering much better views. Sunscreen is essential in summer months, jackets in winter/early spring/late fall. Earphones are offered when you first get on so you can hear the commentary as you drive by significant locations. Outlets near every seat let you choose among many languages and playback volumes. 1-day ticket €27, 2 days €38; tickets can be bought at the bus stops, some hotels, etc. or online with 10% discount.
Aeri del Port de Barcelona (Telefèric del Port), C/ Taquígrafo Garriga, 97 – Esc.B -2º9ª, ☎ +34 934 304 716, e-mail: tebarsa@hotmail.com. Jun-Aug 11:00-20:00; Mar-May, Sep-Oct 11:00-19:00; Nov-Feb 11:00-17:30. Have a ride at Port Vell Aerial Tramway. Port Vell Aerial Tramway is the 1450 meter long harbor aerial tramway with red cars connects Montjuic and Barceloneta. It starts in Barceloneta on the top of the 78 meters tall Torre San Sebastian tower, which also has a restaurant at its top accessible by an elevator. It has an intermediate stop at Torre Jaume I tower (close to Columbus monument), which can be reached by elevator from the ground— 107-meter tall tower, the second-tallest aerial tramway support tower in the world. The final point of the line is Miramar at the slopes of Montjuic hill. Overall, the whole system is quite old (built in 1929, albeit restored a couple of times), and the car is packed with tourists during the daytime — particularly sensitive for a stroller or a wheelchair. But if one starts from Montjuic side, there are fewer people waiting.
Torre Jaume I.
Torre San Sebastian.
Stroll along the following famous streets in Ciutat Vella:
Las Ramblas or La Rambla, a gorgeous tree-lined pedestrian walkway, the busiest and most lively street of the city. Mostly occupied by tourists, expect to pay higher prices for food and drink. Avoid the groups of people supposedly betting on a game played on a cardboard table; they are thieves. Head off into some of the side streets for a cheaper, more local, and authentic experience of Barcelona. Often called Las Ramblas, because it is actually a series of several different streets each called 'Rambla de ____,' the sections also have distinct feels. As you get closer to Plaça Catalunya, you find more street performers doing stunts. In the middle, you'll find street performers in costumes. Towards the pier, there are artists who will do pencil drawings, paintings, etc. Beware, you might find it boring.
La Plaça Catalunya. Connecting all the major streets in the city, the Plaça is known for its fountains and statues, and the central location to everything in the city. A favorite meeting spot for locals.
El Portal de l'Àngel. Large pedestrian walkway with many new and stylish shops to browse in.
Football. Barcelona is home to, of course, F.C. Barcelona and the somewhat less well known R.C.D. Espanyol. With a long history of politics behind it, the rivalry between F.C. Barcelona and Real Madrid is by far the biggest in Spain, and one of the most intense in the world. As both F. C. Barcelona and Real Madrid attract many of the world's top players, matches between the two are guaranteed to feature star-studded sides and world-class football.
Cruise miles of beachfront boardwalk starting from Barceloneta or get a tan on the beach.
Sit on a wooden bridge to Maremagnum in Ciutat Vella and cool your toes at the water's edge: with a book, sandwich or just for a short rest.
Wander the Barri Gotic in Ciutat Vella, the largely intact medieval center of the city.
Enjoy your Sangria at La Plaça Reial in Ciutat Vella, near the La Rambla Street. Great place to sit, relax and drink. While visiting La Placa Reial
Walk in Born in Ciutat Vella, a very popular area with great restaurants and places to have a few drinks. If your accommodation is on Rambla, Born is a great place to escape the crowds, enjoy a relaxed atmosphere and meet off-the-beaten-track travelers and non-tourist-industry locals—especially in the evenings.
Visit a Flamenco Show in a real tablao. One of the best is Tablao de Carmen in Sants-Montjuïc. A cheaper alternative is in the jazzclub Jazz Si in Ciutat Vella.
Ride the Cable Way to get from the sea front to Montjuïc mountain in Sants-Montjuïc
Sit and sip on a coffee in Plaça dels Àngels in Ciutat Vella, while admiring the whiteness of the MACBA and the best street skate tricks in town.
Catch a performance at the beautiful Teatre del Liceu or the Palau de la Musica Catalana both in Ciutat Vella.
Rent a bike or join a bike tour and get to see the highlights of the city differently. Ride from the magic beaches of the Mediterranean to Gaudí's modernist buildings through the medieval atmosphere of the Gothic Quarter.
Sail 3 hours to see Barcelona from the sea.
Mail boats serve almost all populated in Barcelona and are the cheapest way to reach many areas, though far from the fastest or most comfortable. The government has a mailboat schedule of mailboat routes online nine which may or may not reflect reality.
Sail on a classic yacht. Enjoy a day trip sailing along the Barcelona coastline on a classic yacht.
What to eat and drink in Barcelona, Spain
Barcelona's cuisine is inconsistent in quality, as with all highly touristic cities, but good food does exist at reasonable prices. The golden rule of thumb applies well in Barcelona; to save money and get better food, look for places off the beaten track by fellow travelers and seek out cafes and restaurants where the locals frequent. The good idea is to avoid restaurants with touts outside.
Set menus (menú del migdia) Most restaurants (and some bars) offer a menú del migdia (menu of the day), which usually means a simple and unpretentious two course meal (one salad, main dish and a drink; plus a dessert sometimes), 3 or 4 options each, with a drink and a dessert. Depending on the restaurant, the portions may be quite generous, or rather small. During the week, some smart restaurants offer lunch specials from 2PM to 4PM. The savvy traveler will try the hip places for a fraction of the price during the day.
If you're looking for a place where everyone can choose their meal, ask for restaurants that serve plates combinados, which is the closest thing to an American/Northern European meal.
Smoking: Is not permitted in restaurants anymore.
You can get food from any part of the world in Barcelona, but make sure you try some Catalan food.
The selection of seafood is consistently great, although not a lot of it is local (this part of the Mediterranean is pretty well fished-out).
A treat to try that no travel guide mentions is waffles sold at street stands. They will tempt you with their mouth watering smell and taste.
Even though tapa restaurants are now endemic all over the city, tapas originated in Andalusia in the south of Spain, are NOT a meal, and most importantly are NOT native to Catalan cuisine. Catalans eat a more French style three-course meal (appetizer, main dish, and dessert) and would more likely go for a pre-meal beer/vermouth and some snacks (olives, chips, etc.) than a meal consisting entirely of the new trend in tapa-only dining. This pre-meal snack is called 'fer el vermut' or 'making the vermouth.' As you travel to smaller towns in Catalonia outside of Barcelona, it is less likely that you will find tapas and more likely to see restaurants serving traditional Catalan food in three courses.
If you feel lost in the variety of food choices there are - Catalan, Basque, Spanish, and beyond, it may be helpful to do a food tour to quickly get oriented. Many independent tour operators run food and wine tours in the city.
Foodie&Tours. A third party website that has selected and listed best gastronomic tours in the city, including cooking classes, tapas walking tours, and vineyard visits. Bookings are possible through their website.
Areas to eat
Depending on where you are in the city, there may be restaurants galore, or none at all. The following areas tend to be restaurant "hubs", with a large variety of restaurants to choose from:
Barceloneta: A popular quarter for locals, where you can try fish based dishes, such as Paella (a name that may hide many different kinds of rice concoctions) or Arròs negre (Black Rice), that takes its color because it is made using squid ink. It's a very good place to eat tapas as well.
Eixample Esquerra (between Gran Via and Mallorca)
Barri Gòtic (especially for tapas)
"El Born" (next to Barri Gòtic)
Around Plaça Catalunya there are dozens of restaurants serving excellent tapas.
For budget eating, you may choose "menú del migdia" in small bars on the Avinguda del Paral·lel for €9-€11 per person. Be aware that sometimes the menu and the staff are only in Spanish.
The large cafes that line the Passeig de Gràcia and the Rambla Catalunya, just north of the Plaça Catalunya, offer a variety of acceptable tapas. This part of the town is quite touristy and a bit expensive.
Try a "café con hielo" an espresso served with a glass of ice cubes on the side and any local 'cafeteria.'
Chupitos, are located in several locations throughout the city, including one in Barceloneta. Chupitos is Spanish for "shots" and offers hundreds of unique shots including the "Harry Potter" (a shot that sparks as cinnamon is sprinkled over it), and "Monica Lewinsky" (a variety of flaming shots) among others. As much a show as it is a place to get a drink, it's a fun night out.
L'Ovella Negra (The Black Sheep), Carrer de Zamora, 78, 08018 Barcelona, Spain, ☎ +34 933 09 59 38. Is a great place to meet up with a large group of friends or to make a large group of new friends! It is a beer hall styled in a traditional Catalan manner. It has been around for decades in the Poble Nou district of Barcelona. It has huge wooden tables that seat no less than ten people. It has exposed stone walls, and large wood supports, so you feel you are in a barn or old farm house. The Black Sheep is also immediately opposite one of the finest clubs Barcelona has to offer "Sala Razzmatazz" and acts as the perfect pre-gamer spot (Inc. Sangria & Beer pitchers!) before heading across the road to dance late into the night / early morning! Please note: There are 2 bar locations. One in Raval close to Las Ramblas and one in Poble Nou (The one mentioned here).
Shopping in Barcelona, Spain
Most shops and shopping malls are closed on Sundays because of law restrictions, but not all. In Ciutat Vella, you will find plenty of small fashion shops, souvenir shops, and small supermarkets open on Sundays. The souvenir shopping scattered throughout the Barri Gotic and all along La Rambla are tourist traps, none of them sell Catalan or Spanish products but the typical array of general Chinese souvenirs, they should be avoided. Moreover, on the Port Vell, right at the end of The Ramblas there is Maremagnum, a shopping mall that stays open all Sundays.
Secondhand English books in Gràcia.
Design lovers head for Gràcia.
El Corte Inglés. Spanning several floors and several buildings, and in several locations around town, many in Eixample and Inland Suburbs and a couple also in Ciutat Vella. You can find anything and everything in this department store, from gastronomy to pneumatics. Tax return checks are made on a separate floor of the store. See a review for the whole chain in the Spain article.
La Boqueria. In Ciutat Vella. Large public market with a diverse range of goods and produce. Enjoy freshly squeezed organic fruit juices for €1.5 per cup. If you go near closing time (20h, 8PM) sellers will make you a special price. Closed Sundays.
Stamps are sold in 'Tabacs' or tobacconists. Once you know what they look like, you'll notice them on every block or so. To post your mail, you need to find one of the yellow letter box located rather infrequently along the sidewalks.
Records For vinyl records, try the wonderful shop Discos Revolver located at 13 Carrer dels Tallers.
Safety in Barcelona, Spain
Barcelona is Europe's pickpocketing capital. Never keep your wallet, cash or important documents in trouser pockets or in bag pockets: a money belt is an easy and inexpensive way to prevent being robbed. As always, be alert in crowded places, such as public transport, train and bus stations, La Rambla and Raval. People may approach you asking for change, or to change money. Just ignore them. If you are asked to change money, then official looking police may approach you afterwards to 'check' your wallet for ID, etc. These are not police, so be at your most vigilant or you might find they have taken a few cards or cash upon returning your wallet. If you are in a crowd of spectators watching street entertainment, beware of anyone getting suspiciously close to you.
Pickpockets use the football trick as the local specialty. At certain tourist hotspots, there are people who will try to show you a 'magic trick'. This involves tying a piece of string around your finger. While you are distracted (and your arm is effectively disabled), an accomplice will pickpocket you. It is also possible that criminals will pose as tourists and ask directions to approach their victims. Keep your distance and be careful in tourist places.
