Oliver M. Takuji's life was honored with the posthumous release of his music on YouTube. On the 69th birthday of the late jazz icon and legendary musician Oliver Takum Takuji, the world will finally get to enjoy his hits on streaming platform YouTube. After the Zimbabwean musicians passing in 2019 in Harare after a long battle with Diabetes Melodis, the star will have all his best hits uploaded to YouTube for his fans to enjoy. With his career spanning more than 40 years, the cultural icons bops can be enjoyed on the streaming platform by all his fans. Speaking on his birthday in a statement to F5 News, Gallo marketing manager Caroline Morave said they would be launching his official YouTube channel with the hit song Tatiye. As a company, we're honored to be working on the legacy of Oliver M. Takuji's music. We are excited for the upcoming music project to be released in a few weeks. At Gallo, we believe it is important to keep his legacy alive. Oliver began performing in 1977 when he joined Wagon Wheels, a band that also featured Thomas Maff Fumo. Their single Jandi Mamatero went gold and took his first album Followed, which was also a major success. Takuji is also a contributor to Mahoobi, Southern Africa's super gruff. Oliver has collaborated with a number of local and foreign musicians and was instrumental in developing young talent through his Pakare P-A-Y-E Art Center. The star is known for hit songs such as Nirya, Tatiye, Chairi Nani, Hajveriv, and Wasikara, just to name a few. Oliver released his 67th album 10 months before his passing and was concerned about spreading the message that people needed to love one another in these hard times.


Good evening. I'm Gene Bergman. I'm City Councilor for Ward 2 here in Burlington, and this is the Burlington Progressive Show. And I want to thank you again for coming and watching. We've been doing this now for about seven, eight months, and the purpose of this is not only to talk about what Burlington Progressives are doing, but also to integrate the work that we're doing into the work that is happening out in the street, in the community. My theory of change is that government is a piece, but it is not the only or maybe even the primary piece. The most important thing is when we've got an active and involved citizenry that works independently and also with elected officials to get things done. And I'm really pleased to have had people for police accountability to talk about the ballot item on police oversight, to have Representative Kate Logan and City Councilor Joe McNeill to talk about houselessness, the houselessness crisis in the city and the state. We've had the Progressive Caucus here to just talk about general city affairs. I've been really pleased to have Public Assess Institute talk about public progressive taxation in terms of municipal taxes. And the last show that we had was with UVMMC's support staff, workers who were engaged in a contract struggle. I'm very happy that we were part of the struggle to get them justice. And tonight I am really excited to be talking with Jim Dumont and Nick Parasympiary. Excuse me, Nick, for having just botched that to talk. The title of the show is In the Shadow of McNeill, Thermal Energy Networks and Other Alternatives to Decarbonize. We do this for one very basic reason.  And for ourselves and our elders not only our grandkids are three and two and one year olds, but their babies. We got to do everything that we can to stop that. And on a specific basis, and this is where it's in the title, In the Shadow of McNeill, we are burning a lot of biomass down at McNeill. Nick will talk about the carbon impact of that. And there are proposals to have about a 45 to 50 million dollar project to pipe steam up to UVMMC. And we'll get to talking about that. But I want to start with you, Jim. You're an attorney, been involved in environmental activism for decades. And why don't you just sort of talk to us about what you're doing and about it in relationship to these big climate change issues. And then we'll try to segue into the real subject of this, which is thermal energy networks. Sure. Thanks, Gene. As Gene said, I've been working on environmental issues for most of my life. And about a year ago, I learned from Debbie New, who is a South Burlington resident, about thermal energy networks. Thermal energy networks are an incredible alternative to what we're doing now. And they're in use all around the country and in other parts of the world. It's a proven technology that we need to have here in Vermont. Thermal energy networks basically means using geothermal boroughs and capturing waste heat from other activities could be waste heat from a hockey rink, waste heat from supermarket refrigerators. So maybe, Jim, while you're going over this, we can get this slide put up on the screen so people can, there you go. This is a PowerPoint that Jared Rodriguez, who you might want to explain who he is, has put together. And I know that I got this from you. So this sort of begins to explain that. And we can go back, we put that on there, and then maybe we'll switch back in. Sure. Go ahead. Go deeper into it a page or two. So we'll talk somewhere about thermal energy networks. This is all about thermal energy networks. So you tell me, okay, let's just stop there and let's get into it. Basically, thermal energy networks use water, not gas. They use water at about 55 degrees. That's piped underground between buildings, between geothermal bore holes, and it's used to provide heating and cooling. And it uses ground sourced heat pumps instead of air sourced heat pumps. So the ground sourced heat pumps are about five times more efficient than air sourced heat pumps. So when you heat your home with a ground sourced heat pump, you use about a fifth of the electricity that you use when you're heating your home with air sourced heat pumps. And the ground source is what? Is water that is circulated among buildings in the community underground, year round, and it stays, you know, 52 degrees, 55 degrees, summer and winter. So it's pretty easy to understand that when you're, instead of using an air conditioner or an air sourced heat pump, which is exchanging heat or coolness with the atmosphere, you're exchanging heat or coolness with water, that's 52 degrees. So when it may be 20 below outside in a Burlington winter, but that water is still going to be about 52 degrees. So what you're starting with is much warmer, and also the physics of exchanging heat with a liquid are much better than the physics of exchanging heat with a gas. And so, and the reverse works in the summer. You can use these for air conditioning and cooling homes, and it's much more efficient than an air conditioner. It uses much less electricity than an air conditioner. So this is such, it saves so much energy, and it's so reliable, and it's so safe because it's water that it's spreading all across the country. Last year, it's about a year and a half ago, a bipartisan effort in the state of New York led to a passage of a statute that the governor signed promptly into law that requires every electric utility and every gas utility in Vermont. In New York. I'm sorry, in Vermont. I'm sorry, in New York, to start working as the thermal energy, have at least one pilot thermal energy network. And it was such a bipartisan effort that the bill passed the New York State Senate unanimously. So Senate districts in upstate New York, which went overwhelmingly for Trump, their representatives voted for this. So let's, Jordan, if we can get this slide, I think it is page three up here. And it talks about here, the steps to resource efficient decarbonization include, in other words, the steps that we're going to do this include. And the first thing that it's got is maximize efficiency in energy savings. Perhaps you could just sort of chat about that. And if you need to see something closer for our young eyes, here it is over here on the computer. So this PowerPoint was prepared by Jared Rodriguez, who's an engineer, who's an expert in building decarbonization. He's based in New York, and he was instrumental in passing the New York statute that the New York Senate passed unanimously and the governor then signed. And so he's prepared this. And what he points out is the first thing you need to do is take the low hanging fruit, which is make sure your buildings are as insulated as possible and as efficient as possible. That's the lowest hanging fruit. And then once you've done that, the next low hanging fruit is thermal energy networks. So, I mean, that really does require us to be looking at what we have currently and doing that deep dive for the energy efficiency that what our existing buildings are doing and then just investing in them. Maybe it is for bigger commercial places and we'll get into UVMMC, but they have an old campus. It may be that retiring certain facilities or really doing major substantial renovations. Right. So you mentioned the word campus and what Mr. Rodriguez can point out and others who are experts in this, and I'm not. I'm just acting as a citizen. The experts will point out that this is really easy to do on campuses because it's being done on college campuses across the country. And with the college campus, you have heating and cooling. You can capture waste heat from one kind of building and use it to heat another kind of building. And the one that I know the most about is Colorado Mesa University, where they've been doing this for several years and they've saved millions and millions of dollars in heating and cooling. And that's a place where it gets cold in the winter and hot in the summer, like Vermont, and they've saved so much money on energy. They've reduced tuition. It's extraordinary what this technology holds for us. I think we have a slide about it later in this. Talk about the waste heat recovery aspect of this. Sure. So it could be a sewage treatment plant. There's a special technology that harvest the heat from sewage treatment plants. So not necessarily just the methane or whatever. I guess it would be methane that's done, but this is something else. It's completely separate from that. You used closed loop piping so that there's no contact between the sewage and the water that is circulated through buildings and homes. The pipes are adjacent. The pipe, the technology extracts the heat from the sewage, but there's no connection between the water of