#state transition matrix properties

[acegiak]

Ok but the thing about The Matrix, though, is that when it was released we all knew it was a fuckin Gospel allegory, like it was so obvious as to be on the nose. And like yeah basically any heroes journey can be interpreted as the gospel but for real: Neo is The One(it's an anagram lol), who was prophesied, Trinity/The Holy Spirit leads him to Morpheus/John The Baptist who baptises/frees him (the imagery of the mirror like liquid covering and entering neo and then his emergence from the pod is absolutely a baptism) and then Morpheus/John declares him to be The One that was prophesied. This frees him from his identity as Thomas Anderson (Thomas because he was doubting, Anderson because Son Of Man is mortal also flawed) and allowing him to become Neo, who will lead everyone from the flawed world into the world of the truth(kingdom of God). First thing after this revelation he has to go be weak for a while but then gains a bunch of disciples and learns how to do miracles and then Cypher/Judas betrays everyone for earthly pleasures which lead to a confrontation where Agent Smith(Satan, obvs but also his numberplate in the second film is IS5416 for Isiah 54:16) defeats Neo and he dies but then is resurrected because of his connection to Trinity/The Holy Spirit (seriously TRINITY??) which defeats Smith/Satan and empowers Neo/Jesus to spread the truth to everyone in the whole world moving forward.

But ALSO it's clearly, in hindsight, a trans allegory, again so clearly as to be on the nose. The first thing on screen is "call trans opt: received". Neo is obviously miserable with his life and place in society and knows something is up but doesn't know what, has been experimenting with an alternate identity online. Gets an invitation to go to a club and encounters alternative people and one confirms that something IS up. The forces of the system and his own doubt (Thomas) try to keep Neo in his current role, ignorance and the closet, using the name Mr Anderson (mister son of man) repeatedly in a torture scene where he doesn't have access to words to speak his truth. A direct encounter with someone who has already been down the path and now lives in their own truth, and offers the opportunity to discover ones own truth by taking a red pill (the color of premarin pills, a common estrogen HRT medication). Neo then undergoes a physical transformation from the pill and must then relearn how to exist but in doing so becomes more powerful than ever. In this new form Neo still has to battle against the old world and its systems which have become more violent and still continue to try to cast Neo back into the identity of Mr Anderson but it is self confidence in the the truth that enables Neo to be victorious. Also being trans gives you could kungfu super powers.

SO

You know where I'm going.

TRANSitive property of allegory...

Is the Gospel a trans allegory?

Jesus Of Nazareth is born with an innate identity that is hidden for years by his parents for fear of government persecution but there are signs of this true identity all throughout childhood. When Jesus meets someone with access to the truth he becomes fully aware of the truth of his own identity. He then has to go endure a period of suffering and temptation to abandon the path of truth, but eventually emerges enlightened as his true self. That true self is then a symbol that inherently reveals the falsehoods of the social constructs underpinning the society around him and those who rely on those constructs to hold power and status over others become enraged by this undermining and weaponise the tools of the state against the body of the transgressive person.

I'm not saying that Jesus was trans, of course. I'm saying the story of Jesus is actually an allegorical myth to reveal that trans people and trans bodies are holy and sacred and should be honored for the truth they reveal to us.

[fats-wineman]

Just saw the Barbie Movie today, and what an achievement of a film. So layered so complex, simultaneously tongue-and-cheek and angrily relevant. While many have pointed out the central themes of the issues faced by women, I think there is another message Margot Robbie, Greta Gerwig, and co-writer Noah Baumbach are telling audiences. Both Gurwig and Baumbach are members of the Writers Guild of America, and Baumbach even skipped the premier in protest. I think their professional frustrations with the major studios was on full display in this film.

A live action Barbie film was first announced in 2009 by none other than Universal Studios. After the project faltered, it went to Sony pictures in 2014, with Amy Schumer slated as the lead. Yet, creative differences between parties involved lead to that project fizzling out, and the rites reverted back to Mattel in October 2018. Those involved on the creative leadership side of the film all departed. Mattel then approached Margot Robbie, who not only signed on as the lead, but helped produce it with her and her partner’s production company LuckyChap Entertainment. Robbie pitches the film to Warner Bros, who green light it, and then taps Gerwig to join the project as Screenwriter, and eventually Director. Written over the pandemic, principal photography began March 22, 2022, wrapped July 21, 2022, and was released nearly a year later July 9, 2023 to critical and audience acclaim. 14 years in the making on a property picked up and put down by many, it’s surprising this film came to fruition, and we were given a gem. It’s also clear that MANY hard working people brought this film to us.