The subway is a hotbed for pickpocketing activity, which can range from simple opportunistic thefts to coordinated attacks. Be especially wary on the subway platforms at Sants train station and Sagrada Família. A group of men will come out of seemingly nowhere while you attempt to enter a subway car and block your entrance and exit in a coordinated manner, effectively pinning you against the doors while they close. They will act as if the car is just crowded and they are trying to get on as well, but, in reality, they have already gone through your pockets.
Once they take stuff, they quickly return to the platform and walk off calmly while you are trapped in the departing subway as they make sure they exit just before the doors cannot be reopened. Violence in these situations is rare, and in most cases, the goal of the thieves is to rob you undetected. Stay vigilant: do not leave anything in a back trouser pocket (except maybe a map of the city). Hold on to your bag or purse at all times. Do not leave anything unattended while you sit in a cafe or restaurant.
One guy acts like reading a newspaper and is about to go into the subway gate (he's scanning his target). While you insert your subway card to enter and before the gate opens, that guy immediately enters his subway card also, which causes the gate to jam and alarm sound. Immediately 3-4 other people appear and, while acting like trying to help, (pointing to the gate telling you 'the door is jam') will try to snatch your backpack or wallet while you are still surprised. Check and make sure no one tailgates on you, or, simply, just let the guy go first.
While you are at an outdoor table of a café, don't leave your smartphone on the table. Someone will try to steal it. For example, a guy babbling for change with an unreadable poster in his hands, getting closer and closer to the smartphone until he eventually picks it up, passes it to a second guy that will run away with it.
People in Barcelona are often very friendly and love to practice their English, so don't be unfriendly. That said, you should, of course, be suspicious if someone approaches you in a touristy area speaking your language and asking you for help. This should put your guard up immediately. Do not be tempted to sign their petition, give them directions, or help them with their problem. You don't know anything about where you are, since you're a tourist, so you won't be able to help them in any case.
Professional scam artists exhibiting a high degree of coordination are active in many areas of the city. Be careful in tourist areas. A variety of methods are employed, including the No Change trick. A common scam involves fake cops who will show up ask to see your passport, then take your belongings at the first opportunity. The story varies, but they are almost certainly not real ones. When it happens, the best strategy is to just walk away instead of starting any sort of conversations with them. Another trick is that one seemingly confused person will ask you for directions, diverting your attention and then suddenly fake police will appear asking for your ID. This is a co-ordinated move to divert the attention and steal whatever is possible. If such incident happens, just walk away, without listening to any of their conversation. Stay alert, especially in busy tourist area near the Sants station and Plaça d'Espanya.
Another popular scam happens in the metro. A group of scammers (often middle-aged women) will take advantage of the fuss while people are entering the metro and surround a tourist, frantically asking for directions. Most tourists won't know what to say while one of the scammers empties their pockets. They will try to confuse the tourist while the metro stays in the platform, and will get out just before the doors are closed. When you realize you've been scammed, the train will have already left and they will be safely outside with your belongings.
The bird excrement scam is also common. One or more accomplices will secretly spray or throw a smelly liquid on you. When you look up thinking a passing bird has pooped on you, they will run up to you and tell you that they saw a bird poop on you. They will offer to help you clean up, and while you are cleaning they will go through your pockets and any bags you have set down. It is wise to beware of anyone who is attempting to touch a complete stranger.
A version of Three Card Monte is one of many common scams played on Les Rambles. There are also people holding petitions to install a wheelchair lift in locations with a lot of stairs. Once your signature is obtained they will then aggressively ask for a donation. Sometimes there can be crowds of children demanding money with hardly anyone else in the area, making it difficult to get away.
Barcelona offers ATMs in many locations. Many provide a wide range of services (withdrawals, transfers, mobile credit recharges, ticketing, etc.), and most accept ATM/debit/credit cards of various banks. Choose an ATM in a secure or highly-public space (e.g., in a bank lobby or airport terminal) to avoid machines modified by criminals to skim/video your card data or where you might be robbed after use. Ensure early in usage that the ATM supports a language you understand. For a full discussion of safe/effective charge/debit/ATM card usage and their cost trade-offs, see Money.
Areas of caution
Be very careful in the Barcelona Sants train station where thieves prey on new arrivals, even on the platforms.
Women traveling alone should exercise caution while exploring the more isolated parts of Montjuïc. The city beaches, particularly the ones adjoining Barceloneta, have proven to be quite lucrative for bag snatchers. Anything that one would rather not lose is best left, locked, in one's hostel or hotel.
Men traveling alone should expect the prostitutes on Les Rambles, St. Antoni, and Raval in the early hours to be very aggressive and in league with pickpockets and robbers.
Also, people need to be careful when leaving the bars of the Olympic Port late as there are many pickpockets around.
Women should be wary of wearing exposed jewelery such as gold chains and necklaces. People walking down a street may be attacked from behind by a thief who may grab the necklace and try to rip it off the woman's neck before quickly running away, often down a convenient side street. Be especially careful of seedy looking men on bicycles as there have been many grab and snatch assaults in recent years.
In the event of such a robbery, people will need to find the local police station to report the incident, especially if a travel insurance claim is going to be made. Don't expect any police action beyond the report though as these types of events are par for the course and arrests, even when made almost never lead to prosecution due to a slow, antiquated, and overburdened legal system.
Parts of Barcelona are covered by closed circuit TV surveillance, but only the more popular spots.
Tourist drivers may attract special attention, such as Red light bag snatch or Flat tire scams
Reporting crimes
If you need to report a crime (for example, to claim on travel insurance), be prepared for the reality that in the downtown police station, officers generally do not speak English, despite that fact the official theft report form is in English, Spanish, and Catalan. The police station most often used to report theft is the one underneath Plaça Catalunya beside metro station, where they have some translators for common world languages.
Language spoken in Barcelona, Spain
Barcelona's official languages are Catalan and Spanish. However, most signs are indicated only in Catalan because it is established by law as the first official language. Spanish is also widely used in public transport and other facilities. Regular announcements in the Metro are made only in Catalan, but unplanned disruptions are announced by an automated system in a wide variety of languages including English, French, Arabic, and Japanese. On the other hand, FGC announcements -either regular or disruptions- will be made only in Catalan, and disruption announcements on RENFE's network will usually be broadcasted only in Spanish. As in most other cities, any attempt by visitors to use the native languages is always appreciated. Most locals are bilingual in Catalan and Spanish, and instinctively address foreigners in Spanish. Catalan is a language, not a dialect, and sounds closer to Italian, Portuguese, and French in many ways. Avoid referring to Catalan as a dialect, which will offend Catalans.
The main cause of Spanish and Catalan social bilingualism in modern Catalonia is a large scale immigration process from the rest of Spain which occurred over the 20th century, as Catalonia started significant industrialization which demanded an increased workforce from elsewhere. Nowadays, 60% of the people in Catalonia use Spanish as their first language whereas 40% use Catalan.
These issues regarding language, national identity, and politics are like politics anywhere, and there's no way to summarize them here. Some Catalans feel Spanish and some not, and there is a portion who are anti-Spanish (and feel opposed to Spain and the Spanish language), as there are Spaniards who are not very fond of Catalans or Catalonia in general.
In tourist areas, almost all shops and bars have some English speaking staff. People will make an effort to try to help you if you speak English. If you are a native English speaker, you will not have any problems as Barcelona is a very touristic city.
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Sagrada Familia, Barcelona, Spain
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The Basílica i Temple Expiatori de la Sagrada Família (Catalan pronunciation: səˈɣɾaðə fəˈmiɫiə; English: Basilica and Expiatory Church of the Holy...
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Casa Batlló (Catalan pronunciation: ˈkazə βəˈʎːo) is a renowned building located in the center of Barcelona and is one of Antoni Gaudí...
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The Palau de la Música Catalana (Catalan pronunciation: pəˈɫaw ðə ɫə ˈmuzikə kətəˈɫanə, English: Palace of Catalan Music) is a concert hall in...
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The Museu Nacional d'Art de Catalunya (Catalan pronunciation: muˈzɛw nəsiuˈnaɫ ˈdard də kətəˈɫuɲə, English: "National Art Museum of Catalonia"),...
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The Gothic Quarter (Catalan: Barri Gòtic, IPA: ˈbari ˈɣɔtik, Spanish: Barrio Gótico) is the centre of the old city of Barcelona. It stretches from La...
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The Parc de la Ciutadella (Catalan pronunciation: ˈparɡ də ɫə siwtəˈðeʎə, "Citadel Park") is a park on the northeastern edge of Ciutat Vella,...
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I had 8th of 12 picks. Key scoring settings: 4 pts for passing TD, not PPR.
I know I'm a little light on WRs, but I took fliers on guys that could potentially blow up like Brown and Mendenhall instead of taking a boring 60 catch-type receiver. Nobody was touching JJ either, so I thought I good him for good value in the 9th round. Shockey was a no risk late-rounder, so I won't be disappointed if he does nothing.
I would look at shopping Brown or Taylor to the Addai and AP owner for some more WR depth.
I wouldn't mind shipping off Taylor, but no thanks to those NYG WRs.
I would do Berrian for Brown but I doubt he'd go for it. I'd rather hold onto Brown's upside than give him up for one of those bench bums.
AP's owner has Ryan, Cassell, and Campbell. I currently have all my eggs in the Brees basket, so what about Taylor for Cassell?
Not too crazy about the Chiefs this year. You might think about something like Brees/Taylor for Ryan/Jennings, dunno. I know you probably really want to keep Brees since you picked him early. Just a thought. Or look at the Addai owner's QB and do the same kind of trade getting Colston or Fitz?
I'm not crazy about it though. Even though I expect Ryan to get better, I'm pretty high on Housh (#1 in Seattle with a healthy Hasselbeck instead of splitting catches with Ocho from Fitzpatrick) and Gonzo (#2 in Indy), and I think they'll put up considerably better numbers this year in their new locales/positions. I dunno, I'm happy enough with Gonzo as my WR2 to not have to trade my stud QB. I'd rather go after a backup fantasy QB like Garrard on the cheap than make a blockbuster at this point.
Ok, team #2 drafted last night. Had pick 11 of 12. Key stats: 5 pts for passing TD, 0.7 PPR. The PPR changed up my rankings a bit and I def got a few chuckles when I drafted Kevin Faulk (3rd in RB receptions, dummies!). I'm hoping to have the last laugh.
For the second time in two drafts, I seem to have enough man-love for LT that I could not pass on him when he fell to me. I was very happy to get Calvin on the way back in the 2nd considering Fitz, Andre, and Moss went 4, 8, 9, respectively.
I think my RB2 and Flex position could potentially get sticky, but I'm pretty happy with the rest of my squad. Thoughts?
I am starting to worry about Smith. As long as he gets that #2 WR slot he'll be ok, but there won't be enough passes in that offense to give a #3 receiver enough fantasy stats.