the piping and the sewage. And you harvest that tremendous amount of heat that right now is largely being pumped out into Lake Champlain and the Winooski River in the case of Burlington. That's all waste heat. We're just pouring into the environment. You collect that heat in the pipes and then you distribute it to homes and businesses, in this case in Burlington. So it can be from sewage treatment plants, which has been doing, being done elsewhere. It can be from the refrigerator units at a grocery store, which right now they dump enormous amounts of waste heat into the atmosphere. Why? We can capture that and use it. Part of this technology is geothermal boreholes, but it's a mistake to think of this as just geothermal boreholes. It's part of a system that uses waste heat and the boreholes. And if you have lots of waste heat, you can actually store it in the boreholes, in the rocks or earth that surround the boreholes. Instead of having to create a battery, for example, or in having this huge bank of batteries which has its own issues. Right. And since the boreholes act as a battery for the waste heat and you're not converting heat to electricity and then back into heat, it's still heat and you use it when you need it. So we've got a waste treatment plant in Burlington that's on the central waterfront right next to Perkins Pier. And the closest community that is there is the King Street neighborhood, which is actually subject to serious environmental racism as a result of the way that we've constructed our highway system. And that is the fight around the Champlain, so-called Champlain Parkway, that hopefully we will finish by having a railroad enterprise project that will not dump all the traffic into the neighborhood. Very important environmental justice piece. But is that something that you think, you know, is that close enough? So if Mr. Rodriguez were here, he would say you need an engineer to actually look at what's on the ground, what's underground, what the heat sources are, and then give you an engineering report on what's feasible and what the cost would be. So every one of these projects will need an engineer to do the planning. But having said that, the experience around the country is it's very successful, low cost, reliable, and safe. Well, let's try to find some examples. You were talking about Mesa, so we're just gonna and here Jordan, there's this one right here. It's just an example, is that right? Yes. So what is that showing? Well, this is an example that Mr. Rodriguez uses to show in an urban environment how even within a building, there are heat sources that you can use elsewhere in the building. So instead of having your air conditioners dump your waste heat into the atmosphere, you harvest it because other parts of the building need heat. One part of the building needs cooling, one part needs heat, and you keep it within the building and reuse it rather than using electricity for any of those purposes. So New York is mandating a pilot project. In every gas utilities district and every electric utilities district, it's happening all over the state of New York. And this could implicate building codes, standards, right? Because in order to do this, buildings have to be built in a way that's going to accommodate them because you need the HVAC systems. Well, I'm not an engineer, but from what I've seen, because we're dealing with water, the code issues are pretty easy. We're piping, not even boiling hot water, not steam hot water, it's 52 degree water. So it's really compatible with human use. But you make a good point because economically, it's much easier to do this when you're building a building for the first time, whether it's a residential community, commercial building, it's much more efficient to install this then retrofitting an existing building. And that's a big issue down at UVMC. To sort of wrap up this introduction to the subject, H242 is in the legislature. It's in house energy and natural resources. The Vermont legislature, okay. And H242 is modeled on the New York bill, but it has two important differences. The New York bill mandated that every gas utility and electric utility get into this business. And I will say the utilities and the unions all supported this because, and the environmental community all supported it because they saw that this is a way to get skilled workers, high paid skilled workers, usually union workers, into jobs that were green jobs instead of losing their jobs when natural gas is no longer acceptable. It keeps those jobs, they have the same skills largely to do, use largely the same skills as an existing gas business, but it's not gas anymore. So the one difference is the Vermont bill authorizes the PUC to recognize, say, Green Mountain Power or Vermont Gas as a thermal energy network utility, but it does not require any utility to go through this process. It's entirely optional with the utilities. That's one major difference. The second is, they have to opt in, they have to opt in, exactly. The second is this bill says that a city or a city sewer department, a city water department, or a nonprofit homeowners association, or it could be a mobile home park ownership association, any of those groups can go to the PUC and say, okay, we want to do this, and the PUC can authorize it. Almost like a community solar project. It's exactly like community solar. Okay. Yes. And that's the New York bill doesn't didn't do that. So we're broadening it from utilities to saying anybody can get into this business. And the utility model is really useful to get this started because the utility model means that your upfront costs, and this is, once you build these, they're almost no costs. It's all the capital to get it built. Once you, if you're using a utility model, you get your guaranteed that your capital expenditure will be repaid over time from the ratepayers. Yeah. Under the supervision of the public utility commission to make sure the rates are fair. So that's the basic model of H242. It's had lots of support. Representative Stebbins from Burlington has been highly supportive, and we're hoping it will make it off the wall and through both houses this year. That would be great. I believe that we have some buildings at the electric department named after a relative of hers because I think that she comes from a long line of BED people. And I was talking to you earlier today about the green energy times, which I find to be very helpful. And it's got an article saying that we don't need as much energy as we thought. It's on this this month. It's at the co-op in other places on page 13. And they talk about the import of having sources of power and light, so to speak, thermal and electric, that are close so that you're not losing all of the power through the distribution lines and also just the inefficiencies of the burning process. So this is a way to do that. And let's just, before we're going to turn to Nick, not to worry, Nick, we're here for you, is let's talk. So on the screen, just as examples for people, we have something like right here in Burlington, I see. So it's not some crazy out of the area thing. It's not just what's happening on the moon. It's happening here in Burlington, right? And then if we go to the next one, there's something in, is that Ontario? And that's a hospital center. They may be a newer facility than what we have here and we'll have to work on since it went in in 2017. And then there's another hospital, obviously not as old as what was the old Mary Fletcher, but 2009 that's a hospital in Elgin, Illinois. I think Princeton University is on the slide deck, somewhere. Next is Colorado Mesa. And that's, the next one was the Colorado Mesa. And probably earlier up is a Princeton. Do you have something to say? So Princeton did a study and what they determined is, I don't, let me distract you, just keep talking. Princeton is a vast sprawling campus and they're converting the entire campus to thermal energy networks. Okay. The entire campus and they're in the midst of that right now and here's the slide deck on it. We estimate that 20% of the energy we create never makes it to the building since it's lost into the ground. So Princeton really studied this and they found out they're going to save money as well as massive amounts of energy and emissions avoidance by doing this. So it's, what's great about these thermal energy networks is there are no losers. We can argue about McNeil and are there winners and losers there, but in general the concept of thermal energy networks only has winners. There are no losers. We just need to do it. Well, there you go. I mean, I think that the key will be the commitment to invest, the commitment to make the changes that we have necessary. Nick, we have left you out. I'm so sorry that... No, it's been a fascinating discussion. I'm glad to be here and to have heard more about thermal energy networks. So you're award three resident and you've been active on climate change stuff for a long time. Why don't you just introduce yourself to folks. I've been doing exclusively environmental law since the mid-90s and I started working on climate issues in 2006. I've worked for a specialized unit at the Justice Department for six years and I also spent four years at the largest non-profit environmental law firm in the country, Earth Justice, as well as time in Vermont State Government. So you are a resident with some particular expertise that perhaps those of us who are elected officials and have positions where we need to decide things should be paying attention. And the title of this is actually In the Shadow of McNeil and that's because of both the biomass issue and the... Let's see, you might want to come on to here. We've got a little slide presentation that maybe we can get up on there. Jordan, we'll get there. There we go. Let's close down this other one if we could. Maybe we know... Yeah, let me just try to close that. Can we close that down and we get this one up? All the technical things... I'm a lot out. I'm sorry to say. Maybe we just maximized that. Maybe we'll try to maximize that. There we go. Look at that.  