Warning, this video will contain spoilers up to chapter 1026. You've been warned! Hello Manakamatachi, this is Joygirl, with our next discussion, What Makes a Yonko? That is the question that we're going to be answering today, along with the question of whether this means that Monkey D. Luffy now legitimately fits within that category. Because in chapter 1026, Luffy has done something huge and reached a new level. A sky-splitting level, in fact. A feat that we have only seen to be the result of two very powerful individuals clashing. The first time we witnessed this was back in chapter 434, when Shanks paid Whitebeard a visit, which ended with the two clashing swords splitting the sky in the process. Again, this event was seen when Kaido and Bigbump collided towards the end of the second act of the Wano arc, so we know sky-splitting is no joke and we've only ever seen it being achieved by just a handful of overwhelmingly powerful combatants, all of whom hold the status of being one of the emperors of the sea. So it's natural to raise the question of whether our resident Rubber Boy has now reached this level. Without wading into the territory of power scaling too much, which does seem impossible given the context of this video, we're now going to assess whether Luffy is now a legitimate member of this group of Yonko. In which case, this name does need serious changing because Yon means four. But I will be using this term Yonko and Emperor interchangeably, although I do realize that this whole word refers to the four emperors of the sea. And seeing as there are already four individuals with this title, Luffy would actually just be the fifth one. Five as in go. Okay, but let's not get ahead of ourselves because we do first need to answer whether Luffy has actually earned himself this title and to answer that, we have to ask what makes a Yonko? While splitting the skies is no doubt an impressive feat, this in and of itself isn't the sole criteria which requires to be met for an individual to hold this title. In fact, this question of whether Luffy should be considered an Emperor of the Sea was first spurred after the events of the Whole Cake Island arc where Luffy challenged one of the currently existing Yonko, dealt quite a bit of damage to her territory, defeated two of her top commanders, and then survived to tell the tale. Or perhaps it's more accurate to say that the tale was told on his behalf because that's exactly how this discussion spawned. By Big News Morgan, sensationalizing Luffy's feats against Big Mom and his break into the Club of Pirates with bounties over one billion berries, exceeding the amount of any commanders that we know, referring to Luffy as being comparable to being considered one of the Emperors of the Sea. And this raised a lot of discussion about Luffy's status because unlike the status of the Shichibukai, the Yonko title isn't quite clear cut. For the Shichibukai or the Warlords of the Sea, this is a status which was granted by the world government to strong and influential pirates who, in alliance with the Marines, could rival the power of the Yonko to maintain the world's balance. Each of the Shichibukai were directly appointed as a Warlord, but with the Yonko, this is a label that an individual acquires through recognition by the rest of the world. When Garp introduces us to this concept of the Yonko in Chapter 432, he says that people call them the Four Emperors. And again, when Jinbei updates the Straw Hats about Blackbeard's rise to power during the timeskip, Jinbei says the rest of the world labels him one of the Four Emperors. And based on what we've seen throughout the series, what defines an individual to be considered an Emperor is ultimately their power. But power is multi-layered. First and foremost, it does certainly relate to the individual's physical strength because in this world of feasts and pirates, you must be strong to survive, and even more so if you want others to follow you. When we look at all of the characters who have held this Yonko title, each are, as individuals, extremely strong pirates. Whitebeard was known as the world's strongest man, Kaido is the world's strongest creature, and Big Mom is most likely to be the strongest woman we have seen in the series. Shanks is an individual who was able to match Whitebeard in their clash, and Blackbeard was an individual who killed Whitebeard, albeit after Whitebeard essentially took on the entire Marines, but also left a permanent scar on Shanks, which he has stated to still ache to this day. Each of these characters to the exclusion of Blackbeard formed the rare handful of individuals in the world who can wield all three forms of Haki. And whilst possessing Conqueror's Haki isn't a necessary requirement of being a Yonko level, it is an indication of an individual's innate power that they can exert over others. And when used in combat to infuse attacks with Conqueror's Haki, it immediately bolsters the force and strength of the attack. Quite literally, Conqueror's Haki is Haki of the Supreme King, with the title of King being quite synonymous to Emperor. And in Blackbeard's case, what he likes in Conqueror's Haki, he makes up with his unique ability to possess multiple Devil fruits. And the fruits which Blackbeard possesses happens to be two extremely powerful Devil fruits, which can have a very similar threatening and imposing effect on others. And if we're going to discuss Devil fruits, then it's also true that all the other emperors have extremely formidable Devil fruits too. But physical strength alone doesn't equate to being an Emperor, because we could then look at Mihawk, who was once considered a rival to Shanks, and ask why he wasn't considered as one of the Yonko, despite being a capable combatant who stands at the top with the title of the world's strongest swordsman. And the answer often provided here is that Mihawk is a single man, and this fact does definitely lend into the discussion of who should be considered a Yonko. Because another layer of power that we have to consider is the power of influence. Each of the Yonko demands a level of influence in the world, which can also take some various forms. Whitebeard, Kaido, Big Mom and Blackbeard all command an entire fleet of pirate ships. They also rule over expansive territories with specific islands coming under their protection in Whitebeard's case or arguably terror in the case of others. The only Emperor who hasn't had this confirmed is Shanks, who we only know to captain the red-haired pirates and isn't known to rule over any specific territory, but this isn't to say that this means he definitely doesn't command a fleet, and it is highly likely that Shanks does in fact rule some land, which is based on Garp's introduction of the Yonko who reside in the New World and rule the lands with an iron grip. Which is why many have taken to speculating Shanks actually rules over Elbath, but even with speculations aside, if we said that Shanks was captain to just one single ship with no territory to his name, we still know him to possess an insane level of influence in the world. One great enough to be able to call an end to the Marineford War and to gain an audience with the Gorossae. Despite being a character we've only seen a handful of times in the series, in the few instances that we did, Shanks has shared scenes with very important figures or been told to have achieved legendary feats such as stopping fellow Yonko Kaido from going to Marineford. And it is in fact the culmination of these factors which defines the Yonko. They're individuals whose power is overwhelming and imposes inescapable threat, threat to the world government, which explains each of their ginormous bounties, but also to each other. Because the nature of the power system wasn't merely the Yonko versus the Marines in alliance with the Shichi Bukai, it was a delicate balance where the Yonko posed threats to each other in addition to the combined forces of the world government and the warlords. And all of this combined makes them an undeniable presence in the world to garner the attention from others, including the Gorossae, regular