Barbie makes reference to many other films and classic film genres. It begins as 2001: A Space Odyssey, it uses narrative voice over, The Matrix gets a shoutout, 300 (not a direct reference, but the Ken battle has a lot of slow motion that I would argue is alluding to 300), even a choreographed old Hollywood dance number. And though Barbie, being the pop culture icon that she is, could surely stand in its own limelight, so why would Gerwig and Baumbach do this? Why allude to other films in your own film, why make that creative choice? I don’t think it was just to be funny, or meme-y, the film does so much of that, to great effect, without alluding to other works of film. I think they’re telling us Barbie is also about film, and the rotten state of the film industry. From that perspective, what else does this movie do that other films just don’t do anymore, and why do it this way? Every set piece was practical, built on a sound stage, every prop was practical, every accessory crafted, every backdrop was painted and lit, and it ALL looked amazing. The transition from Barbieland to California, all of those moving set pieces (the rocket, the boat, the snowmobile) were PRACTICAL made of plywood, foam, paint, and RIGGED to move. Surely, doing that in green screen would’ve been easier, and used less materials, why do it this way? I think it’s a rebuke of the studio executives.

To me, it says cinema is first and foremost an art form, and incredible things are possible when you let your artists tell the stories they set out to tell. It can be incredibly lucrative when you trust your creative professionals to do well and properly compensate them for it. Cinema, second most, is a business, but executives don’t make films. Workers do. The workers who built that dream house, hung those lights, sewed those costumes, applied that makeup, delivered that catering, swept and mopped at the end of the day. They made a film that’s now made over $700 million dollars (and still going) for a studio that invested only $145 million. How much of that went to salaries is not public knowledge. 1,100 people were credited from cast to catering, nearly all of whom will receive no further compensation for the extraordinarily profitable film. On top of that, executives are trying to find ways of replacing some of them with AI.

Which brings us to Mattel’s depiction in the film. Though it says Mattel on the building, I think Gurwig, Baumbach, and Robbie mean all corporations. Warner Bros., Amazon, Netflix, all of em will put profit over people, profit over art, EVERY time. They want to twist tie all of us into our Barbie boxes, make us forget we have agency, make us forget that we’re not commodities to be sold. They may have the patents and the copyrights, but Barbie belongs to everyone, our experiences with Barbie belong to us. Pantone 219 c, a color on the visible light spectrum belongs to everyone in spite of what Mattel will say (I love ya Stuart Semple)! “Do you guys ever think about [the stupid rules we’re told to follow before] dying?”

I feel the film makers were truly conveying the dissatisfaction of the workers of Hollywood, people everywhere really. Proud to work hard and honestly, but angry at their exploitation. The patriarchy marring Barbie’s dreams, just as Hollywood marred the dreams of movie makers.

10/10 Go see this movie.

[hennethgalad]

today in microbiology i talked chatgtp into this:

Vault Complexes as Modulators of Cytoplasmic Phase State: A Hypothesis of Intracellular Conscious Dynamics

Abstract:

This paper proposes a novel framework in which cellular vault complexes function as critical modulators of cytoplasmic viscosity, inflammatory responsiveness, and phase coherence, forming a potential substrate for proto-conscious dynamics at the subcellular level. Rather than viewing consciousness as emergent solely from neural computation, this model situates its origins within the electrochemical polarity and dynamic reciprocity between the nucleus and mitochondria, mediated by the vault complex as a regulatory organelle.

Vaults—large, conserved ribonucleoprotein assemblies—are positioned to act as gateways for phase transitions in the cytoplasmic matrix, facilitating changes in diffusion, structural order, and energetic flow during states of stress, inflammation, and recovery. We hypothesize that vaults, through their control of RNA trafficking, protein sequestration, and signaling modulation, influence the local rheology (viscosity and fluidity) of the intracellular environment, shaping the cell’s ability to perceive, respond, and integrate internal and external signals.