Thank you and you can manage the slides. Why don't you talk to us? So the McNeil power plant burns wood chips that are harvested from forests in Vermont and New York and it burns the wood chips to generate electricity. It's the largest electricity generator in the state and it's also the single largest stationary source of greenhouse gas emissions in the state and that's why it's concerning. It's owned 50% by Burlington Electric Department and Burlington Electric is also the operator. I live in the shadow of the plant. I have lived there since 1987, raised my family there. I see it many times in the course of the day and I hear it. I mean to be quite honest, I think as a power plant it's been a decent neighbor to me and they had really worked hard to fix a number of the issues like the ash that was flying from their waste piles but that took a lot of work. I know that Jim you were involved in early. They had to spend a lot of money that they didn't expect to do enclosures for the unloading of the chips because most of them come from by rail and this is good because the chip dust was just flying into the neighborhood before that so. And the smell. And the smell, yes as Peter Frayne of CCTV fame in part wrote about low those many years ago and I'm happy to say that the smell issue has been taken care of but I divert. I digress actually and divert only because I'm a neighbor and this is my neighborhood so. So it started operation in 1984 and it seemed like a good idea to a lot of people at the time although I know Jim you tried to prevent it from operating and you seem to have a lot of foresight because our scientific understanding of burning biomass has really advanced since then and we now know that burning wood to generate electricity emits more carbon dioxide per unit of energy produced than any fossil fuel including even coal and that's why continued operation of the McNeil plant is a concern. The Biden administration has proposed that nationwide we move to zero carbon emitting sources of electricity by 2035 that's in 12 years from now. However rather than have a conversation about whether and when we might close down the McNeil plant instead we're having a conversation about expanding it by building what's called the district energy system which involves extended collecting steam from the plant building a steam pipe a mile and a half to UVM Medical Center and providing steam to the hospital through the plant. Well let's get into the critique a little bit later like next after I ask you to just preview what your thoughts are in terms of that conversation that we should be having now about what I consider to be a just transition in the effort to decarbonize something that takes care of the people who are working at the plant because it's essential that if we're going to deal with climate change that we don't exacerbate the inequalities that already exist and that the workers shouldn't be made to pay twice pay on the job front and in the what will they will clearly pay in the climate front just like poor black folk and brown folk have to pay throughout the country in terms of the environmental racism that that exists so maybe just sort of preview and then we'll get into more of the mechanic go back to the mechanics and then maybe come back to this as well but I just wanted to get you. We definitely need a just transition both for the workers in the forestry industry who might be impacted if we end up taking down less fewer trees and also we need to be concerned about burlington electric employees whose services might not be needed if the plant were to be decommissioned so and part of this also is not necessarily about managing forests but it's it's really about burning right of it so that forestry products that continue to store what was sequestered carbon that's still. Right I'm not suggesting that we should put an end to logging and we need you know responsible logging to continue to supply very important needs for example for furniture etc and as you mentioned when you take down trees and turn them into lumber that's used for you know building buildings or making furniture a portion of the carbon from those trees is sequestered in the product what what we're saying the people I work with are saying is that we should not be taking trees down for the purpose of burning them which puts carbon dioxide into the air immediately and it's really not necessary to do that because we have alternatives now that can much more cleanly produce electricity for the grid without the carbon emission problems. If you'd like to talk about that that would be great. I mean Burlington Electric is always trying to make a comparison between burning wood and burning gas and actually burning wood is worse it emits more carbon dioxide than burning gas but we really should at this point in time so the whole question of the life cycle and the fact that well you're going to be growing trees this is good and then that's how it becomes carbon neutral really the the problem with that argument has to do with the timeframes that we're dealing with am I am I right on that? Well that is a way to look at it I mean that's my simple way of looking at it yeah let me pull up a couple slides to try to explain that yeah so can we get that yeah so this is Burlington Burlington's electrics theory is that when you burn wood magically all the carbon dioxide is is instantaneously absorbed by the trees but if you burn fossil fuels it just goes up into the air and contributes to climate change this is junk science the trees did we just lose everything the trees what do I need to do I don't know go forward and back well just keep talking just so the trees can't tell where the carbon dioxide came from they absorb carbon dioxide from biomass plants they absorb it from fossil fuel plants what we should be doing is moving towards more wind and solar power and in fact and this geothermal network and the geothermal network well that's not for electricity generation but that's for supplying heat the buildings of course I mean I got an electric heat pump you know it's a cold air heat pump that you know is going to run on electricity and so we need to have electricity so we got to pay for that but if the geo if the yeah the thermal energy networks don't require that or you don't require as much of that then all of a sudden what we've got is as the you know the climate chain you know the the green news here whatever this thing is called we don't need as much energy as we thought because we're actually capturing the energy that we are already creating so right yeah the thermal energy networks can can serve to reduce the amount of electricity that we need right and you know that's really important because we're we're trying to electrify a lot of things and that's going to require you know more power generation from clean sources like wind and solar and it's also going to require a massive increase in transmission capacity which is very expensive so the thermal energy networks can take some of the pressure off doing those things and that's one reason why I think they're really important but um right now the ISO New England grid is much cleaner than using McNeil I mean even if you don't accept my argument that wood is dirtier than burning gas because for example in 2022 um the grid was 46% of the grid's power came from gas 23% came from nuclear which is low carbon 6% from hydro and 11% from renewables mostly wind and also solar and some other things we probably would fit in the bio the biomass probably is in that is probably characterized unless it's got its own data I'm not sure where that is it's probably included in the New England states with the exception of Connecticut do not count biomass as renewable okay I know Massachusetts used to and they repealed that so most New England states do not count burning biomass as renewable interesting and right now just to give you an idea as of January one of this year of the generation that's in the pipeline getting ready to come on to the ISO New England grid 50% of that is wind only 2% of it is gas 35% is battery storage 12% is solar so the grid is already cleaner than McNeil and it's rapidly becoming an even cleaner and that's why committing to long-term continued operation of McNeil is very concerning to myself and the people whom I've been working with and so the idea is to start to plan right not the immediate shutdown but that to start to plan and to bring the voices that will be affected into the table on you know around the table into the room and around the table and I think what I'm also taking from this is that we should be not just looking at that transition actually relates to in state in Vermont state generation of power that is decarbonized and that we need to do that you know we've got an old dump right oh it looks at McNeil actually it's down I usually I live at that top of the hill where the old dump was and they used to pipe out the methane they captured the methane and they made power right there and then they sent it to McNeil and that became part of the system and that has died I when I retired from the city in 2018 it was basically done and now we have a very big area that has a great exposure you know to have a great southern or southwestern exposure that I believe people have said when they've looked at it solar energy companies and consultants that there could be a couple of megawatts that would be created with a solar field up there and obviously that two megawatts if say you get the maximum doesn't replace 50 but you begin to make those incremental steps you know for Burlington so is that what you're what you're talking about in part in part yeah yeah of course the ISO New England grid draws energy generated from throughout New England and I agree that we want to be developing more wind and solar here in Vermont you know we want to keep dollars flowing locally that's good for the state's economy we seem to be falling behind some of the southern New England states for example there's a lot of offshore wind generating capacity being developed off the coasts of the southern New England states so I hope we can start doing more wind and solar development in Vermont believe it or not we don't have a lot more time and I've probably spoken more than I should so are there other things that you'd want us to to get to that we haven't nick I mean I guess I could comment on the hospital sure you know I indicated that we're concerned about the district energy proposal because it would have McNeil continuing to operate I'm also concerned that it might delay the hospital's transition to thermal energy networks and other low carbon sources of heat the hospital currently uses steam for