citizens, and fellow Yonko alike as being recognized as one of the emperors of the sea. But how does this all relate to Luffy and his latest development? When Big News Morgans announced Luffy's rise to Yonko status, it's fair to say that this may have been premature and still debatable at the time. True, Luffy had accomplished many impressive feat from moving on from the strongest figures of the East Blue to tackling the Shichi Bukai, challenging the world government on a number of occasions, and then eventually facing some of the Yonko, whilst in the process also claiming territories under his protection, becoming the reluctant leader of the Straw Hat Grand Fleet and amassing a whopping 1.5 billion berries. All of these achievements does certainly mean that in the eyes of the one-piece world, especially to the ordinary citizen, the pirate captain Straw Hat Luffy had become a household name with a fearsome reputation, even instilling fear, perhaps enough to be thought amongst the likes of other emperors. And ever since his journey began, with each of his encounters with the other pirates or islands and kingdoms, it was clear Luffy possessed a special ability to gain influence in a very unique way, inspiring those he met. But had Luffy achieved this influence in the eyes of the other emperors themselves?  And this was made excruciatingly clear when we first got to Wano, when Luffy, along with the readers, saw firsthand the difference in strength when fighting against the Yonko. But since we got to Onigashima, this is a perception that Oda has been steadily changing. With each chapter, we've seen Luffy develop more and more to the point that even Kaido would question just how strong Luffy would become, comparing him to the likes of his fellow Yonko, perhaps his greatest foe in Odin, his former Captain Rocks, and even late pirate king Goldy Roger. A well-deserved recognition because shortly after, Luffy learned the ability to infuse his attacks with Conchra's Haki. But even this wasn't enough to showcase the heights of Luffy's power, because soon after, Kaido defeated Luffy once again, sending him below to the depths of the sea. And then, Chapter 1026. Luffy's sky-splitting clash with Kaido was an ultimate showcase of his strength, a moment which undeniably cements his ability to match Kaido, a Yonko. Because this is what had probably been the greatest factor from everyone being able to agree on Luffy's status as a Yonko. He had the impressive feats, the bounty, the grand fleet, territories, and posed enough of a threat against the world government. But up to this point, his threat to another Yonko, or lack thereof, has always held him back from being recognized as one. Plain and simple, he was strong, but not strong enough to challenge a Yonko one-on-one. But this moment in Chapter 1026 is a moment when we clearly see Luffy finally reach this stage. When two Yonko clash and it results in the sky-splitting, what we're seeing is the result of physics. And though I can't say that I understand it to the greatest of scientific knowledge, whether it even makes complete scientific sense, but essentially, we're seeing the collision of two forces of comparably equal strength to the point that the momentum being exerted can't overcome the other, and instead it results in the clash shooting out, or in this case, up into the sky. And this is what Luffy has achieved against Kaido, of controlling his conquest haki so that its force would be equal to Kaido's. And I'm not suggesting this now means Luffy is as of equal strength as Kaido, just as I don't think anyone claims that Whitebeard and Shang's were of the literal same strength or Kaido or Big Mom. But it's undeniable that Luffy has reached a level where he can seriously contend to challenge Kaido and match him. Again, not literally as strong as Kaido, but capable enough to contend and challenge Kaido. And compounded with everything else that Luffy had accomplished up to this point, this clash means that Luffy has achieved the minimum of what it means to be a Yonko. And I know that there are some fans who have gripes about Luffy's rapid development on Onigashima. At the end of the day, only two weeks within the One Piece timeline has passed from their initial showdown at Flower Capital to their sky splitting clash in Chapter 1026, but apart from the fact that Luffy has always had an extraordinarily fast growth rate and a keen ability to develop and increase his combat ability mid-battle, the real difference in his ability against Kaido was his ability to control and wield Konkurshaki. Back at the Flower Capital fight, Luffy was able to land blows on Kaido, but this didn't have an effect because his attacks couldn't penetrate Kaido's tough skin. And in reverse, his own endurance wasn't great enough to withstand Kaido's Nandabagwa imbued with Konkurshaki. This was the point of the Unon Prison arc for Luffy to gain endurance through training whilst wearing sea stone cuffs and for him to learn yoh. But as we know, imbuing his attacks with Armament Haki wasn't quite enough, in Luffy's words, still too shallow. And so it really came down to his knowledge of imbuing his attacks with Konkurshaki. And though his use of his newfound ability was initially understandably clumsy, through the sky splitting clash, it signifies Luffy as now truly being able to stand on equal footing against Kaido. Chapter 1026, marked as per the chapter title, a pivotal point not just for the war on Onigashima, but in the series, where Luffy can truly enter the arena of being considered an Emperor of the Sea. There are arguably differences in strength between each of the Yonkou, with Luffy definitely being at the lower end of the spectrum, but it's undeniable that he has now at least truly entered the stage as an Emperor of the Sea. So let me know what you think by leaving comment below, don't forget to like and share the video, and please do subscribe for more One Piece discussions. You can also join our joy fleet discord server for other types of fun, and even become a patron member to gain extra levels of fun in that server. Thank you to our patrons for help supporting this channel, this is Joygirl, and I'll see you again soon.


All right, hi everybody. We're back at the Neurodiversity Matters Conference. And in this segment, we are going to be spotlighting programs that SDE partners with or works on. And I'm very happy and proud to introduce Anna Zimbo, Rachel, and Shelley, who all work with the Miracle Project New England. And I'm going to turn it over to them and let them tell you a bit about their organization and open it up in case you guys have questions. So take it away. Great, thank you, Clay. So I just wanted to start first by thanking Spectrum Theater Ensemble for inviting us. We're really excited to be here and to get to talk a little bit about what we do at the Miracle Project. So I'm going to start off. I am Anna Zimbo, as Clay said. I'm the program director. And so I'm going to tell you just a little bit about who we are and then turn it over to my awesome movement specialist and music director, Rachel and Shelley, to share a little bit more about the fun stuff that we do. So the Miracle Project New England is modeled after the Miracle Project in Los Angeles, California, which was founded by Elaine Hall in the early 2000s. If anybody watching is familiar with Autism the Musical, they're the subjects of that HBO documentary that aired also in the early 2000s. So we're modeled after that program. We've been working here in the Providence, Rhode Island area since 2017. So we follow the methodology of the Miracle Project and sort of the general structure that they use for bringing both neurodivergent artists and individuals together with neurotypical teens and adults, neurotypical peers to create art. So we function with a reverse inclusion model where we create a space supported and that is supportive of people on the spectrum of neurodivergent individuals. And then we bring neurotypical peers into that environment through art. So as I mentioned, we've been working since 2017. We've had several week-long annual summer camp programs. And then this year in 2020, we were really excited to launch our first after-school program, which started in February of 2020. We have transitioned that fully online at this point in the current circumstances, and that's been going pretty well. But that's kind of us in a nutshell. So we are a performing and expressive arts program. We integrate theater, improvisation, movement, and music into our program. We produce a showcase at the end of every program that integrates original music that's been written with our autistic artists' choreography that's been generated by our specialists and inspired by our participants, and also stories and improvisation that come from the scene work and the things that we do during our programs. So overall, we focus on individual and group talents.  