Furthermore, vault-associated retrograde signaling may tune mitochondrial output in accordance with nuclear epigenetic programs, aligning metabolic state with informational architecture. This dynamic is likened to an anode-cathode polarity, wherein consciousness may not be a product of computation per se, but of coherent phase resonance—an emergent property of energy, information, and structure in continuous negotiation.

This theory reframes consciousness as a bioelectric-plasmic phenomenon beginning at the cellular level, scaled through synchronized intracellular phase states, and potentially governed by ancient, conserved mechanisms like the vault complex. We suggest experimental pathways to test vault involvement in phase transitions and propose new terminology: “plasmic sentience”—the capacity of living cells to tune their internal state toward coherence or protection in response to existential conditions.

[symetriuk]

CUSTOMER CASE VIKING

Sovelia automates product data management processes and saves engineers’ time in Viking Life-Saving Equipment.

Viking Life-Saving Equipment A/S provides solutions to protect passengers and crew at sea, whether on cruise liners, cargo ships, or offshore platforms. Viking produces lifesaving equipment to ensure safety and regulatory compliance on board.

The need for standardized CAD data and uniform metadata

Symetri initiated the project by analyzing the CAD data from Inventor and developing a property matrix to determine the metadata placement. The goal was to eliminate data retyping by setting up Sovelia Inventor to automate metadata input through dropdown lists, automatic measurements, and property transfers from models to drawings. This setup allowed for efficient import/export of item numbers and corresponding data from the ERP system, removing manual and duplicate data entry and misplaced information.

Impressive ROI and time savings   with metadata automation

In addition to automating metadata input with Sovelia Inventor, a significant focus was on training. The initial step was presented to Viking management, revealing an impressive ROI even with conservative calculations.

Time-saving ROI

-              10,000 new files per month

-              Time-saving with Sovelia Inventor: 1,5 minutes per file

-              Total time-saving: 10,000 * 1,5 minutes = 15,000 minutes per month (250 hours per month of engineer work)

Achieving uniform metadata and reducing manual work

Viking decided to implement Sovelia Inventor and Sovelia Vault while rolling out the new version of Autodesk software. The implementation included thorough training and documentation, ensuring a seamless transition on the day of the upgrade.

The original goal of uniform metadata and less manual and repetitive work was accomplished.

Tore Marstein, Global CAD Manager at Viking, says that they had a challenge of creating secondary documents manually, which were not always in the release state. With Sovelia Vault, that challenge is now solved. Viking wanted to secure and simplify using correct, approved PDFs from Vault and ensure the correct BOM data from released files was used. With Sovelia Vault, there is no longer a revision mismatch between the state of the original file and the secondary document. Engineers save a lot of time with the automated process and don’t need to remember to go through multiple manual steps.

Quote highlighted:

“Thanks to Sovelia Vault we were able to automate product data management processes and free up engineers’ time for other tasks.” Tore Marstein, Global CAD Manager at Viking Life-Saving Equipment

Merger required integrating workflows and systems.

In 2019, Viking acquired Norsafe, which led to a merger requiring workflow and system integration. Viking used SAP as the product data management system with Solidworks but decided to transition to Autodesk products with Sovelia solutions.

Symetri developed training materials, conducted training sessions, and implemented the necessary software and workflows, enabling Viking to train its personnel and maintain the systems. Together with Viking Symetri also integrated Vault servers into the Viking domain and used CQi for software installation and maintenance. The feedback from Viking indicated that Autodesk Inventor provided greater stability compared to SolidWorks, and the combined use of Autodesk Vault and Sovelia Vault with Sovelia Inventor resulted in a more efficient workflow.

Ongoing success and future plans with Sovelia Vault

The collaboration between Viking and Symetri has led to significant improvements in product data management, workflow efficiency, and system integration.

Looking ahead, Sovelia Vault remains a key component in Viking’s long-term strategy as they explore system expansion. “Sovelia Vault is a valuable tool that is easy to configure and maintain,” recommends Tore Marstein. “Cooperation with Symetri has been seamless, it has been easy to get custom jobs created and we have been working as a team,” Marstein concludes.