heat in its buildings and my understanding I think Jared Rodriguez would agree with this that that makes conversion to a low energy network more difficult and expensive so we need we certainly need to have an engineer come in and do a feasibility study like Jim mentioned but I really think we want the hospital to start moving in that direction now and you know implement the thermal energy network and other alternatives gradually over time and I'm concerned that a long-term contract to supply steam to the hospital may delay that process that's interesting and I I don't know maybe Jim in the regulatory environmental work but other work that you've done you know you've got a green mountain care board that regulates hospitals and their concern is you know the cost the cost of care rightfully so that's a whole another show but is there a you know are you aware in terms of the regulatory system that we've got of a way to really engage UVMMC so they were doing the planning for this climate emergency within in Vermont be it through the PUC or through the green mountain care board and we don't have a lot of time so that one's above my pay grade there you go mine as well but I do think I mean part of shows like this is you know the reason that we do this is to raise the questions because if only the experts are talking to themselves and then coming from on high to tell us all the wonderful things that are that we have to all do and have to all pay for without being involved in the process it's a it's a recipe for the destruction of democracy I guess that my low pay grade answer would be probably the Vermont legislature could answer could provide a solution and if we looked at the Princeton example they did a cost-benefit study with experts and said it's not interesting to make this change for the entire campus so not just talking here about the medical center but the whole UVM campus it'd be great to have somebody fund that study and then we would all know what the facts are that's interesting and so in your work on on the house bill that you were talking about H 242 242 do you think that that's something that the the sponsors co-sponsors would start to think about no it's probably would be a separate bill yeah maybe maybe part of an appropriations bill and since some of UVM's budget goes through the legislative process every year that would that's where I would expect to see this that this could be addressed yeah but H 242 we need to keep it as narrowly focused as we can I was really not trying to add to glom on but to say are the same people who may have an interest in that be interested in making sure that the the biggest hospital in the state of Vermont you know the you know one of the largest employers right of course the medical center is a separate entity from yes the university which makes life very complicated I think that that study needs to be done to see to educate and to get information out to all the decision makers including the public and the city council well good we got about two minutes I've used up far too much of your guys time so let me ask you to give me some closing thoughts jean I want to thank you for having this discussion both tonight and I know over the past several months you've been forcing people to have this discussion around Burlington so thank you you're welcome and I want to echo that I really appreciate your leadership on these issues and the lengths to which you've gone to try to introduce these important topics and the conversation in the community I appreciate that you know it's not easy to integrate the work that community people are doing with the work of governance and policy making and far too often there's a messiah concept that's out there you know we elect people go solve it and I've never in the the fifth more than 50 years getting close to 60 years of working on this stuff I've never seen that as being a way that has anything but you know has lasting change so you know when I sit at the table I need the support from folks like you and organized folks that you're working with before to be able to give me the ideas and the information and the questions to ask people who are supposed to be supplying those answers those experts and then to be there as part of the process because when people are absent right then bad stuff happens right so it's like Woody Allen said what what did you say just showing up is half the game yes showing up yep that's a sort of like running races if you you cannot do very well and Nick and I are runners you got to show up you got to show up you got to show up I saw a great movie about running last night yeah 21 what was a 21 to life it was about the San Quentin prison marathon yeah yeah I've seen that uh seen that advertised um this work that we're doing is an ultramarathon it is not a marathon marathons are short in comparison I want to thank you for being on my team this this ultramarathon team uh for giving me the support and for a hope for me to be able to to do likewise and uh to the folks out here who are going to be watching this thanks I hope this has been been informative these are tough issues and complicated issues the McNeil plant proposal is before the city council in in a number of different ways it's in front of the electric commission it has it's going to have great impact on the future for a trust a just transition um into a decarbonized world that as I was saying before not only we but the are the generations that are going to come behind us need so um um thanks and I hope uh that uh we'll get to do this again soon have a great night and uh thank you good night


So, last class we are discussing about the solution of H N U V D control problem state space formulation framework. So, our planned description is x dot is equal to A x plus B 1 W B 2 U, W is the exogenous input whose dimension m cross m 1 cross 1 and this is the control input whose dimension is m 2 cross 1 and z is the regulated output whose dimension you can write it P 1 cross 1 and W U R as I mentioned earlier and y is your measured output that will be used for control purpose to generate the control U. So, that dimension you can write P cross P 2 cross 1. So, this is the description of the plan and if you see we have a 2 inputs U control input and W is the exogenous input in all equations. So, as we know our let us call we if we have a system x dot is equal to A x plus B U y is equal to C x plus D U which we have discussed earlier then what is the trans function of this one nothing, but if from the knowledge of the A B C D matrix we can write is C S i minus A whole inverse B plus D when D is equal to 0 the transformation will be strictly power trans functions and this thing the transformation if C with the knowledge of A B C D we can find out the trans function of the system. So, pack notation means in short hand we can write G S if you know the information A B C D I can easily generate trans function it does not mean G S is equal to this one mind it G S if you know the A B C D matrix I can write this trans function into this form. So, keeping this thing in mind then we can write our given set of equation in state phase form we can write in packed form on short hand form our A is this one as I told you our input are 2 inputs are there if you see earlier equation that these are the 2 inputs one is input control input and another is the exogenous input in all equations. So, this thing if you want to find out the trans function of this one we can write in compact form A B is combined B 1 and B 2 C is combined C 1 and C 2 and D is all inputs with this input. So, similarly I can write it trans function of P of S C this is our C you can compare D this is our S i minus A this is our B and this is our D. So, if you expand and write it into a matrix trans function form we will get 4 block like this way and now you see this 4 blocks where the 4 blocks are the what are the inputs w and u w is the exogenous input and u is the control input and z is the regulated output y is the measured output.   So, in other words you can say when input is 0 find out the trans function between w to z w to z when input is and that transform this from is not there and that will be this one what we got it here now similarly the transformation between w to y when u is 0 that transformation P 2 1 is nothing but a P 2 1 is nothing but a you see C 2 S i minus 1 inverse B 1 plus D 2 and that I can write it straight away from the description of that state base equation if you see the state base equation that you can write it when input is not there agree then one input is now transformation between w to w to z what is the transformation u is not there this is not there. So, it is a b c d I can write it simply when transformation between w to z when u is not there these two term will not be there this matrix is a b c d that is what I am writing for all this cases then P 1 2 P 1 2 you see when w is 0 when w is 0 then what is the transformation between z to 2 y that transformation is C 1 S i minus a inverse B 2 plus this and that you can write from basic state base description of our plant from there you can write it similarly I can write it P 2 2 S if you see I can write it the P 2 2 S transformation between y to u when w is 0 that transformation is that one how can write it as I mentioned from the plant description of this one from this one I can write transformation between u and y when w is 0 this. So, or a b c d w is 0 means this term will not be there. So, each block 4 block representation P 1 1 P 1 2 P 2 1 P 2 2 we can find out is transformation just this way now if somebody interested because our ultimate aim to reduce the effect of w on measure what is called regulated output that. So, what is the transformation between these two things as you recall you can recall that our 4 block representation is that two inputs w is the exogenous input u is the control input z is the regulated output y is the measured output which will be used for control purpose.  