text:
\section{Introduction}
The Czochralski (Cz) process is the industrially dominant process for the production
of monocrystalline silicon ingots. The ingots produced are cut into thin wafers,
which are the basis for the production of photovoltaic cells and computer chips. Any
variation in the ingot radius will increase the material waste in the subsequent
production steps and might also initiate defects in the crystal structure during
growth. Good control of the ingot radius is, therefore, important. Unfortunately,
the quantity measured for feedback control, the \emph{bright ring radius}, is
affected by an \emph{inverse response} behaviour \citep{gevelber1994dynamics}.
That is, when the crystal pulling speed is increased, the radius measurement at
first increases and thereafter decreases. However, in general, the steady-state effect of the increased pulling speed is a decreased radius measurement, and vice versa. The term
\emph{inverse response} refers to the phenomenon when the initial response of
the controlled variable is in the opposite direction of the steady-state
response. Such inverse responses are one appearance of what in control parlance
is termed \emph{non-minimum phase behaviour}, and causes fundamental limitations
in achievable control performance \citep{skogestad2007multivariable}. This paper
presents a control design approach, where a conventional PID feedback controller
is combined with a so-called \emph{parallel compensator} to circumvent the
limitations on feedback control caused by the non-minimum phase dynamics of the
system.

\subsection{Paper Organization}
A description of the Cz process is given in the first part of this article
series \cite{BUKHARI2020A}, where the model relevant for the control of crystal
growth is developed. The model combines rigorous descriptions of the meniscus
shape and the camera-based radius measurement with simplified temperature
dynamics. The analysis of the developed model verifies the presence of the
inverse response from pulling speed to radius measurement. Based on this, the
present paper is structured as follows: Section\,\ref{sec:GrowthModel} studies the
dynamics of the crystal radius control problem, elucidating the requirements and
limitations in relevance to the control design. For this purpose, the heat
transfer from the heaters to the melt is of minor significance, and a reduced
model with a constant melt temperature is used. This model is linearized in Section\,\ref{sec:Linearization} so that in Section\,
\ref{compensator_controller} the linear controller and parallel compensator
can be designed. In Section\,\ref{sec:temp_model}, the controller design is verified in
simulations involving the overall system model from \cite{BUKHARI2020A}, and it
is shown that the controller achieves stable control also of the nonlinear
dynamics, as well as good suppression of disturbances entering through the temperature dynamics.