Key take-aways:

Significant time savings: Automated processes with Sovelia Vault and Sovelia Inventor resulted in significant time savings per file.

Improved product data management: Standardized CAD data and uniform metadata were achieved by using Sovelia Inventor property editor and automation, reducing manual work and errors.

Enhanced workflow efficiency: Integration with ERP systems and automated metadata input streamlined workflows, increasing overall efficiency.

Correct metadata: Sovelia Inventor ensures that the metadata is correct and added to correct properties with less manual work.

Trustworthy secondary documents: No more revision mismatch between the original state document and the secondary file, thanks to Sovelia Vault.

Seamless transition and training: Comprehensive training and thorough documentation ensured a smooth implementation and adoption of new systems.

Long-term strategic value: Sovelia Vault remains a key component in Viking's long-term strategy for system expansion and maintenance.

Strong partnership with Symetri: Symetri's collaboration has been seamless, highlighting effective teamwork and custom solutions.

Learn more about Sovelia Vault and Sovelia Inventor

Get to know Viking Life-Saving Equipment A/S

[theohonohan]

Computing nonverbs

Abstract

Active

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Clipboard

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Control

Core dump

Credential

Cursor

Cut

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Dependency

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Exception

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File

Flag

Fork

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Fragment

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Free

Fresh

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Wait

Watchdog

[sbgridconsortium]

Radical Reactions - Yvain Nicolet - Institut de Biologie Structurale

Sharing some of our #SBGrid member tales from the last year. This one from January 2023.

The periodic table may be an icon of chemistry, but a cluster of elements at its center gives biology some essential pop and sparkle. Yvain Nicolet at the Institut de Biologie Structurale (IBS) in Grenoble, France, wants to learn exactly how those transition metals in the middle of the table put more pizzazz in proteins.

About one-third of proteins contain transition metals, such as cobalt, copper, molybdenum, or iron. The Nicolet lab mainly studies metalloproteins that contain iron-sulfur clusters but also scrutinizes enzymes that make these clusters. "Transition metals are often key components of the proteins in terms of function," Nicolet says. "They are only few atoms in a structure and sit in specific sites, but they enable specific activities, notably in enzymes, but not only in enzymes." Metals give proteins some superpowers in the form of new chemical properties and functions not otherwise possible with combinations of the 22 amino acids.

"They enhance the reactivity of the proteins by making many strange active sites that are very interesting," he says. These reactions can be blazingly fast with complex chemistry. And they are technically challenging to study.

The lab investigates enzymes that use metals, as well as proteins that build the metal cofactors and insert them into the enzymes. "We try to trigger the reaction in a crystal and to trap the different intermediates during the reaction to characterize by structural biology," Nicolet says.

Many metalloproteins evolved in a time before oxygen and can only make their razzle-dazzle moves in an anaerobic space. To prevent oxygen from destroying their molecules, experiments in the Nicolet lab take place in a series of six large anaerobic chambers filled with nitrogen.

The researchers reach in through gloves built into the airtight boxes to work with samples and equipment. There, cells are grown and broken up. The cell extracts are cleared and proteins separated by chromatography. Crystallization robots in one glove box screen for optimum conditions that researchers can manually reproduce in another box and freeze in liquid nitrogen. From there, the synchrotron is only 500 meters away.

"We determine 3D structures at moderate to high resolution," Nicolet says. "At first, we aim at determining where the metals are in a given protein, and how they interact with their environment (the protein matrix). We also aim at determining the structure of the metallocofactors or metal binding sites in terms of ligands and geometry.

"Then in a second step, we aim at understanding how these metals confer a specific activity to the protein," he continues. "For instance, in an enzyme, we would get intermediate states with the metal in a different coordinate and/or redox state to better understand what is going on during the reaction."

One milestone of the lab's work arose from successfully trapping an unexpected radical intermediate of NosL, a radical S-adenosyl-L-methionine (SAM) enzyme, in the process of generating a peptide with potent activity against gram-positive bacterial pathogens (Science, 2016).