So, if you want to find out the transformation between the w to z the lower loop this is the lower loop of P this is the lower loop of P is closed with the block P. If you want to find out the transformation between w to z transformation and the k of s in the lower block of P that is closed with the block k s. So, how to do it when you are lower block. So, this is the lower block matrices again. So, it will be starting with the upper block matrices you see P 1 1 and it suffixes 1 1. So, I will start with first suffix. So, what will be P 1 2 s into k of s this is we have to merge into P block break it I now P 2 2 s P 1 1 already P 2 2 s into k s whole inverse. So, I have already taken the what is called that first suffixes already taken over the second suffix I have to take last first suffix I have to taken first and second suffix I have to take last. So, it will be P 2 1. So, second suffix will be last this one P 2 1. So, this is the transformation between this to this of this one. So, our if you look our statement of the problem is solution of h infinity control problem standard h infinity control problem means that design a suboptimal control k of s that this you design a suboptimal control k of s such that our closed loop this closed loop system should be internally stable not only that and effect of disturbance on regulated output should be less than some pre specified positive quantity. So, our goal is this design of suboptimal what is called design of suboptimal h infinity controller means or standard h infinity controller means design a suboptimal controller k of s such that closed loop system is internally closed loop system is internally stable agree and not only stable our motivation to design k such that h infinity norm of transformation between w to z will be less than some gamma. So, there are two folds in our motivation they have to design k of s in such a way that it should stabilize the closed loop system internally as well as the h infinity norm between the signal w, exogenous input w and regulated output z h v norm will be less than gamma and gamma is some p specified value positive p is greater than 0. So, before I as I mention as I am now telling you detail derivation of standard h infinity control problem we will not discuss derived only we will give you the algorithmic steps for this one what the before that we have to make some assumptions the h infinity suboptimal solution is obtained by the following assumptions the h infinity suboptimal solution is obtained by the following assumption what is this following assumption first thing to controller just to obtain is stabilizing controller k s to obtain stabilizing controller k s the necessary and sufficient condition is these two a b 2 this pair b 2 associate with u in the state equation and c 2 associated c 2 associated in the output equation in the output equation c 2. So, our a b 2 must be stabilizable and a c 2 must be detectable. So, these two ensures these two condition is the necessary and sufficient condition for existence of for existence of stabilizing controller. So, this is the first before we apply the h infinity suboptimal control problem solution of suboptimal we have to check whether the system is stabilizable or detectable a b 2 n s n next assumption is because when you will design the h infinity controller we have to solve two Riccati equation and the existence of two Riccati equation agree guarantees that this rank must be satisfied this rank must be satisfied what is the first a j omega i b 2 associate with a u 2 u and c 1 in measurement equation matrix c 1 and d 1 2 and this matrix should have full column for all frequency whatever the frequency you train you let us call frequency is 0.1 because I know a b a b 2 c 1 d 2 find out the for particular frequency find out the rank of this one and that rank must be full column rank for all frequency when you will sweep the frequency from 0 to infinity the rank should not differentiate from full rank that means n plus m 2 this is the a 2 1 condition and a 3 condition is the rank of a b 2 c 1 d 2 find out the j omega i b 1 associate with the exonation put c 2 is associate with the what is called measured output and d 2 d 2 1 associate with the exonation that rank should be a full row rank full row rank for all frequency means some frequency omega is equal to omega 1 find out the rank that rank must be n plus m 2 another frequency omega to find out the rank of this one that also must be n plus m 2 for all frequencies this rank should be full row rank. So, this dimension column is n this column will be how much m 1 and this row is p 2 and naturally this one will be n. So, this should be a full row rank. So, a 2 and a 3 condition ensure that the two Riccati equation which will be necessary to design the h infinity controller one Riccati equation for designing the controller another Riccati equation will be necessary for designing a estimator. So, these two existence of solution of these two Riccati equation ensures the rank row rank full row rank and full column must satisfied and not only this the h infinity controller when you will design it it will ensure there is no pole zero cancellation on the imaginary axis on the imaginary axis. So, this ensure that the system will be internally stable. So, this is the condition three and condition four is the rank of d 1 2 d 1 2 associate if is the state page description our original problem d 1 2 associate with the input in measurement equation and d 2 1 associate with the output equation in the what is called exogenous input. So, this should be full column means rank should be m 2 and this should be full rank that means rank of this one will be p. So, this ensures this two condition ensure that whatever the controller you will get it after designing h infinity controller that controller will be proper that controller will be proper not only this you will be able to realize this controller it will not be improper trans function of that one that controller. So, this condition also necessary to be satisfied. So, condition 1 to 4 is essential to design a h infinity controller standard h infinity controller or suboptimal controller when you will go to design based on h infinity controller approach then this a to 4 that condition must be satisfied. Other condition is the simplify the our control algorithms. So, a 5 conditions that means fifth condition this condition is simplifies the h infinity control problem only. So, if b 1 d 2 1 d 2 1 dimension is p 2 m 1. If b 1 d 2 1 transpose is equal to 0 physically it implies b 1 associate with the noise in the state equation means noise means exogenous input d 2 1 if you see the d 2 1 is associate with the measurement noise d 2 1 associate with the measurement noise. Though we have considered both are same that means they are correlated if this will be 0 when they are uncorrelated this that mean process noise and the measurement noise are uncorrelated then this product of this one will be 0 because this product will come in the h infinity control algorithms. There will if it uncorrelated there itself we can write it b 1 d 2 1 transpose whenever we will get it will put it 0. So, from this one I can write it d 2 1 always we can make into this structure 0 i by using that what is called some transformation I can any d 2 1 I can convert into this structure agree. So, if you make it this structure then d 2 1 d 1 2 transpose is identity from this you see identity further implies that b 1 d 2 1 if you multiply by d 2 1 transpose this into this 0 this into this is i identity matrix this. So, if the structure of d 2 1 is this one I can write b 1 d 2 1 and d 2 1 into d 2 transpose is identity and b 1 d 2 1 is 0 when process noise and measurement noise are uncorrelated. This is the fifth condition, but that is not the essential to design a h infinity controller. So, sixth condition is again d 2 1 transpose d c 1 if it is 0 and d 1 2 d 1 2 associate with the regulated output noise it is d 1 2 associate with the regulated output equations and it is associate with the existence input. So, if this structure d 1 2 structure if it is 0 i I can always make even it is not that structure I can always make it 0 and i structure. If it is this implies d 1 2 transpose d 1 2 is identity matrix and further I can write it d 1 2 c 1 d 1 2 that this multiplied by c 1 d 1 multiplied by c 1 this is transpose agree d 1 2 transpose c 1 is 0 that is we have seen and d 1 2 transpose d 1 is identity degree. So, this simplification is if you can simplify the our h infinity standard control problem this is not the essential what is called assumption that 5 and 6 similarly 7 also. What is 7 d 1 2 is 0 if you see the d 1 2 is 0 state way we can see from this equation I will show you this one if d 1 2 is 0 if this is 0 that means our p 1 1 s is equal to c 1 s i minus a whole inverse v 1. So, this p 1 1 matrix which has transformation between w 2 z will be strictly proper transformations if d 2 2 is 0 see if d 2 2 is 0 just here that is if d 2 2 is 0 that is then c 2 s i minus inverse v 2.  So, these two assumptions d 1 2 0 d 2 2 is 0 is not essential, but if it is 0 p 1 1 s will be strictly proper transformations and this is will be strictly proper transformation p 2 2 if d 1 1 is 0 p 1 1 will be strictly proper transformation and this will be strictly this assumption as I told you not needed, but it is simplifies the what is called the solution of Riccati equation other things and also the transformation between w 2 z. So, our main basic assumption a 1 to a 4 and other assumption 5 6 7 is not a essential assumption to design the standard h infinity control problem. So, let us as I told you I will not go for details derivation of the h infinity standard h infinity control problem we will just write the algorithm steps how to design sub optimal h infinity controller k of s. So, our algorithm step for sub optimal h infinity control problem solution. So, first step you write in state page description of the plan into this form this is a state equation and is x is the state vector whose dimension n cross n w is the exogenous input whose dimension m 1 cross 1 u is the control input m 2 cross 1 and z is the regulated output and w is exogenous input u is exogenous u is the control input and hence I can find out the dimension of a b 1 b 2 c 1 d 1 1 d 1 2 and y t is the what is called measured output since I know the dimension of w d u and x I can find out the dimension of c 2 d 2 1 d 2 2. This is the first you have to make it into this structure if you want to design h infinity controller based on state page model approach then you have to make it in this structure it is called four block representation is something like this form two inputs w and another input is u and this input is your output is z regulated output this output is y and we have a controller u