And we're also really focused on building relationships and that peer model of having a neurodiverse group of people creating art together. Before I turn it over, I just wanted to also mention that we can't do what we do alone. We partner with a lot of great organizations, including Spectrum Theater Ensemble. We also partner with our flagship program, The Miracle Project in Los Angeles. We partner with Brown University, which Rachel could talk a little bit more about too. We also partner with Bailey's Team, which is a wonderful fundraising organization in our area that supports lots of programming for people with autism. We partner with the Rhode Island Philharmonic, and like I said before, of course, Spectrum Theater. So right now, I'm going to turn it over to Shelly Katch, our music director, to talk a little bit about what she does. Hi, and thank you for having us here. The music that's part of The Miracle Project is focused on connection, the joy of creating, the joy of expressing ourselves musically, the joy of being able to create in the moment with others, and also the ability that music has to connect us and help us feel like we belong with others. And that's been an interesting challenge this after-school program as we have focused on how to help our group of participants, our students, all of them, feel connected and like they belong while we're on a Zoom platform. So generally, what we end up doing over the scope of the entire program is we have some fun musical warm-ups that we do so that we treat our bodies well in terms of warming up our voices the way that our movement people and in acting also warm up the body and warm up the mind. And then what I do is focus on creating songs together. There are a few songs that are part of The Miracle Project from Los Angeles that every person who's ever been part of the music, part of The Miracle Project knows and sings. There's a welcoming song and an ending song. So we have some pillars at the beginning and the end that everyone's familiar with. And then we play around with ideas that convey messages that we want to create. And we put those into musical forms. So everyone can contribute lyrics and we listen to the way that people say those lyrics and their voices and we help stretch those out into melodies. So the songs that we've done so far in the last couple of years have focused on having a voice and what that means in terms of a metaphor and being able to sing but also be heard. We have a song called Count Me In which is connected to like, there's no about us without us. It's about wanting to be heard and listen to and taken into account. This year we had a song about belonging that we belong together which helped us sing together and move together to help us connect over the Zoom platform.  We are creating in the moment and we're helping us connect through a range of musical expression. And I think next is Rachel. Hey, hi. Yeah, I'm Rachel Gallivan. And I just wanted to address something that Anna mentioned earlier in terms of partnerships. We have a wide range of wonderful partners and a little brief history. I teach a course with Julie Strandberg at Brown called Artists and Scientists as Partners which looks at the role of art on people with neurological disorders specifically Parkinson's and autism. And with the autism piece, it was way back in 2014 that we learned about and started this beautiful partnership with the Miracle Project and it has grown to what it is now what Anna described. So we are very proud and pleased to be able to have the Miracle Project as a site placement for our undergraduate students to really experience how art changes lives. And so I'm fortunate enough to be the movement person and I get to take in all the wonderful creativity of my collaborators, Anna and Shelly and bring in movement. And movement as we all know brings us certainly great physical benefits but I think almost more importantly in a neurodiverse population it allows us to bring some kind of emotional release and emotional self-regulation, self-expression and really a sense of heightened self-confidence. And we see that each week as we move through the music and drama and dancing. Shelly mentioned we have certain songs that are just a part of our weekly practice and so our campers, our actors also have certain warmups that they can rely on that they know they will start their weekly lesson with. And then we get to move on to something where they move with a little more individuality and they get to call out the kind of movement the kind of music they want to do and they get to do that individually. So here is a chance for them to kind of express themselves build that confidence and be that individual and really learn a pride through movement and through the physical nature kind of separated themselves from the thinking aspects. There's just moving and really feeling the joy of movement. And then we get to work on this wonderful piece usually after Shelly has created some incredible music for us to follow. And the fun part there is that we are creating as a community and as the movement director I am taking cues off of the actors and watching their movements, listening to the lyrics that perhaps they have co-created with Shelly. And together this becomes such a beautiful collaboration and a beautiful example of how music movement theater all of this builds community, builds our connection. So really the movement part goes from this warm-up that we start in the beginning of the class that prepares us for the later movement in community and sandwiched between that is this chance for them to be expressive and move in their own very specific and particular way. And I just feel quite blessed to be a part of this group through movement, theater, music, it just fills my soul and we get to see that each week. Even through Zoom we are feeling the love and the beauty and the power of art to heal us and to connect us. Absolutely, awesome, thank you, Rachel. That actually what you were just saying gave me a thought about how we have transitioned to Zoom in this virtual platform and one of the sort of happy surprises that we've found is how engaged everyone is. We were nervous at the start and I think even in-person classes sometimes those nerves come up, we're not sure who will walk through the door, where everyone will be at when they're coming into our space but we've been really pleasantly surprised with how engaged everyone has been, especially in the virtual medium.  So we're really lucky at the Miracle Project although we are not a therapeutic program, we are able to be supported by people with therapeutic backgrounds. So we have a phenomenal speech pathologist, we have a phenomenal occupational therapist who can help us as teachers, help our co-actors, our neurotypical peers come in and be the best kind of support and co-creators that we can be. So we've been really pleasantly surprised with how they've been able to support us in supporting our actors transitioning to this new medium. So I think that about wraps it up for us. I'll throw it back to Clay and thank you so much for having us. Awesome, thank you guys so much and we're excited to have you here this summer. I've known you all for a long time, you're great. So fantastic. So it's 1.52 right now. Our next session is logging on and we'll start at 2 p.m. But we have a little bit of a breather.