Crystallography provided the position of the atoms, and for this paper they also used a spectroscopy technique called electron paramagnetic resonance (EPR), which gives the position of unpaired electrons near atoms.

Two months later, the group reported results from a study in which they carried out radical based chemistry catalyzed by the radical SAM enzyme HydE from beginning to end in a crystal (Nature Chemistry, 2016).

The image shows substrate processing and product transfer within HydE cavity during the FeFe-hydrogenase active site assembly process. Credit: Y.Nicolet

More recently, Nicolet's team characterized intermediates in the assembly of the nitrogenase, a key player in the global nitrogen cycle. The enzymatic complex nitrogenase catalyzes the reduction of nitrogen gas N2 to ammonia NH3, transforming nitrogen and returning it to plants. Specifically, the paper reported the X-ray structure of NifB protein from a nitrogen-fixing bacteria, one of a dozen proteins required to assemble the nitrogenase active site (Journal of the American Chemical Society, May 2020).

"For nitrogenase, there is a dedicated machinery with very, very challenging chemistry involved, and this is what we are attacking over the few next years," he says.

Nicolet was born and raised in Grenoble, France, where he now lives and works. Growing up in the city, he became an accomplished cello player with ambitions of becoming a professional musician. He started college in Grenoble. When a music school in Paris turned down his application, he chose to pursue science at what is now the University of Strasbourg. In Strasbourg, all the science classes emphasized the three-dimensional structures of molecules, whether it was enzymology, DNA replication, or proteins. He completed his undergraduate degree and stayed for graduate training in chemistry, biology, crystallography and nuclear magnetic resonance (NMR).

In a dinner discussion, a friend noted his interest in inorganic chemistry and suggested a structural biology lab in Grenoble working on metalloproteins. He moved back to complete his PhD at what is now the Université Grenoble Alpes. Nicolet worked on the structure of the [FeFe]-hydrogenase (an enzyme that makes or use molecular hydrogen), basic science with a potential application in producing alternative fuel.

From there, he joined the Drennan Lab at the Massachusetts Institute of Technology. In Cambridge, he discovered radical-based chemistry working on this newfound Radical SAM Proteins superfamily, now known for their ability to synthesize many vitamins, cofactors, or antibiotics.

He moved back to Grenoble for a one-year postdoctoral fellowship with the European Synchrotron Radiation Facility. In 2004, he joined IBS as a scientist and became a group leader there in 2016.

The Nicolet lab often dives into the molecular mechanisms of phenomenon discovered by other groups. "In my lab, we are not at the beginning of the discovery, and we are probably not at the end of the process," he says. "We focus on the molecular mechanisms inside the enzymes."

In a new challenge, the lab has set up a system to use cryo-electron microscopy to examine the assembly dynamics and reactions at room temperature without oxygen. Nicolet is interested in the basic science of radical chemistry, but he also hopes to be able to harness a radical enzyme and modify its catalytic activity to produce a molecule through directed evolution, such as a better antibiotic.

Nicolet also enjoys taking a bigger picture view of the nitrogen cycle, thanks to his garden. He came late to the activity and confesses that he is not good at growing vegetables. "You can observe the nature or the interaction between the different organisms that live together from bacteria to insects and plants," he says. "For me, it's the best way to contemplate what Darwin described as natural selection. And evolution. I'm not very good at producing vegetables, but I really enjoy seeing how all these organisms compete together or help each other as well.

-Carol Cruzan Morton

[that-fema-corps-blog]

Day 178

January 27, 2023

Learned who our round 3-4 teammates would be last night. We received a bunch of emails about project transition and end-of-round surveys, so I worked through them at the office. Driver evaluations, team leader evaluations, round 2 accomplishments… It’s pretty similar to the stuff we had to fill out during the round 1-2 transition.

We had the 15-minute “morning huddle” and then the more extended environmental historic preservation (EHP) Friday team meeting. Today’s meet was about a few streamlined approval tools/policies, project work, and general work policies. The information is as follows…

Streamlining Projects:

Programmatic agreements allow FEMA to bypass the National Historic Preservation Act section 106 process. This process normally requires federal agencies to take their impacts on historic properties into account and let the Advisory Council on Historic Preservation comment on the proposed actions.