we have designed based on this our controller k of s. So, this is our p of s the four block representation you have to write like this way. Next step is that as I told you the check the assumption one check the assumption one a 1 a 2 a 3 are satisfied now if they are not a 2 and a 3 this is the corresponding a 2 and a 3 if it is not satisfied then what you have to do it then you have to modify that our system by introducing the weights. So, this as I mentioned what is the useful assumption for a 1 is what for a 2 a 3 for what you are doing a 1 is assumption is that a b 2 a c 2 must be stabilizable and detectable in order to get the controller stabilizing controller. So, this is the second step check the all assumption a 2 a 1 a 2 a 3 the third is check the assumption a 4 a 7 though I told you it is not necessary in a 4 and a 7 you see the a 4 and a 7 assumption is what it means the a 4 the assumption full rank column rank full row rank is used for power getting the proper controller even if it is not proper it is a by proper then hence we can this will give you the proper what is called transfer function of the controller. Hence, you can realize for a 4 and a 5 a 6 a 7 agree this assumption a 4 assumption check the assumption a 4 and a 7 a 7 assumption is what a 7 assumption d 1 2 is equal to d 1 1 0 d 2 2 is 0 means to get the p 1 1 p 2 2 as strictly proper transform and that does simplify the algorithm only. So, check, but as I mentioned earlier in our assumption this assumption this is our assumption if you see this our assumption is this is the assumption is 5 we have considered 0, but this assumption you can relaxed this if you see b 1 d 2 1 we assigned in assumption 5 0. So, that assumption you can relaxed and this is the assumption 6 if you see that assumption also you can relaxed it this assumption. So, I am relaxing that assumption step 4 select a large positive value of gamma positive value of gamma where the h and v norm will be less than gamma. Gamma is positive quantity large positive initially you have considered large positive number of gamma where gamma interprets is what the h v norm between the exogenous input to the regulated output solve two Riccati equations. Now, next step is after checking all these things you have to solve two Riccati equation. What is this two Riccati equation before I write the two Riccati equation in details that our recall our LQG problem or LQR problem what is this or LQG or when we are going to design a controller we have to solve a Riccati equation this is called algebraic Riccati equation.  If you want to if you once you solve this one and you see I need the information of A B Q R agree if that Hamiltonian matrix this is called Hamiltonian matrix A minus B R inverse B transpose minus Q is the Q is the weight is associated with the state vector and R is the weight is in the control vector and minus 8. So, this is the Hamiltonian matrix and from the Hamiltonian matrix I can create what is called the Riccati equation once you know the Hamiltonian matrix of this one I can create the what is called algebraic Riccati now how would it see A transpose A A transpose P then transpose of the P A minus P this quantity minus P this quantity B R inverse B P minus P this quantity B R inverse B P this quantity that minus will come and then P plus Q what is the sign is there plus Q. So, from the in short I am writing Riccati of this one means from the knowledge of Hamiltonian matrix this is nothing but a Hamiltonian matrix this is nothing but a Hamiltonian matrix from the knowledge of Hamiltonian matrix one can create the algebraic Riccati equation. So, keeping this thing in mind what I am doing it now I am writing the Riccati equation that we have to solve for the controller. So, now you see the x infinity is a solution of Riccati equation for designing controller. So, this our Riccati equation this is the Hamiltonian matrix this is the Hamiltonian matrix and Riccati equation I can form the knowledge of Hamiltonian matrix what is this I can consider in equivalently you can consider this is A this is this whole thing equivalently and this is whole thing equivalently I can consider if you consider L Q R then this is nothing but a B R inverse B R inverse this is equivalent if you consider A this is whole thing equivalently B R inverse B transpose this whole thing equivalently you can consider minus Q and if you this is A then it will be A transpose this whole thing you can minus A transpose. So, I can easily write the Riccati equation A transpose P sorry A transpose P means our x infinity here I have considered the matrix the solution of Riccati equation A is x infinity A transpose P then P A then minus because minus then what is I am writing P that quantity that quantity minus is there here then P. Then this quantity this quantity is minus Q plus U we have to write it this. So, this is the Riccati equation and what is the Riccati equation for designing the controller H N V D controller designing therefore, controller part and what is here we introduce the new thing that D 1 to bar D 1 to bar is D 1 transpose D 1 2 that is I am considering D 1 to bar inverse again the whole thing is D 1 to bar inverse. Now, if you consider the special structure of D 1 2 as I mentioned earlier D 1 2 as I mentioned earlier if you see that one anyway the 0 I 5 just minute. If you consider D 1 2 structure you see D 1 to transpose D 1 2 is identity. So, if you that structure this will be identity again it does not matter even if you not that structure it will be you will calculate and put the value is here, but it is known to you. So, you have to solve the Riccati equation we have already discussed how to solve the Riccati equation different methods that you recall. Once you know the solution of the Riccati equation x infinity then controller gain k consequently again I can use by using that one and this term will be 0 if this term is 0 if the if this is 0 then this will not come into the picture in our things. So, our controller gain is that one this is 0 if this quantity is 0 then this term will not be there agree or you forget it is this will not be 0 if this is 0 that what we have consider in this assumption. If D 1 2 transpose C 1 is 0 then naturally this will not come into the picture if this is if. So, similarly that what is called that what is called we can design this is the controller this is the your estimator this is the Riccati is the estimator Riccati equation. What is the Riccati and this is the knowledge of A you again you can consider this is A this is our minus B R inverse R inverse B transpose then this is our Q this is our if it is A this will be A transpose. So, you can write it and our D 2 1 is what that one and B 1 bar expressed by this one. So, D 2 1 bar if D 2 1 has a having a special structure then this quantity will be identity even though it is not a special structure one can compute by knowing the knowledge of D 2 1. So, from this Hamiltonian matrix this is nothing but a Hamiltonian matrix I can write the Riccati equation.  So, this is the algebraic Riccati equation this is you can say algebraic Riccati equation you have to solve the algebraic Riccati equation why infinity of this one this you know all matrices then you can solve, but this is a matrix and non-linear algebraic equation. So, this is a step 8 is the solution of what is called Riccati equation for estimator agree that you have to solve it. Now, step 9 is estimator gain for estimator or observer gain you have to find out is nothing but a that z infinity into K e what is z infinity is related with this expression. I know x infinity I know y infinity gamma I have assigned initially very large. So, that the z is no z infinity is known and K e is what y infinity you know all these matrices you know you can find out K e not in many K e. So, I can write this is nothing but a estimated gain K e l. As you know estimated equation now estimated equation x hat dot from basic equation I can write it from basic equation I can write the estimated equation you see the our basic equation see that this is where the basic equation estimated equation I can write it x hat dot is equal to a hat b 1 w hat plus u 1 w hat plus correction term. So, I am write x hat dot is equal to a hat plus b 1 w hat plus w 2 b 2 u of t plus correction term and this is the output measurement error is the actual measurement and this is the estimated measurement that multiplied by what is called estimated gain this is called estimated gain. So, this is the how is calculated w hat that this expression in this right hand side everything is known to us from this one and the y hat that output estimated value of the output is that one. And if you see this one our standard what is called LQG problem where the estimator is there this term and this term are coming extra in H infinity H infinity controller in comparison with LQG.  