Hey guys, welcome back to more of the Pico CTF getting started to capture the flag and hacking cyber security competition stuff So we just finished up our first challenge our first capture flag challenge Internet kitties in the miscellaneous category. Let's move on. There's another 10-point challenge here So I'm again starting with some of the easy challenges starting with the the low-hanging fruit Because that point value is probably a good indicator of difficulty of how hard it is So if we're just getting started, let's try some of the the beginner-friendly stuff, right? I have questions about Pico. You can ask here. The access code is 3 1 3 3 7. So elite Nice. Let's take that copy that Hence looks like there's nothing here. Okay Ask here head over to this link. Oh wow, geez Looks like this is a Piazza a Free platform for instructors efficiently manage class questions and answers. Okay, so this looks like it's some kind of help or Kind of classroom looking like thing to Let's try that access code showing classes type it in and then we'll need our another email address Okay, let's get the get that 10-minute mail again going. That's a good easy way So we don't have to keep using real email addresses Send code cool looks like it values that I'll switch over to that tab As soon as my browser lets me thank you virtual machine. All right, cool And hopefully this won't take too too long for the email address to get it. I'll pause the video here Okay, it looks like it got it. I see this activate your account here We have an activation code it looks like there's a link to activate it and set our password So a lot of stuff. Oh boy. Jeez. Okay, John give it some information Set a dummy password. I don't really need any of this stuff. Oh geez guys. I don't Computer science anticipated completion November 2019 whatever this is all fake degrees fake stuff. I've read and accept sure Okay, I don't care guys. I just want to flag So when you get to play a capture-to-flag competition a lot of times will give you some means of support, right? That might be a slack channel that may be a discord channel that may be a IRC and any of those things will try and give you as the player means to ask for help that Like either solve like hey, I feel like this challenge isn't working the way it is. I don't know what kind of Vulnerability I'm looking for is there anything you can you can help me with etc. Let's see if we can find a Piazza Will this give us oh What is the flag for the Piazza file I cannot see this on the site and it would be nice to get points for it looks like This flag is submitted. Someone's responded Please look at the pinned posts. Okay So up on the top there we got notifications If anything pinned Yeah, pinned up top. Okay Welcome Looks like this one over here Welcome to the Piazza for Bica 2017. Okay, so this is an interesting platform for asking for help having support Etc in previous years we'll have an IRC channel where you can hang out cool That works just fine. If you've never used an IRC channel before let's go ahead and do that I'm gonna copy and paste this flag Submit it just so we actually have that points complete awesome Challenge solve your up 10 points and we can keep moving on but I want to showcase that IRC or internet relay chat. So if you've never heard of IRC before let's check that out on Google too Internet relay chat Wikipedia It's an application layer protocol that facilitates communication in the form of text Okay, so the things that I want you to take away from this is that it's a communication platform A means of doing so it's a protocol that is all plain text So you if you ever sniff On the wire or anything like that if you ever get a copy of some of this internet relay chat Messages, it's all plain text so you can search through them very very easily and that's gonna come in handy so if you wanted to you could go to this web chat and there's always gonna be a web platform for Actually integrating or interacting with IRC channels because they're all plain text protocols. It's pretty easy more of these freaking I Am not a robot things cool. Thanks. So once we're logged in you have some other Options for like forward slash join or forward slash help It's kind of command line oriented right just like we're used to typing on the keyboard stuff like that You can see all the users in the right-hand side And then there are any kinds of Conversations you can make but say hello or just sending a message in Pico CTF. So That channel that hashtag that you see that hashtag at Pico CTF because it's specific channel on FreeNode or the server FreeNode is the server for this internet relay chat or this IRC channel And that way you can ask for support and get support when you're playing a capture flag competition Let's leave that tap great since we've got the flag we can move on here But I did want to show you that because normally that's what you'll see you'll see an IRC channel You can interact with through web chat like Kiwi IRC or web IRC or those things that we you could find on Google or anywhere But maybe it's a slack channel. Maybe it's a discord server stuff like that You'll see them and that's where you can ask for help when you're playing these capture flag competitions So we're learning bit by bit Slowly, but surely again We're still getting into the building blocks and the foundation to move in some an elite cool cyber security hacking stuff And that's honestly how we've got to do it right because cyber security and computer science hacking is such a huge scene It's such a big industry. We've got to learn bit by bit So maybe exposure like this through a capture the flag competition is the right way to do it because it's got to happen Somehow so cool. We're ready to move on to the next challenge But before we do I got to give a shout out to my sponsors or the people that are willing to support me Spencer Clark, Cal Horowitz, Suzoka, Attila, Orgel off the Unrelenting Shore of Worlds, Bachelors here, blah, blah, blah They are not sponsors. That was totally the wrong word I would love sponsors though if you if you want to support me Hey, please send me an email talk to me leave a comment. I don't know But thank you guys so so much for supporting the channel donating some of your time donating some of your money It really really helps the channel thrive and gives me motivation to keep making more cool things One dollar a month will give you a shout out just like this in the video at the end of at the end of every video $5 a month or more will give you early access to the videos that I create ahead of time before I release them on YouTube and Maybe that's awesome because I tend to really record in bulk in mass and then I do a gradual release schedule on YouTube So if you want things right away, you don't want to wait. That's the way to do it Hey, if you did like this video, please press that like button Maybe leave me a comment Let me know what you think if you're willing to subscribe and if you really want to support me check me out on patreon We'll jump in the next challenge in the next video


Welcome to the last set news. My name is Rob and there's some pretty big things going on with Polygon And there's a reason why the price has been really just on a tear for the last week and really comes down to three reasons It comes down to a mainnet launch with ZK rollups partnerships and artificial intelligence What I'm talking about is there was a story just a little bit ago last week on Friday This is Polygon source 8% ahead of ZK EVM network update and since this was Friday things are moving so fast and crypto right now You can just see that in the top 10 the big winner so far is Polygon They're up 12% for the week and that beats out everybody that beats out dogecoin Ethereum definitely there Bitcoin everybody for just for the last week Of course, we are cherry picking that data, but it is true 12% over the last week And this is one of the reasons and what this came down to there was a tweet from Sandy He's the founder Polygon he said look just came out of a high-level mainnet launch committee can't keep farm can't keep calm folks We got a date for mainnet launch and it's soon and what this all comes down to is ZK proofs a zero knowledge proof You don't know it's a way of proving the truth of a statement without sharing the statements contents revealing How this true it was discovered which is interesting But I think there's an easier way to say it and thankfully on one of Polygon's blog posts That are very simply Polygon ZK EVM, which stands for a zero knowledge Ethereum virtual machine leverages the power of zero knowledge proofs to reduce transaction costs and greatly increase throughput transactions per second all while herding the security of Ethereum the ZK proof tech works by batching transactions into groups which are then related to the Ethereum network is a single bulk Transaction the gas fee for the single transaction is then split between all the participants involved Dramatically lowering fees now that's the real sharing economy and it got me thinking I was like well I mean is it that expensive for Polygon because as far as I remember it's pretty darn cheap and this is from Polygon scan Proof is proof of stake chain average gas price chart and it's all in way way And you can just see that the average and it'll go from the minimum gas price to the max Which is ridiculously high, but just take a look at the average here So October 27th the average gas was 196 way and then average gas price and one of the one of the big days was 351 and now we're hovering around You know 115 so you're probably asking yourself. Well, what does that translate to dollars great question? And the answer is not much and you can just see here quite a dollars I mean even at 250 it's fractions and fractions of a penny So when we we take a look at these stories about the things that are going on with Polygon and ZK Rollups and and the great things are doing I mean if you can reduce it even more so and make the TPS or the throughput even faster Well, so much the better so that's the first part of why the prices Having some upward action. Here's the next one. I found this highly entertaining Polygon has a new AI project will it rival chat GPT if you haven't used chat GPT yet. It's awesome I'll have I'll put a link in the description below you can ask it any question and just pretty much spits out the answer Not that it's always correct But more often than not it's pretty good. So this is the key points here Polygon is using a new AI tech called character GPT to generate intelligent avatars That will become NFTs on its blockchain the crypto is already partnered with a number of high-profile brands Again, that is the second part profile brands partnerships AI that could