\section{Cz growth model and inverse response behaviour}\label{sec:GrowthModel}
In the first part \cite{BUKHARI2020A} of this article series, two models for the
crystal growth and radius dynamics are developed. These two models differ in
how the heat transfer from the melt to the melt/crystal interface are modelled:
\begin{enumerate}[label=\Roman*., widest=II,labelindent=1ex,leftmargin=*]
\item In this model, the heat transfer across the meniscus is modelled based on conductive
flows, whereas the transfer of heat from the melt bulk to the meniscus is
governed dominantly by convective flows.
\item Here, the overall heat transfer from the bulk of the melt to the
melt/ crystal interface is dominated primarily by the convective heat flow.
\end{enumerate}

Of course, the two models are clear simplifications of reality, with the actual heat transfer across the meniscus likely to be somewhere between pure conduction and pure convection.

As a consequence of these assumptions for \textbf{Model I}, the overall heat
transfer to the interface depends on the meniscus height (cf.\,Eq.\,(8) in part
I of this article series), while in \textbf{Model II}, the heat transfer to the
interface is independent of the meniscus height (cf.\,Eq.\,(12) of part I). The
same holds for the growth rate since it directly depends on this heat transfer
(cf.\,Eq.\,(1e) in part I).

To illustrate the difference between the two models, both models are simulated with the smooth profile for the crystal pulling speed shown in Fig.\,\ref{fig:vp_input} while the heater power is kept constant. The resulting
responses of the two models are depicted in Figs.\,\ref{fig:non_lin_conduction}
and \ref{fig:non_lin_convection} for models I and II, respectively.

\begin{figure}[ht!]
    \centering
    \includegraphics[width=0.8\linewidth]{fig1-vp_input_grayscale.pdf}
    \caption{Applied pull speed profile}
    \label{fig:vp_input}
\end{figure}
\begin{figure}[ht!]
    \centering
    \includegraphics[width=1.0\linewidth]{fig2-non_lin_responses_conduction_grayscale.pdf}
    \caption{Nonlinear plant response for \textbf{Model I} subjected to the applied input shown in Fig.\,\ref{fig:vp_input}, crystal radius ($r_{c}$), bright ring radius ($r_{br}$) and crystal growth angle ($\alpha_c$) in top-left and right panes, respectively, the meniscus height ($h_{c}$) and the growth rate ($v_{g}$) in the bottom-left and right panes, respectively.}
    \label{fig:non_lin_conduction}
\end{figure}

\begin{figure}[ht!]
	\centering
	\includegraphics[width=1.0\linewidth]{fig3-non_lin_responses_convection_grayscale.pdf}
	\caption{Nonlinear plant response for \textbf{Model II} subjected to the applied input shown in Fig.\,\ref{fig:vp_input}, crystal radius ($r_{c}$) and bright ring radius ($r_{br}$), crystal growth angle ($\alpha_c$) in top-left and right panes respectively, the meniscus height ($h_c$) and the growth rate ($v_g$) in the bottom-left and right panes, respectively.}
	\label{fig:non_lin_convection}
\end{figure}

It is apparent that a decrease in pull speed causes the crystal radius to
increase. However, the measurement of the bright ring radius, (which is used as an estimate
 of the crystal radius) initially moves in a direction opposite to that of
the actual crystal radius, thereby confirming the presence of inverse response. Moreover, the heat flux into the interface based
on convective heat transfer (Model II) yields a constant growth rate $v_g$, whereas it
varies with height for the case with pure conductive heat transfer across the
meniscus (Model I).