So, and w hat you know how to calculate w hat this one estimated for this. So, I know the estimated equation well defined now. So, I have given the equation number 1 is our if you see the our equation number 1 is the our controller gain control law this is the equation where u is equal to k c x hat of t equation this is the estimated equation is 2 and w hat y hat is 3 and 4. So, now one can easily find out the if you put this if you put the value of y hat here w hat here y hat here and after that u you put u is equal to minus k c x hat in this expression then I can simplify this equation in final form. So, that is why we are writing the using equation number 1 then 2, 4, 5, 6, 7, 8, in equation 4 we get this expression is nothing but a if you see you can get this expression by putting the value of y hat by this expression sorry w hat and y hat by this expression in this and u u u of t you can put minus k c x hat of t in this expression then finally, estimated equation this is the estimated equation you will get this one. Now, if somebody wants to find out the transformation of the controller as you see from the very beginning I have written a transformation of this controller here the transformation of the controller between y to w y to u. So, one can easily find out the transformation of this one step 11 transformation from y, y is the input u is the output of the controller input to the controller y output to the controller u how you will find out using equation 5 and our equation 1 and our equation 1 is what is nothing but a u is equal to minus k c x hat of t this is our equation 1. So, from this one I can easily find out the this is find out the transformation k of s what is it is something like that x dot is equal to a x plus b u y is equal to c x plus d find out the transformations. So, in our case this whole thing will be our a y of t is the input of the controller. So, this is our b our output is u of t. So, this will be our c. So, it is a c here b here and d there is no d term here d is 0 d bar and whole thing is you can think of is a bar b bar all this thing. So, our controller transfer function this is the transfer function of the controller generally this controller transfer function will be very large order the even it is more than the our original system order. So, one can if you one one can find out the transfer function of the controller in this one. Then finally, there exist a stabilizing controller k s if and only if necessary and sufficient condition two Riccati equation one Riccati equation for controller another Riccati equation for the estimator are solvable and they are solvable provided the assumption which we made it in the beginning of the solution of the problem assumption that must be satisfied. And following condition is satisfied that means rho x infinity y infinity of less than gamma. That means spectral radius of the of this matrix spectral radius of this matrix spectral radius means maximum Eigen value of the matrix maximum Eigen value of the matrix. If it is less than gamma square again that condition also must satisfy this condition following condition the following condition must also satisfied. That means there exist a controller, but that does not mean that controller what we have designed the controller that does not mean the h infinity norm of h infinity norm of T z w will be minimum will be minimum. So, what have to do it next is whatever the initial value of gamma we have selected decrease the gamma and proceed this whole process that following repeat the you see repeat the steps six and eight six is then you when it is you got you have got the gamma initially you have the large value of gamma and we got this solution. Let us call this condition we satisfied then what we mean the gamma value we can reduce it reduce the gamma value. And then again you solve what you have solved it the two Riccati equation find out the controller gain observer gain or the estimated gain agree and then again you check this two condition. If it is less than this one further you reduce the gamma in this way process you go on until unless you are able to reduce the value of gamma. So, if this condition is satisfied that means and repeat the steps six and eight what is the steps six and eight see repeat six and eight that this is a six and eight that solution of controller Riccati equation and eight is the solution of what is called observer Riccati equation observer Riccati equation. Once you solve x and y infinity you can easily find out this if this is less than that one then further you reduce and solve x six and eight agree step six and eight. So, this process will continue until and unless you will be able to reduce the value of gamma in the sense that when you have solved the two Riccati equation spectrum norm of this two Riccati product of two Riccati equation spectrum norm should be less than gamma square if you get it then further you reduce it. So, finally I can say compute this you see this is important compute the spectral radius of product of this two Riccati equation until satisfactory solution is obtained then compute finally you compute k c, k l, k s s etcetera to design our controller. So, this is the algorithmic steps of that one now let us see basically how you will realize this h n v d controller in block diagram representation. This is the block diagram form basically I am doing if you see this one basically I am representing the plant first then I am representing the estimator that is all. So, I am just showing you the plant equation that plant this is the plant equation that I am just doing first thing and I made it assumptions that d 1 2 that assumptions anyway. So, this is the equation the plant descriptions plant description is this one I made an assumption in order to draw the what is called that block diagram form I made assumption d 1 1 0 d 2 2 0 this indicates that our the transformation p 1 1 s and p 2 2 s will be strictly proper transformation. In other words we made an assumption that our what is assumption number I think 6 assumption number 6 possibly yes 7 sorry this assumption I made it in order to do this one. So, I made an assumption assumption 7 is please say assumption a 7 means assumption 7 is assumed a 7 is assumed. So, if a 7 is assumed that means d 1 1 d 1 2 d 1 2 d 1 1 d 2 2 is 0. So, first you see plant I have represented with a block dotted box. So, what is x dot look at that plant description x dot is equal to A x. So, A into x plus b 1 into w. So, b 1 this is b 1 w it is coming signal then b 2 u. So, b 2 u that is x dot. So, x dot and our regulated output z, z is what c 1 x d 1 1 I have considered 0. So, there is no input from w. So, d 1 u down part is 0 then what will come d 1 2 u. So, it is coming d 1 2 u this signal. So, that is the regulated output and that dimension is if you consider p 1 cross 1. So, our regulated output this a measured output is what y c 2 into x c 2 into x plus d 2 d 2 1 into what w d 2 1 into w you see d 2 1 into w. So, this is the regulated output. So, this dotted box is the plant description this is the plant descriptions made it and in other words I can 4 block representation I just can make it p s form. Now, it is a estimated equation if you see the estimated equation here that is we just written it estimated equation this is the estimated that is I am now representing in block diagram form. Now, you see the estimated equation is what A this is the estimated y hat what is y hat y hat is a c c 2 x hat c 2 x hat and also you see this one c 2 x hat and also that that one x hat into gamma square you see c 2 x hat and x c 2 x hat where is c 2 x hat and the gain see this one estimated equation. I just written all this equation from the basic estimated equation see from this equation putting the w and y hat and u print I got this block diagram again this with the dotted things and controller is what k c into x hat and k c into x hat with the this is a x hat k c into x hat and our estimator is a A into x hat plus B 1 into y hat B 1 into w hat B 1 into w hat a w hat value you put it this is B 1 into w hat again then B 2 into u then B 2 into u you see B 2 into u this block is coming then will be correction term what is correction term k l into y y hat y minus y hat this is the correction term is coming. So, this and what is y hat y hat is nothing but a your c 2 into x hat plus d 2 1 plus d 2 1 into d 2 1 w hat. So, you write it w hat this one so note that this block and this block gamma square d 2 1 gamma square d 2 1 gamma square B 1 transpose x and gamma square B 1 B 2 transpose these two blocks are extra term in comparison with L Q you see this block and this block where you have written here and here are the extra terms in comparison with L Q R. This is the HMVD standard control problem in structure wise this one estimated is there and this block is called estimated this dotted board is estimated and that is obtained using equation 2 to 3 this whole block is obtained this one. So, this is the all about the course then I will give you the assignment sheet and the one problem I will solve give you the in the assignment sheet how to solve HMVD control problem using MATLAB program because hand calculation as I told may manual calculation is just impossible for higher order system. So, I will work out one example before I give the what is called the assignment sheet you will find everything in then assignment sheet how to solve the HMVD control problem for higher dimensional problems. So, this is all about the course and you will get your assignment sheets from static optimization and dynamic optimization and HMVD control problems all assignment sheets you will get it in the website. Thank you very much.


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The most important thing I ever learned from my father is the same thing I want to teach my children. Work hard, treat everybody with respect, and put your family first. My dad would always say, and I say this to my all kids, never ask somebody to do something that you're not going to do yourself. One piece of important advice that my father gave me was that happiness lies within and not within possessions. To surround myself with good people and to enjoy the little things in life.


Hi everyone, Joe for Jaspy's casebrakes.com coming at you with 2017-18 Panini Prison Basketball. 10 box, random team break number one. It's a blaster box break. There you go, Nick's popping it open right now. Random team, I will. Actually, so let's, screen's really quick so he's gonna help us rip these boxes here. So we'll go one, two, three, four, five, six. And I'm gonna select that die right there. Oh, it's off camera, oh no. There it is, it's five. So one, two, three, four, five, six. We'll save that for the next break, which is coming up right after this. All right, let's flip back to this screen right here. Big thanks to these folks for getting into it. Now one spot gets you three teams. Willie sold 10 spots in this one. And all 30 teams are in. Let's roll it, let's randomize each list. Six and a one, seven times. One, two, three, four, five, six, and seven, then final time. After seven times, we've got Corey all the way down to EA. Six and a one, seven times for the teams. And seven and final time. After seven, we've got the Sixers down to the Wizards. Corey with the Sixers, Scott with the Pistons, and the Nets. Mac, you got my Lakers and the Knicks, Jesse with the Mavs. Mac with the Magic, Kevin with the Rocket, Scott with the Cavs. Mac, you got the Grizzlies, Sons and T-Wolves. Corey with the Hornets, Kevin with the Clippers, EA with the Heat, Kevin with the Jazz, Jesse with the Spurs, EA with the Pacers, Jesse with the Bulls, Oliver with the Pelicans, Mac with the Bucks, Rich, Laspod, Mojo, Celtics, nice. Oliver, Trailblazers, Thunder, Mac with the Kings, Rich with the Raptors, Corey with the Nuggets, Mac with the Warriors, Rich with the Hawks, and EA with the Washington Wizards. Trades