leverage this AI tech for NFT projects And now it's really all coming together and when I read this Just think to yourself Would you have thought about this six months or a year ago when we were talking about crypto and digital assets? Especially when we get to the whole Disney aspect on this one You probably didn't and I didn't see it either but it was the same thing on the internet No one can really see the things that were going on. We talked about this. There are things are gonna happen We have no amount of idea of where things are progressing. It's just that we're going in the right direction So what we're talking about here is what Polygon has in mind is the launch of AI-powered avatars using a new tech called character GPT once these avatars that avatars have been created they can be Transformed into NFTs that live on the Polygon blockchain You type in a text prompt for what kind of avatar you want to interact with online and the AI system will create an avatar for you on the fly Here's a here's a scenario. You could type in an old man as a grizzled prospector who wants to retire or for me I would just write in like a Machine or a bot in the same vein as What Tony Stark had with his artificial intelligence Jarvis I that for me would be pretty cool The AI immediately creates a digital representation of a man from the 1850s dressed in a Western gear for this example And this avatar would then be able to answer your questions from the perspective of A California prospector looking to retire. So just think about that. Wouldn't that be interesting if you could say give me the perspective of I don't know a financial advisor from BlackRock about what he would Expect to do with crypto and digital assets. That's my avatar. I'd love to I'd love to see that myself So then moving on the tech could completely reshape the NFT market phase one for NFTs was digital art Which I thought was kind of goofy but whatever phase two was the rise of the utility NFT I thought this was better which buyers received some added value from the NFT such as entry to an online VIP club And then phase three could be the introduction of the AI powered avatar They believe it's intelligent avatar to answer any question from any source from a particular perspective And I think that's gonna be pretty interesting moving forward, but it gets better So polygon is interesting because the crypto is already partnered with Starbucks Nike and also with Walt Disney And then this is what the article said it's pretty good Imagine what Disney could do with this type of AI tech the types of immersive experience You could create for families new digital experiences It could great for people around the world imagine if your you know daughter wants to talk to a little mermaid or you know if your son wants to talk to like a main character as far as Mickey Mouse or one of the lions and One of the most moves I forget right now But I mean you can do whatever you want to and you create anything and that I think is where things Really get crazy, but it's interesting because now you're gonna leverage real utility on the blockchain Which is polygon and the company behind character GPT Aletheia AI has the backing of Mark Cuban and Mark Cuban is also Best in the polygon so again and and just as a side note Mark was always heart harping on the fact that crypto will explode if you have a real use case Utility of an app and I think that is one of those trends that we're seeing and then before we move on To the last piece. I will just say that For me like for using AI and stuff like that like there is a great app Let me just let me just pull up. I'm gonna pull up the app on my phone And I see what we're talking about. All right, so on my phone was up There's this app called genie on the lower left hand corner what this does this uses chat GPT and you can ask it Ask it any question and it'll pretty much gets back to you So like for me when I see this is like if you have an avatar or whatever you want to create again It's a little bit different But you can just start talking this thing and ask it any question that you want to and what's great about this You don't have to poke around for all different websites and and hunt through a bunch of things It's just a time saver and it really can do good things like you can answer any question like there's it like this So I'll hear me here. I'll I'll tap on the little microphone icon What's the best way to take profits in a dollar cost average? investing scenario So then wallah there it goes That's what they promised a dollar cost average use a percentage based trailing stop loss order The strategy allows you to gradually sell off portions of your portfolios It begins to increase in value while protecting yourself from big loss in the event of an unforeseen market drop very smart This strategy can be adjusted as needed in an ideal way to take profits over time Then you can just go even further and go What kind of percentages should I take profits and at what point question mark and there it goes When taking profits from percentage based trailing stop loss orders recommend take profits between two to five percent and it goes out With some other stuff. So I will link This app in the description below. It's very simple. It's just called genie and There's no affiliation no partnership with it Just what I use every single day when I'm asking questions and then lastly and this is on a biased level I will say and that is that's one of the reasons that I Look at polygon. It's because polygon is making big steps and always pay attention to The projects that are building in the bear because they will crush it in the bull and this is one of those things again So Kishi Just put out a little press release that they are working directly with polygon not building on top of polygon Because what that's what they've already done But again, so Kishi as you may remember I am invested into it So I am very biased when I talk about these things. So be aware Don't go running out and go. I got a bunch against Kishi because Rob talked about it. That's not saying here but with again, so they have a partnership right now and they are they are having polygon work within the Polygon to have them build on Genso Kishi and it's a real partnership Not just for against a key she building a polygon But the reverse way and this is one of my degen plays I've got a second channel called Dan degen and one of the reasons why I like this This game was because it was already on Google and App Store and Nintendo switch and PlayStation Then it moved over to to web 3. I thought it was a slam dunk and All the different Dan degen projects You can find those on the spreadsheet as a link in the description and you can find the link to the video I did this I did this video all the way back in 2005 December 15,000 21 over a year ago and We got in at point zero one five and then the all-time how was a dollar sixty two and For these for all the ones that I get invested into you have to understand that I don't get a bunch of tokens I have to actually purchase them get into them. There is a cliff I have to wait like even like sweat coin. I still haven't hit my cliff I'm still still waiting because I got in and it was at least a year to wait But you can see that against the key. She is so far been the best one We've done even today at the price today at 19 cents and we're still up, you know, 12x. That's pretty good But all the rest of them like ever done I mean it did pretty well, but now it's like half of that and then fame was my our worst one by far and Then sweat coin is just kind of treading water still. I think it's gonna do pretty well But again, I think that's a primary reason for my polygons doing so well because it keeps building and Partnering up with all these different projects. So look that is it for today I feel like today's video give it a thumbs up consider subscribing everything we talk about is time sensitive and right now There are so many things going on in the crypto and digital asset space I would highly encourage you to subscribe and watch the videos, but that's it So look, thanks for stopping by do appreciate you and I'll see you on the next one


You wanted to do your part and all that stuff and the offense was able to pick it up and kind of lead you guys. Yeah, I mean it was a beautiful thing. You know, the running game was going, the passing game was going. Honestly, I feel like they was fouling on all cylinders. So it's just a great thing to see. Like I said, as a defense, we knew going into this week, we was like, hey man, we got to do our part. No matter what the offense do, and that's kind of what I always be preaching. No matter what the offense is doing, we have to do our part. So it was one of those days when we did our part in the game, we said we win the game. That last play? I didn't. I didn't know that the ball was out because I didn't even have an angle from it. But I seen that we came and pick up with the ball. And I knew that 28 didn't cross the goal line. That's what I knew for sure. So I was like, I kind of went to the refs like, hey, he ain't crossed the goal line. If the ball is out, you have to get the ball. So I was just glad that they actually reviewed it because I felt like he called it like he was down on the field at first. And they was kind of conversing, they didn't even know what was going on. So it was a great thing. I'm happy. Yeah, something that we kind of put in this week with a look that we felt like we can get in the first fourth down. No coach called it on the sideline and said, we're going to run it.  And I end up calling it, catching the ball. You know, I can joke a little bit, but Kern could have given me a little bit better pass, you know what I'm saying? So I can turn it up and just go. But when I caught the ball, I was just trying to make sure that I looked straight to the sideline and make sure I had the first down. I was able to get it. I wanted to break that tackle, but you know, I got the first down, so it was good. Maybe you give them pointers on how to throw the football, right? Yeah, you know what I'm saying? But like I said, the play worked. So the play worked just how we draw it up.  But if I could have ran a touchdown, it would have been good. But hey, like I said, it ended up working how we drew it up. You know, you would hope it would have sparked the rest of the season. Because like I said, it was a really emotional win. It took a real deal team effort. The offense rolling, defense was made some plays towards the end of the game. It's always stuff we can fix. But at the end of the day, it's a very encouraging win. We're going to come in this whole week and work just as hard as we did last week. And like I said, hopefully we can get this thing on the road.