\section{Linearized model} \label{sec:Linearization}
For the approach presented in this paper, it is necessary to linearize the nonlinear
model around a steady-state crystal radius. While the equations describing the
meniscus dynamics and temperature effects are given in closed form, the
dependency of the measured bright ring radius on the crystal radius and the
pulling speed is not. Hence, a full-model numerical perturbation linearization
is carried out around a steady-state crystal radius of \SI{87.5}{\mm} and a
pulling speed of \SI{1.2}{\mm\per\minute}. The obtained linear ordinary
differential equations are then transformed into a corresponding transfer
function $G(s)$ in the complex-valued Laplace domain with the complex-valued
Laplace variable $s$ (cf.\,Section \ref{sec:control:models}).
This transfer function describes the linear response of the bright ring radius
$R_{br}$ to changes in the crystal pulling speed $V_{p}$, where the uppercase written variables indicate being in the Laplace domain.

It will prove useful in this paper to formulate this transfer function as a series connection of the process dynamics $G_p(s)$ between pulling speed and crystal radius $R_c(s)$ and the measurement dynamics $G_m(s)$ between the
crystal radius and the bright ring radius,
cf.\,Fig.\,\ref{fig:series-connection} also:
\begin{equation*}
	G(s) = \frac{R_{br}(s)}{V_p(s)} = \frac{R_{br}(s)}{R_c(s)} \cdot \frac{R_c(s)}{V_p(s)} = G_m(s) \cdot G_p(s).
\end{equation*}

\begin{figure}[ht]
	\centering
	\includegraphics[width=0.75\linewidth]{fig4-series-connection.pdf}
	\caption{Series connection of the transfer functions describing the pulling speed - crystal radius dynamics $G_p(s)$ and the measurement dynamics $G_m(s)$.}
	\label{fig:series-connection}
\end{figure}

For model I, one has
\begin{subequations}
\begin{align}
	G_{p,I}(s)&=\frac{-0.0047626}{(s-\SI{8.78e-6}{})\,(s+\SI{1.684e-3})} \label{Rc_by_Vp_I}\\
	G_{m,I}(s)&= -47.1864s+1.0041,\label{Rbr_by_Rc_I}
\end{align}
\end{subequations}
and for model II
\begin{subequations}
	\begin{align}
		G_{p,II}(s)&=\frac{-0.0048849}{(s-\SI{4.63e-7}{})\,(s-\SI{7.602e-6}{})} \label{Rc_by_Vp_II}\\
		G_{m,II}(s)&=\frac{R_{br}(s)}{R_c(s)} = -46.0050s+1.0043\label{Rbr_by_Rc_II}.
	\end{align}
\end{subequations}
The units are omitted here for the sake of clarity. The static gain of
\eqref{Rc_by_Vp_I} and \eqref{Rc_by_Vp_II} is in $\SI{}{\minute}$, while that of
\eqref{Rbr_by_Rc_I} and \eqref{Rbr_by_Rc_II} is dimensionless. The roots of the
numerator polynomial of a transfer function are called \emph{zeros}, the roots
of the denominator polynomial \emph{poles}. These roots are real-valued or occur
in complex conjugate pairs, since the coefficients of the polynomials are real.
Their unit is in $\SI{}{\radian\per\second}$. A system is stable if a finite
perturbation in any input signal results in a finite response in all output
signals. For a pole at $s=p_i$, the corresponding dynamics are stable if
$\mathrm{Re}(p_i) < 0$, i.e., if the pole $p_i$ is in the left half plane of the
complex plane. If $\mathrm{Re}(p_i) > 0$, the corresponding dynamics is unstable.
Unstable poles are often called \emph{Right Half Plane} (RHP) poles.  The system
is stable if all poles are in the left half plane. Clearly, stability (possibly
through control) is a basic requirement for operation of any system. The two models
differ in their pole configuration: Model I has one RHP pole at
$\SI{8.78e-6}{\radian\per\second}$, while in Model II both poles are unstable
with $p_1 = \SI{7.602e-6}{\radian\per\second}$ and $p_2 =
\SI{4.63e-7}{\radian\per\second}$.

A real-valued zero $s=z_i$ for which $\mathrm{Re}(z_i)>0$ is called a RHP zero, and
will cause an inverse response from the control input to the measurement. All
RHP zeros cause fundamental limitations in achievable control
performance\footnote{Also complex conjugate RHP zeros, which do not necessarily
cause an inverse response, see \citep{skogestad2007multivariable}.}. It is
apparent from \eqref{Rbr_by_Rc_I} and \eqref{Rbr_by_Rc_II} that both models have
a RHP zero at $\approx \SI{0.021}{\radian\per\second}$, as expected based on the
nonlinear simulations. The location of the right half-plane zero is nearly
independent of the heat transfer mechanism characterizing the heat flux into the
interface.

Finally, note that the transfer functions in \eqref{Rbr_by_Rc_I} and \eqref{Rbr_by_Rc_II}
are not physically realizable because they contain a direct differentiation of
the input signal. They only make sense when multiplied with the corresponding
terms in \eqref{Rc_by_Vp_I} and \eqref{Rc_by_Vp_II}, respectively.

\section{Design of a parallel compensator and feedback controller}\label{compensator_controller}
Using the linear models derived in Section\,\ref{sec:Linearization} a parallel compensator and stabilizing controller can be designed.

\begin{figure}[ht!]
	\centering
	\includegraphics[width=1.0\linewidth]{fig5-basic_feedback_control.pdf}
	\caption{Illustration of a simple feedback control system with the transfer function $G(s)$ of the system to be controlled, the transfer function $K(s)$ of the controller and the transfer function of the disturbance model $G_d(s)$.}
	\label{fig:Feedback}
\end{figure}

\subsection{Basic feedback controller design} \label{sec:constraints:controller}
Feedback control is the most common type of control, illustrated in
Fig.\,\ref{fig:Feedback}.  This basic feedback schematic diagram shows a measurement $Y(s)$ being affected
by a disturbance $V(s)$ through the dynamics $G_d(s)$ and by the control input
$U(s)$ through the dynamics $G(s)$. The measurement signal $Y(s)$ is \emph{fed
back} and compared with its reference/ desired value $R(s)$ such that the
difference, alternatively called error $E(s)$, is used as an input to the
controller $K(s)$, which in turn calculates the control signal $U(s)$.

Feedback control is a remarkably powerful concept. It can stabilize unstable
systems, i.e. moving the unstable system poles to the left half of the complex
plane, and provide good performance, for example a quick response of the controlled quantity $y(t)$ to
changes in the reference $r(t)$, no or only limited overshooting of $y(t)$ or proper disturbance
rejection. However, it is not without caveats. In particular, poorly
designed feedback control may also cause instability, even for systems $G(s)$
which are stable on their own. Furthermore, and most important for this paper,
system zeros are unaffected by feedback.

\begin{figure}[ht!]
	\centering
	\includegraphics[width=1.0\linewidth]{fig6-bode-general-control.pdf}
	\caption{Illustrative and simplified sketch of a Bode diagram showing the frequency response of the open-loop system with $L(s) = K(s) \cdot G(s)$ and $s = j\omega$. The frequency axis is drawn in linear scale for sake of simplicity. The transfer function $G(s)$ of the system to be controlled is assumed to have two RHP poles denoted by $p_1, p_2$ (among other stable poles) and one RHP zero denoted by $z_1$. For a stable closed-loop system showing acceptable performance the crossover frequency $\omega_c$ should be roughly within the grey region and the phase margin $\varphi_m$ must be positive.}
	\label{fig:bode-general}
\end{figure}

A common way to determine suitable parameters of the controller is to utilize
the frequency response $L(j\omega) = K(j\omega) G(j\omega)$ of the so-called \emph{open-loop} system plotted in a Bode diagram. An illustrative example of a Bode diagram is shown
Fig.\,\ref{fig:bode-general}. The Bode diagram consists of two plots, the first
showing the magnitude $|L(j\omega)|$ in a logarithmic scale\footnote{dB or the base-10 logarithm are commonly used.} of the open-loop system depending on the
frequency $\omega$ and the second one showing the phase of $L(j\omega)$.