are allowed if you want. Let's sort by column B by team, and let's keep the video running because Nick's opening up packs right now. Let's go to the NBA Draft class really quick, and I'll drop the link in the chat for you too if you're watching live. If you're watching the replay, you can obviously fast forward through this part. So obviously Jason Tatum for the Celtics is the main chase here, but does Markel Fultz, number one overall pick, does he have Upside? Possibly, Lonzo Ball, I think, does decently on the secondary market these days. Deer and Fox still in the mix, what about Laurie Markinin? Dennis Smith Jr., still pretty young. Zach Collins, Donovan Mitchell is in this class, Donovan Mitchell is Bama Tobayo for the Heat. John Collins for the Hawks as well, both Collins' is's. I like Jared Allen on the Nets. It's got some Upside, O.G. and Obie. Kyle Kuzma's in this class, Josh Hart. So there's some names here. Ladies and gentlemen, there's some names. So no trades? No one's even talking trades. Trade window closed? All right, TWC, trade window closed. Let's get a move on. Let's print, let's rip. This is break number one. Second half of the case is gonna be coming up directly after this. And then after that, we'll get into some 2020 contenders, then some mosaic stuff, and then we'll go through some orders again and see what other kinds of trouble we can get into. So here's the official printout. Right there. Thanks everyone for getting in, really appreciate it. All right, let's see if we can find some treasures. Just grab a stack. Yeah. How many boxes do you think this is? Three or four? Three or four boxes here in this pile. Good luck. I got a box in the box here in Fox and a Silver Faults. Mac McCarthy with the Kings and with the Sixers, Corey with the Sixers. He's a number one, former number one overall pig. Now he kind of washed out in Philadelphia, but has a number one overall pig. If he does decently with, he's on the magic. Now if he does decently, then all of a sudden, you know, that value jumps. LeBron's still a calf in this edition, but he's him, Kobe, if any, will be the only, and Yanis, if any, will be the only ones that only vet commons that'll ship. There's Brook Lopez, Lakers edition, that'll be for Mike McCarthy. Trayvon Graham. Obviously, vet commons don't ship, but vet parallels will definitely ship. I've always gotta save these rookie silvers, just in case. Just in case Trayvon Graham blows up for the Hornets or Corey. And these greens aren't numbered, just FYI.  Could be an interesting team when John Wall's healthy. EA with the Wizards, John Wall, and Bradley Beale can play well together. Hachimura in the mix. Could be some interesting things happening in the nation's cap. Dante Zizic, for the Celtics and Rich, here is an emergent Jason Tata. No silver or anything like that, but maybe we're getting warmer here. Dan Smith Jr., Mavs edition, going to Jesse Dallas. Thanks, Nick. The Angelo Russell, Nets edition. We've got Shaquille O'Neal, Relic. That's pretty cool. Shaq, Shaq Daddy, Big Diesel. Going to the Lakers, Mike McCarthy with my Lakers, game-worn material in here too. I dig it. Can you dig it? Yannis, get hyped for the Bucks. Mack, Harry Giles, Rookie Silver, Donovan Mitchell, Bass, Rookie. Kevin Mendoza with the Donovan Mitchell and the Harry Giles, Silver, Kings. That'll be for Mack. DJ Wilson, Relic. Mack, Derek saying John Wall hasn't played since the Bush, I don't know, it seems like, since the Bush administration, seems like it. Justin Patton, Rookie Silver. He was recovering from one injury and then he had that, I feel like the full story on his, there he is right here. He heard us talking about him. I think the full story about how he ruptured his Achilles heel, I feel like has not been told. He said it happened at home. I don't know if anyone really knows what happened. Was it just a, just an accident? Was he doing something he should have been doing? Riding on a motorcycle or something like that. Cleaning the top of his truck. A little bit of the, when they're cutting, a little bit of that there. I don't know, another Markel Foltz for Corey and the Sixers. Never know. He's in mad bumps, that's correct. Where is he? No one's really done the investigating. Zach Collins, Trail Blazers, and another relic, it's Jonathan Isaac. Orlando Magic, bit of the Orlando Magic pinstripe in there too, for Mac McCarthy. He's a Kuzma Rookie. I feel like Kuzma was just starting to, before the season hit the pause button. Just starting to fit into that Lakers offense, but let's see how they bounce back. We got Jordan for the Golden State Warriors. That'll be for Mac. We got Ocaro White, Silver for EA and the Heat. And we got a BAM Audubio relic for EA and the Heat. Nice, it's really emerged. Second-year Ben Simmons and a Silver Josh Jackson. Disappointed in Phoenix, but maybe wherever his new home is, where is he now? Memphis, Orlando? That goes to Mike McCarthy and the Sons, maybe change a scenery, could do him well. The Glove, Carmelo, Stanley Johnson, Kyle Korver and Reggie Bullock at the end. And there you have it, ladies and gentlemen, Joe for Jaspy's casebreaks.com, that was a quick 10 box blaster break, half a blaster case, random team one of 17, 18, a Panini prism basketball. I'm Joe and I'll see you next time for the next one. Bye-bye.


We talked in the last lecture, we hinted in the last lecture about the different strategies that are the different structural characteristics of the digestive tubing that will enable increased surface area. So now we're going to get a little more specific. So there are four things. We listed them out last time. Go ahead and push pause and list those puppies out there. I'm going to use this diagram to help you remember your layers. So I'm going to try and color code it similarly. So I'm just going to get a little bit of fresh color or fresh space here so that I can draw these pictures. Now, the first strategy for increasing surface area was length.  Yes, that's long. That increases the surface area. Why do we care about the surface area? Because the whole point of the whole thing is to absorb the nutrients that you are breaking down in the lumen of the tube. If you don't absorb them, then it's sort of pointless. They're eating if you're not going to absorb that stuff. So the more time, surface area, whatever you have to carry out the absorption, the better. Make the road longer. The longer the nutrients are on the road, the more likely they are to be absorbed. Okay, I'm not going to draw that one. That one's easy. The second one was this circular fold idea, circular fold. And I'm just going to get crazy. So bear with me while I draw. Actually, let's just list them all out and then I'll draw them all. Circular folds, we have villi and we have microvilli. And I believe, I believe I can draw them all on one drawing. Okay, watch. You'll notice, oh geez. I mean, it looks super awesome. I mean, look at that thing. What? Okay, this is my epithelial layer, okay?  This is like a cross-section, cross-section. Kind of like what I just drew, except now I'm drawing the texture. Consider this a textured lecture. That looks very textured. Epithelial tissue.  However I am, okay, going to change the color of what layer was that, do you remember? That was the laminopropria. I'm going to change the color of the laminopropria because I want to make sure that you are cool that the laminopropria is green. Yes, I'm doing this on purpose. Laminopropria, yeah, yeah, get out of there. I don't know why it does that. It makes those cute little circles. They're perfect. I would never make a perfect circle like this. I'm drawing you laminopropria. What is, yikes, what is something? If this is laminopropria here, what will my little green line actually have associated with it? Uh-oh, did you see that? I think my computer's hot. It's like five billion degrees in my office. I don't know why it's five billion degrees. Dude, yes, I was up all night and I'm still going. Laminopropria, if we want to do our whole mucosa layer, we also have to include, this is not looking good, you guys. We also have to include our muscularis mucosi, which is what I'm trying to draw right here and leave room because what is going to be basal to muscularis mucosi? We're going to have submucosa in there. Now look, here's muscularis mucosi. Ah, why is it doing that? And now, now I'm putting in this color for submucosa.  Look, what is going up here? What? It's submucosa. Submucosa is going all over the place. Yes, and what is basal to submucosa? Well, this is where we've got another couple of layers of muscularis externa. This is my smooth muscle layers, right? Look at this. This is actually really beautiful. I hope I do not have to re-record this thing since I'm glitching in and out over there. Don't make me re-record it.  Let's call it a serosa. Oh, I'm almost ready. I have to draw a couple of epithelial cells. Each one of these is an epithelial cell, okay, with its own nucleus, right? And on the surface of each cell is a set of extensions. They look like crowns. They're not crowns. These are not frog princes or princesses. No, these are intestinal cells with microvilli. Microvilli are these little extensions of cell membrane and cytoplasm found on individual cells. Every single one of these cells is covered in microvilli on the luminal edge. That increases surface area. In addition to that, in addition to the microvilli, each one of these lamina-propria-filled extensions, each one of them is a villus. So here's one villus. Here's two villus. I mean, here's one villus, here's two villi. And the villi are made up of cells that have microvilli. What's this third thing? This third thing that does not have, it does have microvilli, it does have villi. This is my circular fold. Circular folds have submucosa inside of them. If you don't see submucosa, you're looking at a villus. You're not looking at a circular fold. Circular folds are actual folding in, like pinching down of the entire tube all the way around. So the tube narrows. But as the tube narrows, the surface area increases. Which is the point. Okay. You should be able to compare and contrast all those different ways of increasing surface area. And now that you have the generalized tube and how we can increase surface area, now we're going to look at each of the parts of the tube specifically. Sounds like fun. I'll be right back.