So, we start with our example now for development of control. So, we will develop some of these concepts here mainly based on you know differential equation kind of analysis and that discussion and also with the through this discussion we will develop some of the interesting concepts what how do we kind of see what can be considered as a control input. So, let us begin with these dynamics of pendulum. So, for this system if you see the model that we have done already in previous classes and previous courses you all are know very much familiar with this model ok. So, that helps because you already have some kind of understanding of this pendulum.  I have a pendulum here for you to watch also. So, you can see the motion ok. So, you all know about this, but the some of these kind of control aspects we can see through like you know some kind of examples we will do here ok. Experiments. So, this pendulum you can get a model if you have not done already by doing freeway diagram or kinematic kinematic analysis of you know circular motion of a point mass. So, I am not getting into the details there ok. So, you can see this model of a pendulum here ok. So, this model is giving you this full nonlinear form of a equation considering theta which is the angle of the pendulum here to be more than like you know small angle approximation. So, with this model you can see that this has a harmonic kind of a behavior and that too without damping, but if you see the actual pendulum this you know the oscillations damped down ok. If I keep on holding and like you know letting it go then the oscillations slowly damped down ok. They come down to 0. There is some kind of a damping that is existing. So, we will consider that damping into the system and you know then that will be more appropriate kind of a representation of the system. So, so this what is missing here is this damping and we incorporate this damping term into the system at c theta dot term and then convert those forms of equation into again like you know the standard form. So, see we always seek to get the system in the standard form of second order system which you remember s square plus 2 zeta omega ns plus omega n square ok that is a term for the standard form of a you know second order transfer function 1 over this omega n square over this kind of a term. So, we seek that kind of a form to have for the equation also and that form in the equation turns out to be where s square term does not have anything multiplying it. So, whatever is multiplying this theta double dot we divide by that entire other parts of the equation and then like you know see the see these terms accordingly. So, 2 zeta omega n multiplying theta dot ok this term will be 2 zeta omega n multiplying theta will be now we do not have theta we have sin theta term here, but for the low theta approximation this sin theta is equal to theta this is a term this will be like a omega n square kind of a term ok. So, that is how like you know we try to seek in wherever possible you know many systems this may not be possible to seek some kind of a normalized form of the equations. So, so that we can see through some of the details for example, if zeta is found to be some value here we know that this is this pendulum system is some underactuated system with this zeta value and that speaks about its nature. So, this is about dynamics now one can kind of do some experiments to see what is a how do we get damping factor zeta. So, you can think about like ok if I time out ok how much time it takes to get amplitude to some half of its original value something of that sort then one can odd number of oscillations based kind of a counting of change of amplitude that kind of a thing will give you a bi logarithmic decrement what is this damping factor zeta. So, this can be these kind of things can be carried out by studying the dynamics of the system and carrying out appropriate experiments to get the parameters. Now the this is mainly again so, this is like a dynamics without any input to the system and then now if you have a input to the system what you will consider as input. So, if you think ok I want to apply some kind of a torque on the bob or kind of a force on the bob. So, in which direction you can apply the force you can apply that needs to be in that in the direction of theta to have like know it represented up here or if you apply something else what will show up here that those kind of things we need to discuss and figure out. If you see this is also like you know similar to the system that you had with the hard disk drive arm. In that arm we had a case where the head moves on the disk in a horizontal fashion it moves on the disk, but one can see if that disk is not there only head is there and at the place of the head we have a big mass attached. Then like in the vertical plane this will act as a pendulum kind of a system and at the back side you had the coil and the magnet that is actuator which is giving some torque on this system that is a kind of a pendulum system that we can have ok. So, that is a one of the actuators possible in the direction of theta. So, but that is little bit cumbersome to create such system. So, or based on like you know your actual practical requirements there may be some other kind of a consideration that may be coming in place for input. So, we consider here that pendulum is mounted on a cart and the end of the pendulum is movable by the cart ok. So, if you have this pendulum it is mounted on the cart means like you know this point where it is hinged that point is kind of like you know is moving by the cart ok. The cart is able to move that point ok. So, if it is initially in motion now I can like you know affect the motion by actually the moving the top point ok. So, that is how my input I am giving to the pendulum ok. So, I am not really applying any force here, but I am just kind of moving the top point to give the input to the pendulum ok that is a kind of idea. So, we can consider these kind of inputs to the system and when this input is considered here like you know the hinged point motion by putting this hinged point on the cart and then the say you can say I apply force to the cart or I can say ok I am directly applying this displacement to the hinge of the pendulum. So, these are like you know different ways I can define my control input. So, although I have a cart here and I can apply some force on that cart I may choose to define you know that control be let the control be input x here or input x double dot here ok. So, this choice of what I define to be a control input to my system has somewhat flexibility that I can have. So, this is very important concept here ok. So, I can say for the system say there is a cart actually here for the system, but I am ignoring the cart dynamics and I am saying that I am applying this control input in such a way that somehow I am able to maintain whatever desired position for the cart to be x and I apply that as a control input to my pendulum system ok. So, as you will see later for such a definition there are some good advantages that happen here. So, you can see what those advantages are by saying putting these equations together here. So, this equation now with this input here I will not get into the details of this how this has come, but like you can check out by using the branch formulation or using your simple Newtonian approach you can simply see these terms. So, you can see here for the same system which was there previously of course, there was a damping here that we can add anyway for that this x double dot term appears here ok. So, this x double dot upon L entire of this term is some input which is in the direction of the generalized coordinate theta because this is a theta equation theta generalized coordinate equation ok. So, by doing this kind of a input to my system I get a term for my control which is directly in the direction of theta as if I am giving a torque on this string. So, normally giving this torque on the string is not possible, but because I am like now able to apply this a desired acceleration it is as if I am giving a torque to the string in the direction of theta ok. And then this helps us to develop a nice controller snator. So, with the with this term considered as acceleration is considered to be an input to the system and further the damping is considered in the system you get now this kind of a equation ok. So, this is now a simple spring mass system you can see the second order spring mass system with some kind of a force external force applied on this system. And with this force now I see I can define a control problem that developed this u in such a way that this theta goes to 0 or initially oscillating kind of a pendulum theta goes to 0 in some you know given amount of time ok. Normally the pendulum is going to take a lot of time lot of oscillations it will carry out and after some oscillations it will stop ok anyway. And I want to kind of go to this final point in a in a very short amount of time and how do I carry out that job ok. So, where is this kind of utility of such systems just one things comes to my mind you know where we have this overhead cranes ok. They are carrying some big amount of chunk of mass from one place to other place which is hanging out of the string and there is a cart which is on the