A well-designed feedback control system will have an open-loop frequency response with large magnitude at low frequencies, but small magnitude at high
frequencies.  Let $\omega_c$ denote the \emph{crossover frequency}, i.e., the
frequency where $|L(j\omega_c)|_\text{dB} = 0$. Assume that
$|L(j\omega)|_\text{dB} > 0 \; \forall \omega < \omega_c$, and
$|L(j\omega)|_\text{dB} < 0 \; \forall \omega > \omega_c$.  Then, the so-called
Bode stability criterion states that the \emph{phase margin} $\varphi_m =
180^{\circ} + \angle L(j\omega_c)$ \emph{must} be positive. Although some
sources present the Bode stability criterion only for open-loop stable systems,
it can also be applied to open-loop unstable systems -- as the Cz system under
discussion -- provided the number of open-loop unstable poles is known and the
steady-state phase is adjusted accordingly. Each RHP pole contributes a phase of $-180^{\circ}$ at $\omega = 0$. A small phase margin indicates that
the system may become unstable for a small error in the system model, and is
also an indication of poor performance, e.g.,\,large overshooting. Most control
engineers will insist on a phase margin of at least $45^{\circ}$.

Additional criterions can  be utilized to improve closed-loop performance: For
example, as a rule of thumb, $\omega_c$ should be about at least twice as large
as the \emph{fastest unstable pole} to ensure that any unstable dynamics is
properly `caught'. In case of non-minimum phase systems -- as discussed here --
another restriction comes into play: $\omega_c$ should be about less
than half the \emph{slowest zero} so the controller action is not dominated
by any inverse response. Clearly, the last two requirements show that the
presence of a RHP zero will introduce a typical conflict of objectives imposing
fundamental limitations on achievable performance for feedback control. An
extensive exposition of these issues can be found in
\citep{skogestad2007multivariable}, where further details, more precise
statements and theoretical justification can be found. Also refer to \ref{sec:control:frequencyanalysis} for an explanation of the term
\emph{non-minimum phase system}.

Coming back to the Cz system, for Model II, the required crossover frequency
will be determined mainly by the faster RHP pole (the one furthest from the
origin in the complex plane). The faster RHP pole
$7.602\mathrm{e}^{-6}\SI{}{\radian\per\second}$ in Model II is similar to the
RHP pole $8.78\mathrm{e}^{-6}\SI{}{\radian\per\second}$ of Model I. Therefore,
the control limitations of the two models are similar, even though the number of
unstable poles is different. Further details can be found in
\citep{BUKHARI2019129}.

\subsection{Basics of parallel compensator design} \label{sec:parallelcomp:basic}
The parallel compensator accounts for the anomalous behaviour of the measurement
signal, i.e., it moves RHP system zeros into the left plane only without altering the location of system
poles \citep{skogestad2007multivariable}.

Several authors have proposed combining feedback control with
parallel compensation, thereby enabling the latter to remove the limitation in performance for feedback control. Such a schematic, with combined feedback and parallel compensator, is illustrated in Fig.\,\ref{fig:parallel}. Here, a parallel compensator $G_{pc}(s)$ is designed to ensure that the transfer function
from the input $U(s)$ to the compensated signal $Z(s) = Y(s) + Y_{pc}(s)$ does
not possesses any RHP zero to limit the performance of feedback control.

Unfortunately, in most physical systems with a control configuration such as
that depicted in Fig.\,\ref{fig:parallel}, the use of parallel compensation is not of much value.  This is because despite achieving good control of $Z(s)$,
the physical variable $Y(s)$, of interest, cannot be alleviated of the undesired effects of
the RHP zero(s).

\begin{figure}[ht!]
	\centering
	\includegraphics[width=\linewidth]{fig7-basic_parallel_compensator.pdf}
	\caption{Feedback control combined with parallel compensation to remove performance limitations for feedback control caused by RHP zeros.}
	\label{fig:parallel}
\end{figure}

However, as observed in Figs.\,\ref{fig:non_lin_conduction} and
\ref{fig:non_lin_convection}, the inverse response in the Cz process is merely
associated with the camera-based \emph{measurement} of the ingot radius, whereas the
\emph{actual crystal radius} is independent of the inverse behaviour. This opens an
opportunity for using parallel compensation to enable improved control of the
crystal radius $r_c$, even though the control of the measurement $r_{br}$ is not
improved.

\subsection{Compensator design} \label{sec:compensator:design}
Instead of using generic time-/ Laplace-domain symbols $r(t)/R(s)$,
$u(t)/U(s)$ and $y(t)/Y(s)$ as in Fig.\,\ref{fig:parallel} the symbols specific to the Cz
process will be used henceforth.

\begin{figure}[ht!]
	\centering
	\includegraphics[width=1.0\linewidth]{fig8-compensator_block_diagram.pdf}
	\caption{Basic block diagram of the feedback controlled Cz system split into the pure plant model $G_p(s)$ and the bright ring measurement model $G_m(s)$ together with a parallel compensator. The variable $R_{c,ref}$ defines the
	ingot radius reference and $\tilde{R}$ is the compensated radius
	measurement. The ideal parallel compensator $G_{pc}(s)$ is augmented by a high pass filter $G_{hpf}$ according to the procedure described in Section\,\ref{sec:compensator:design}. What is implemented in the real system is the stable approximation of $G_{pc}(s)G_{hpf}(s)$.}
	\label{fig:block_diagram}
\end{figure}

Fig.\,\ref{fig:block_diagram} shows a complete system block diagram that
includes both the compensator and the controller connected respectively in
parallel and cascade with the plant. The controller block marked as $K(s)$ is
the Automatic Diameter Control (ADC) as discussed in part I of this article
series. The parallel compensator used is a stable approximation of the ideal
compensator with transfer function $G_{pc}(s)$ augmented by a high pass filter
with transfer function $G_{hpf}(s)$. The need for both, the stable approximation
and the high pass filter, will be explained later. The following two design requirements need to be met:
\begin{enumerate}[labelindent=0ex,leftmargin=*]
	\item It is desired to keep the dynamics of the compensated measurement as
	close as possible to the one of the actual crystal radius, i.e.,
	$\tilde{R}(s) \approx R_c(s)$.
	\item The practices	in the Cz industry rely on using the camera-based
	measurement, followed by simply applying a bias to the measurement signal.
	By this approach they obtain the true \emph{steady-state} crystal radius
	from the camera measurement. The compensator design should allow the
	industry to continue applying the same bias to the compensated measurement
	$\tilde{R}(s)$. Hence, the compensator obtained in step 1 needs to be
	modified appropriately.
\end{enumerate}