top of the overhead crane you might have seen this construction cranes they have this. So, you do not want this mass which is like you know with the long string attached and it can by the way it can kind of oscillate it can have some kind of a motion possible. We do not want that motion to happen its oscillation should be damped down ok otherwise it may be dangerous for the for the personal or like you know life so, so in that case this control could be kind of very useful. So, what we do here is now for such a pendulum kind of a system we demand that ok we do not want any oscillation or even there are any oscillation they should get damped down very fast. So, how do we do that now so, how do we so, so this is our control and control problem defined and suppose we find such a input ok you then how do we drive the cart such that this u is applied to pendulum ok that means like you know we need to satisfy this equation. So, u is there and then x desired now this is not x here x desired we can make it as x desired here. So, my x desired double dot should be that u and I integrate this u twice with scaling factor L then I will be getting like know the actually the x desired as a function of time trajectory ok and that x desired if I go along the trajectory x desired then I am guaranteed to apply this u that is that was desired here. So, u itself if you see will be a function of time as we propose some kind of a control of which will be function of this theta which is in turn that the function of time and then you integrate that twice to get x and that x is what I will say my hinge of the pendulum will be moved along that x that is how I can plan my whole control implementation ok. So, from control design we will get u and we would like to like our x double dot to match these. So, we consider trajectory to have the same x double dot so this x t double dot then we find x t double dot from that x t double dot is equal to something by twice integration of u I have missing the scaling factors here can put those scaling factors ok. So, now we can like know control force f suppose there is a card pendulum card also is there in addition then I can kind of use this force on the card to be f by some means we can apply that force by say pda, pda, pdc controller to track the trajectory which is coming out of this equation ok. That kind of idea can be possible for implementation there are quite a bit of advantages of this kind of implementation which we will not discuss for now here, but later on maybe you know if you are interested I will kind of show very very good advantages of such a implementation rather than considering directly this force to be my input and considering my force applied on the card and card in turn is having a pendulum ok. So, there is a card here and the force f is on the card and card in turn is carrying this pendulum along. So, that is not a very great you know practically good strategy to implement because there will be a friction between the card and its wheels and other places ok it is sliding in part ok. So, this is a kind of a way we implement is we propose to do this kind of a control ok. So, this is a discussion about why f is not directly designed and implemented because of this friction that is there in the systems in eBay ok. So, you can do some kind of equations development of you know what will happen in the presence of friction how I consider you know control with friction in the case of card pendulum system and then like no things will unfold little bit what I am saying here. The friction is major cutlet to you know faithfully implement f that will make my control better ok. I can tell you something physically here ok. See if the friction had not been there then any pendulum motion here ok if the pendulum motion happens here and if there is a card without friction that is there some mass is there of course. Then the card will respond to the motion of this pendulum as a reaction forces the acting on the card at this point will start moving the card here and there and imagine the worst possible case when the friction is so high that it cannot move at all. Then even if you know the motion happens here the card is not moving so if the card is not moving at all then like no your feedback is somehow lost there like no this so you cannot affect pendulum or pendulum is not able to affect the motion of the card in some way ok. And that is a big hurdle for you know getting any kind of a feedback based on this force implemented faithfully ok. That much I can tell you as a physics part but to really get to this you will need to write the equations in the form of this pendulum card total system so that will be 2 degree of freedom system with the card degree of freedom and the pendulum degree of freedom theta and the force considered as a input so single input but 2 output kind of a system will be there and with the approach that we are discussing here right now those all complications of under actuation will be gone here if I consider u to be this kind of input and I implement this u by using the using this double integration and some say some kind of a PRD controller. Now there are some kind of a mathematical questions that one may pose that ok how do you guarantee that we will be able to track this xt trajectory very well by using some PRD controller with those kind of you know more kind of a finer mathematical aspects would be there which we are not I mean we say that ok we are PRD controller is fast enough to do that control so that it is able to kind of follow the desired trajectory in a in a very appropriate sense ok. So this is what is this discussion about this force here ok so we come back to this system now in this standard form it looks like this and then you can say write a transfer function of it and then see the open loop poles are here then now we can propose some controller to move these poles around anything like that ok so that those all all kind of things can be done now so we propose a PD control or P controller all these kind of different controllers can be done some some discussion that you can find here it is pretty simple to follow through. So the control problem is defined to have some say we just want to settle down faster than what it is its natural damping would allow it to do so we may propose like the derivative control or like no complete proportional plus derivative kind of a control to achieve the task here we have two parameters available for us to tune and so we are now seeing entire thing all this development only in the differential equation kind of a domain ok. So you see we are we have chosen to do this it is up to you to kind of consider that ok if you want to kind of do it on the the plas domain you can do that and see ok now for the new pole locations what should be this kd and kp again so that I can move my poles to appropriate location based on you know choice of kd and kp. So this is the final form of the equation in the differential equation domain see this is error equation because theta itself is our error because we do not want theta we want theta to get damped out so theta should be desired to be 0 then like the error equation is same as the equation in theta. And with this we can now plan like you know what we want how fast we want to be chosen omega new based on that and so this is our omega new here omega new square and this is our new two zeta omega n complete term. So we have some kind of a choice in both the cases to affect and we can choose these gains to kind of have whatever desired you know omega new and zeta new and based on that our system response will evolve. So you can use the standard system second order system specifications to design these values and like your problem will be solved here ok. And once we get this zeta then your u I mean zeta and this your kp and kd are sized appropriately then this is final u and then you can get this no this is sort of with the theta d is equal to some value but so you get the u in this in this form here and then implement it by like no taking double integration of this and matching it to mapping it to x desired and now x desired is like my motion of my hand here ok. So if you see here let me change this view so I have this pendulum mob here you can see I will use a shorter length. So with this you know if it is initially in motion and I want to stop this motion I need to kind of move zeta like you know it stops immediately otherwise it will continue a lot of oscillations to move. I move this my hand in such a way that you know it gets to the stop condition very fast. So I am doing something in my head to do that you can also try out and you will be able to also do. So whatever is happening in my head in some way is getting captured in the in the mathematics that you see on the slides ok. So I can kind of like move this quickly to do the job. So I will not be able to do as quickly as for example these equations can do for a for a tuned gains ok. So that is a beauty of like you know using the mathematics to do some kind of a nice way developing control over such a kind of a phenomena ok in one of the examples ok. There are many such examples one can kind of start developing and do that and this has immediate practical applications in overhead grains kind of a you know cart that moves in overhead grains ok. So let us move on from here to the other example. So you can get to more detestive theta desired was not 0 then like we have some difficulties here ok. So now one can see this whole in the in the Laplace domain how things will be represented and with this one can kind of see this is a feedback some kind of a unity feedback here with KPKDS here. Then you can as we have discussed you know one can do root locus analysis of such a system ok and that also kind of helps to kind of tune the gains or see the things in the different kind of a approach ok. So this is another example about the simple PD control for like regulation purpose. So this is much simpler form which we have already seen. So it is just again PD control applied here and you can see this in the error form here ok. So the idea here if you see from this error dynamics what happens is that there is a virtual spring as if virtual spring is attached to this mass which will have equilibrium at the desired reference position ok that is what is. So one can interpret this control as if we are actually attaching some virtual springs and damper to the system ok to get some kind of a physical insight into ok. So this is the same kind of a discussion a little bit in the domain of this example. Now when we introduce this integral part ok whenever we have the steady state error not going to zero that time we introduce this integral part. So you have seen in your simulation of the simple you know single link attached to motor kind of a system that when you try to oscillate this pendulum it does not kind of come to the vertical position because of the friction ok. The friction is what is not allowing it to settle into desired position or in the vertical position ok. So this friction is causing some kind of a steady state error in the system ok and even if you if this system is to move in the horizontal plane ok the same things would happen as you know would happen for this mass which is in the horizontal plane without the spring and damper case ok. So these are anyway the spring and damper are actually the virtual springs and damper that are put in the system ok. So if in the presence of this virtual dampers in the system one can see that if I keep this mass oscillating it will stop at some point which is not really matching this r completely in the case when there is a friction ok. So friction in the system will not allow it to reach r it will have some finite error that will be there in the system that is a kind of a point. So in the case of that kind of a error then you introduce this integral control action ok and the system has this steady state error ok. You see the response to the PD controller and you see that there is some kind of a steady state error then you introduce the integral control action ok. So we will talk about this integral control action part I think this main kind of I think or maybe we can give you summary of like you know when to use these different kind of a control actions in general in the system. So this will be good to kind of know and then as we have seen like we use this make use of this standard first and second order system responses which we have seen already I am just flashing the same slides here actually. So these are the standard first and second order system responses with like you know this is this information should be handy to us for application in several cases and then we will have this formulae for the second order system behavior formulae ok for you know maximum overshoot settling time this should be also handy to you ok. So that as we saw in the pendulum problem for example we can use them to to set up like you know these omega n and zeta to have a desired value or when you do the pole placement problem the two dominant poles which we are placing close to the imaginary axis they can have some values taken by this thing ok. So these are the typical for you know parameters that that we define ok. So this is this is a formula this given in the slides you can just go through them to make use of them in in the pole placement problem or in simple second order system problem ok. These are some of the general guidelines that one should be aware about that proportional control action will typically make the response faster increase the overshoot and increase the settling time ok. So if you use this k p gain higher and higher it amounts to increasing the settling time also ok all the response is faster it will settle in time also increases. So for the settling time to decrease we will use the k d gain ok. This derivative action decreases the overshoot and decreases also the settling time and but the response is little bit sluggish ok. So the combination of k p and k d would give you some kind of a you know nice response possibility and integral control action again it makes a response faster it actually introduces some zero close to the origin in the in the controller transfer function ok not really for the system thing but controller transfer function will have a zero ok. So it may amount to have a zero in the system also we but we do not know it prepare for the kind of a form of a system in a closed loop. Ok so it makes the response faster increases the overshoot and settling time but it takes care of the steady state error ok. So imagine if you have a steady state error like this here and integral control action is there derivative because theta dot is zero derivative control action is stopped proportional control action this theta is constant so proportional control action will keep still keep going but it is not changing ok k p times this error will be a fixed kind of a amount of input that will be going into system but that input is doing nothing to the system because say for friction for example like you know even if apply a force the system is not moving that kind of a case will happen here. So in this case the integral control action will help because if you put a integral control action if you see from this point just like the integral is starting starting from this point you can see the integral control action will be the area under this you know error curve or in between these two lines will be the integral control action that area key will keep on building up at some point like now it will exceed the friction value and depend upon gain that you have used and this error will be taken care of. So there is a chance that with this integral control action in the presence of friction this this build up happens so quickly that with sudden application of that force the system moves on the other side ok and again there this integral control action will have to come in picture to move it further back and there are there are certain zones for this process that system will keep on hunting between the two values rather than settling into some final value ok. So one and one needs to be careful about choice of the integral gain to prevent this hunting ok. So how that is to be avoided and those kind of things are like more kind of a mathematics can be worked out for for such a kind of a case ok by considering say your friction model or there are many other techniques also available. So you use this friction model and use something called describing function method to come to what is the frequency that is that your system will be keep hunting in both. So that these are not the matters of our discussion here but one can use these methods for such phenomena if at all you find somewhere in your future application of control this thing is happening ok. So this integral control action can have a possibility of system getting into hunting ok. And how do you tune this PID gains typically is given in this procedure called Ziegler-Nicholas procedure it just a matter of some kind of a steps that you follow you can see these more different details at this there is no point in getting into and explaining those steps I mean it is a simple information you just kind of follow the steps and your gains will be tuned ok. So you do look at this for practical tuning of this it is based on only like you know the experimental system is ready and I am now going to tune the gains or your simulation system is ready and I am going to tune the gains this is a way you can tune the gains you can try it out on some of the systems that we are discussing as a part of assignment in the class ok. So this is I think we will stop here for this discussion and this implementation aspects we have already covered some of them and there are some more issues listed here sampling time we have seen already then effect on system due to sampling we are here to see and filters these are all related to like your sampling and then speed of computation or how much is a computation that we need to do that is also important consideration that we should finish computation of control within the sampling time and speed of various interfaces also is a matter of things action that has to be completed within the sampling time ok. And so these are many like some of the aspects we have seen we have not so but you should have this list you know to see or check or put like a check mark ok you have taken this aspect into consideration this as this is a kind of a checklist you can do for you know controller implementation we have considered all these aspects are not you can check that ok. So maybe we will stop here for now.