Under these conditions the compensator -- based on model I -- can be designed as follows: Ignoring (for now) the high pass filter $G_{hpf}(s)$ in
Fig.\,\ref{fig:block_diagram}, the dependency of $\tilde{R}(s)$ on $V_p(s)$ gives
\begin{equation}
\tilde{R}(s) = \bigl(G_m(s)G_p(s)+G_{pc}(s) \bigr)V_p(s). \label{Eq:tf_comp}
\end{equation}

Hence, the ideal
parallel compensator can be derived as follows:
\begin{align}
	G_{\tilde r}(s) &\stackrel{!}{=} G_p(s) \nonumber\\
	G_p(s) G_m(s) + G_{pc}(s) &= G_p(s) \nonumber \\
	\Leftrightarrow \qquad G_{pc}(s) &= G_p(s)\left(1-G_m(s)\right) \label{Eq:comp_ideal}
\end{align}

It is apparent that the ideal parallel compensator as given in
\eqref{Eq:comp_ideal} would contain the same poles as the plant model $G_p(s)$,
including the unstable pole(s). Any system that consists of two parallel branches,
having identical unstable dynamics with common input and output, will not be
stabilizable by feedback as it will necessarily possess hidden unstable mode(s) \cite{skogestad2007multivariable}. It is, therefore, necessary to find a
stable approximation to the ideal parallel compensator $G_{pc}(s)$, i.e., an
approximation that removes the RHP zero, but does not destabilize the control loop.

In this case, the frequency of the RHP zero is higher than the frequencies
of the RHP pole(s) (cf.\,Section \ref{sec:Linearization}). Hence, the main interest is to have a good approximation of the unstable system at high frequencies to remove the effects of the RHP zero. The unstable dynamics are therefore suppressed by augmenting $G_{pc}(s)$ with a high pass filter $G_{hpf}(s)$, designed to cut off frequencies significantly below the frequency corresponding to the RHP zero. With the RHP zero at $\approx
\SI{0.021}{\radian\per\second}$ the transfer function $G_{hpf}(s)$ of the high
pass filter is chosen as
\begin{equation} \label{eq:hpf}
	G_{hpf}(s) = \frac{5000\,s}{5000\,s+1}
\end{equation}
with the cutoff frequency at $\SI{2e-4}{\radian\per\second}$.

Then, a stable/ unstable decomposition is performed on the augmented parallel
compensator. This means that the transfer function $G_{pc}(s) G_{hpf}(s)$ is
split into two transfer functions connected in parallel, one containing the stable dynamics, while the other, the unstable dynamics. The procedure is sketched in
\ref{sec:StableUnstable}. Since the unstable dynamics are slow, the
augmentation of the high pass filter makes the unstable part smaller compared to
the stable part. Hence, it is reasonable to use only the stable part of this
decomposition in the final implementation.

Finally, design requirement 2 has to be met. The stable part of the decomposition is therefore
adjusted to have zero steady-state gain such that $\tilde R = R_{br}$ in steady state. One ends up with the following  parallel compensator transfer function for model I
\begin{equation} \label{eq:pc:real}
	G_{pc,real}(s) = \frac{Y_{pc}(s)}{V_p(s)} = \frac{-0.22517s}{(s+\SI{1.684e-3}{})(s+\SI{2e-4}{})}.
\end{equation}
In the time domain, \eqref{eq:pc:real} is written as
\begin{align*}
	 \ddot{y}_{pc}(t)+\SI{1.884e-3}{}\,&\dot{y}_{pc}(t)\\
	 +\SI{3.368e-7}{}\,&y_{pc}(t)  =-0.22517\,\dot{v}_p(t)
\end{align*}
and this has to be implemented in the control system computer.

\subsection{Controller design}
The design of a stabilizing feedback controller follows the compensator design.
A PID controller is used  in this work because it is easy to implement in the
existing industrial control setup. The PID controller, represented by $K(s)$ in
a series/interacting form is given by
\begin{equation} \label{eq:PID}
K(s)=\frac{K_p\,(T_is+1)\,(T_ds+1)}{T_i s \left(1+\frac{T_ds}{N}\right)}.
\end{equation}
The tuned parameters for the PID controller and the resulting cross over
frequency are given in Table~\ref{tab:PID_params}.

\begin{table}[ht!]
	\centering
	\begin{tabular}{|c|c|}
		\hline
		Proportional gain ($K_p$) & \SI{0.01}{\per\second}\\
		\hline
		Integral Time const. ($T_i$)& \SI{5000}{\second}\\
		\hline
		Derivative Time const. ($T_d$)&\SI{650}{\second}\\
		\hline
		Filter coefficient ($N$)&100\\
		\hline
		Crossover frequency ($\omega_{c}$)& \SI{0.03275}{\radian\per\second}\\
		\hline
	\end{tabular}
	\caption{Parameters of the PID controller $K(s)$.}
	\label{tab:PID_params}
\end{table}

The achieved crossover frequency $\omega_{c}\approx$
\SI{0.03275}{\radian\per\second} is much higher than half of the zero at
$\approx$ \SI{0.02}{\radian\per\second} which would have been the limiting
factor in control design without parallel compensation. So the limitations
imposed by the RHP zero is quite clearly mitigated and a higher system bandwidth is
achieved.  The frequency response in Fig.\,\ref{fig:frequency_responses} shows
that the proposed PID controller with the compensator stabilizes both models, as the phase margin of the compensated plant is around $74^{\circ}$ for both models.

\begin{figure}[ht!]
	\centering
	\includegraphics[width=1.0\linewidth]{fig9-frequency_responses_grayscale.pdf}
	\caption{Frequency response of the compensated plants (models I and II) with a feedback controller.}
	\label{fig:frequency_responses}
\end{figure}

\subsection{Closed-loop performance}

The closed-loop testing of nonlinear Cz growth dynamics, in the presence of both
parallel compensator as well as the feedback controller ($K$), is schematically
illustrated in Fig.\,\ref{fig:compensator_block_diagram_v4}.
\begin{figure} [ht!]
	\centering
	\includegraphics[width=1.0\linewidth]{fig10-compensator_block_diagram_nonlinear.pdf}
	\caption{Block diagram for the closed-loop testing of nonlinear Cz growth dynamics.}
	\label{fig:compensator_block_diagram_v4}
\end{figure}

In Fig.\,\ref{fig:compensator_block_diagram_v4}, $\delta\,v_p$ and
$\delta\,r_{br}$ are the deviation variables, whereas $v_{po}$ and $r_{br0}$ are
the steady-state values (points at which linearization was performed) such that
the input to and the output from the nonlinear Cz dynamics are $v_p\, =\,
v_{po}\, +\, \delta\,v_p$ and $R_{br}\, = \,r_{br0}\,+\,\delta\,r_{br}$,
respectively.

In order to determine the extent to which the nonlinearities in the Cz system may be excited, the responses to two different crystal radius reference
trajectories are simulated.

In the first case, referred to as (\textbf{case-A}) in
Fig.\,\ref{fig:nlanalysis}, the response to a smooth reduction in the crystal
radius reference of \SI{2.5}{\milli\meter} is simulated. In the second case
(\textbf{case-B}), a scaled version of the same smooth crystal radius reference
trajectory is applied, changing the reference by \SI{0.5}{\milli\meter}. In
Fig.\,\ref{fig:nlanalysis}, the responses of \textbf{case-B} are scaled by a
factor of 5 to make them easily comparable to the responses of \textbf{case-A}.
Fig.\,\ref{fig:nlanalysis} shows that the system with the proposed control is
relatively insensitive to nonlinearities for smooth reference changes of
reasonable magnitude.

\section{Responses to temperature disturbances }\label{sec:temp_model}
Hitherto, the simulated growth rate variations did not take temperature dynamics
into account. However, temperature variations are a major source of disturbances
to the crystal growth rate and thereby also to the crystal radius control.  To
assess control performance in the presence of growth rate variations caused by
temperature disturbances, the overall Cz model (with both growth and temperature
dynamics) needs to be used. A qualitative heater model augmented with the
crystal growth dynamics has been presented in Section\,3 of the preceding
article \citep{BUKHARI2020A}.  Thus, in the following, the overall Cz dynamics
(both the growth model as well as heater model) are under the combined influence
of the two system inputs, i.e., pulling speed $v_p$ and heater input $Q_H$.

\begin{figure} [ht!]
	\centering
	\includegraphics[width=1.0\linewidth]{fig11-nlanalysis.pdf}
	\caption{Comparison of system responses to $r_{c,ref}$ with large amplitude change (case-A) and small amplitude change (case-B: \emph{responses are scaled up by a factor of 5}). Top row: compensated measurement $\tilde{r}$, second row: meniscus height $h_c$, third row: cone angle $\alpha_c$, last row: control input $v_p$.}
	\label{fig:nlanalysis}
\end{figure}

\subsection{Temperature effects on the overall system performance}
 During a typical growth cycle in the body stage, a feedforward temperature
 (target temperature) trajectory is applied to the temperature controller to
 compensate for the slow temperature dynamics. In an actual process, the
 temperature feedforward trajectory has an increasing trend (typically in the
 range of $\approx$ \SI{0.1}{\kelvin\per\minute}) to compensate for the
 following phenomena occurring throughout the growth cycle within the Cz growth
 chamber:
  \begin{itemize}[labelindent=1ex,leftmargin=*]
 	\item A gradual uplift of the crucible, therefore progressively reducing the crucible exposure to the heaters.
 	\item With the ongoing crystallization, the crystal continues to protrude into the colder areas above the heat shield, thereby increasing the heat transfer away from the interface.
 \end{itemize}

The perfect temperature feedforward trajectory is hard to establish, due to effects such as aging and continual replacement of components in the hot zone, variations between pullers, etc.  An imperfect temperature trajectory will act as a disturbance to the crystal growth rate and hence also affects the crystal radius
control.  Note that the heater model in this work is qualitative, and therefore
does not include the afore-mentioned phenomena causing a need for an increasing
feedforward trajectory under actual growth conditions.  However, effects of an
imperfect temperature trajectory can be simulated\footnote{High accuracy not
claimed here though.}, since changes to the temperature controller reference
will affect the melt temperature in the model and hence also affect the crystal
growth rate. That is, in our simulation on the simplified model, the temperature
feedforward trajectory does not represent the actual feedforward trajectory, but
rather the error in the feedforward trajectory in an actual plant.

\begin{figure} [ht!]
	\centering
	\includegraphics[width=1.0\linewidth]{fig12-mh1_tempresponse_Td650Kx1_tempPID_grayscale.pdf}
	\caption{Temperature responses for model I. Top pane: temperature sensed by the pyrometer $T_1$ versus the target temperature trajectory $T_{1,ref}$. Bottom pane: temperature of the bulk $T_{bulk}$ of the melt contained within the crucible.}
	\label{fig:MH1_tempresponse_Td650Kx1_tempPID}
\end{figure}

To investigate the effects of temperature disturbances on crystal radius
control, the reference for temperature $T_1$ (sensed by pyrometer) is increased
linearly (at the rate of \SI{0.5}{\kelvin\per\minute}) to simulate the variation
in the target temperature trajectory.

Compared to the typical difference between the actual and the ideal feedforward trajectory, the simulated feedforward trajectory must be considered to represent
a rather strong disturbance. The resultant responses for temperatures in
different lumped volumes (cf. lumped heater model given in \cite{BUKHARI2020A})
is shown in Fig.\,\ref{fig:MH1_tempresponse_Td650Kx1_tempPID}. These temperature
changes, in turn, affect the radii responses ($r_c$, $r_{br}$, $\tilde{r}$) via
variation in growth rate $v_g$.

For the given change in heater set-point trajectory as depicted in top pane of
Fig.\,\ref{fig:MH1_tempresponse_Td650Kx1_tempPID}, the resulting system responses
at the crystallization growth interface are shown in
Figs.\,\ref{fig:MH1_response_Td650Kx1_tempPID} and
\ref{fig:MH2_response_Td650Kx1_tempPID} for models I and II, respectively.

It is apparent from the radii responses (cf.
Figs.\,\ref{fig:MH1_response_Td650Kx1_tempPID} and
\ref{fig:MH2_response_Td650Kx1_tempPID}) that the designed controller and
parallel compensator have successfully overcome the temperature variations
leading to a change in the growth rate, and that the resulting variation in
crystal radius is small.

\begin{figure} [ht!]
	\centering
	\includegraphics[width=1.0\linewidth]{fig13-mh1_response_Td650Kx1_tempPID_grayscale.pdf}
	\caption{Closed-loop responses for model I with a change in temperature set-point trajectory shown in Fig.\,\ref{fig:MH1_tempresponse_Td650Kx1_tempPID}. Top row: crystal radius $r_c$, compensated measurement $\tilde{r}$ and bright ring radius measurement $r_{br}$ versus constant $r_{c,ref}$. Middle row (left $\rightarrow$ right): control input $v_p$ and meniscus height $h_c$. Bottom row (left $\rightarrow$ right): growth rate $v_g$ and growth angle $\alpha_c$.}
	\label{fig:MH1_response_Td650Kx1_tempPID}
\end{figure}

\begin{figure} [ht!]
	\centering
	\includegraphics[width=1.0\linewidth]{fig14-mh2_response_Td650Kx1_tempPID_grayscale.pdf}
		\caption{Closed-loop responses for model II with a change in temperature set-point trajectory shown in Fig.\,\ref{fig:MH1_tempresponse_Td650Kx1_tempPID}. Top row: crystal radius $r_c$, compensated measurement $\tilde{r}$ and bright ring radius measurement $r_{br}$ versus constant $r_{c,ref}$. Middle row (left $\rightarrow$ right): control input $v_p$ and meniscus height $h_c$. Bottom row (left $\rightarrow$ right): growth rate $v_g$ and growth angle $\alpha_c$.}
	\label{fig:MH2_response_Td650Kx1_tempPID}
\end{figure}

\section{Conclusions}
In continuation of the investigation of the inverse response in the preceding
article of this two-article series, this work focuses on controller design for
crystal radius control. The proposed control involves compensation for the
inverse response behaviour with the use of a parallel compensator, and a
conventional PID controller for stabilization and disturbance rejection. The
performance of the resulting system is assessed using nonlinear simulations
including temperature disturbances that alter the growth rate. The results show
that the designed controller stabilizes the crystal radius and has satisfactory
disturbance rejection capabilities for the disturbances that typically occur in
the Cz process.

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