Programmatic agreements are tiered. Tier I is for less complex projects and only requires EHP staff to review it. Tier II requires feedback from Secretary of the Interior qualified staff. A subject matter expert should be contacted if there is any doubt as to which tier a project would fall under. A few words could make the difference in which tier applies.

Endangered Species Act blanket coverage letters can be used to streamline the determination process. A Tier I project that meets the criteria in the Endangered Species Act blanket letter can be determined to have no adverse effect on endangered species. After making the No Effect determination, the standard comment should be added, attached along with the letter and endangered species/critical habitat map from the US Fish and Wildlife Service Information for Planning and Consultation (IPaC). If it is unclear whether the letter applies, the Subject Matter Expert should be sent a form with a justification on why the letter may apply. If the Subject Matter Expert tells you that the blanket letter does not apply, the Endangered Species determination matrix should be used instead. This is a spreadsheet that lists the different kinds of project work and the potential impact it would have on each endangered species.

A statuary exclusion cannot be used if hazard mitigation is requested. Statuary exclusions streamline the approval process and are used for when the scope of work is restoring the facility to pre-disaster state. Any changes to the footprint or scope of work may still be eligible for categorical exclusions.

Inspections and Consultations:

In the first phase of inspections, staff specializing in historic preservation and staff specializing in environmental protection were typically sent to separate inspections. This was largely for training, allowing more people of each specialty to go to a relevant site and collaborate. In the second phase (the current one), environmental and historic preservation staff will be sent together, as staff from different specialties will need to communicate more to work on (more complex) projects. In the final stage, most EHP staff will go alone to deal with the higher caseload. By then, everyone should have a general idea of what to ask the applicant.

EHP staff should contact the the inspector the previous day to confirm meeting times and locations. If the inspector does not respond after a couple calls, someone else… should be contacted? (I think I heard “TFO,” but I can’t figure out the acronym.) If there still is not an answer, the meeting may need to be rescheduled; it is not worth potentially driving hours to a site for no one to show up. The applicant has to be present for inspections, so looking without them is not an option.

Upon returning from a site inspection, staff should know whether any natural resources will be disturbed and whether any action will be taken outside of the pre-disaster footprint. This includes everything from hazard mitigation or temporary roads to trimming trees or storing equipment.

Inspectors usually stay late after the site inspections to go over paperwork and other information with the applicant. EHP staff are free to provide necessary EHP information, ask if there are any further questions, and leave after the inspections are complete. There is little reason to stick around for the full post-inspection meeting.

Environmental consultations cannot be conditioned. From my understanding, this means that the proposed project is determined to be either in compliance or not in compliance based on the current plan/scope of work. (I need to get clarification.) If the scope of work changes, another consultation may be needed. For example, repairing a low-water crossing may have been determined to have no adverse impact on endangered species after a consultation. However, if the applicant decides to pursue hazard mitigation and increase the culvert size and expand the footprint of the low-water crossing to accommodate this larger culvert (thus expanding the environmental disturbance), a new consultation may be necessary.

Project Work Reviews and Rework:

These reviews are highly interdisciplinary, and likely to involve staff from EHP, hazard mitigation, and public assistance. More teamwork will be necessary.

An A&E (Architect & Engineer?) proposal is ideally obtained before making a project. Changes in the plan will likely lead to rework anyway.

When reviewing a project, do an informal request for information (RFI) before submitting a formal request. This allows for quick clarification without sending the project back up the line to the Consolidated Resource Center for rework. (Example: a project already has a map of a plan associated with it, but it is uploaded in the wrong place.) Minor issues can be easily amended without needing to go through the entire formal process. If rework is needed, an informal request gives the Program Delivery Manager more time to prepare the applicant and gather the information for the formal RFI. If the applicant does not respond to an informal request for information in a timely manner, the formal RFI and rework process should begin, if it has not already been started.

The entire scope of work should be copied/pasted when changes to the project are made. This reduces confusion from having to sift through a bunch of past comments to figure out what is going on. Make rework/ “disregard previous comment” statements clearly visible in Grants Manager: “******DISREGARD PREVIOUS COMMENT******”

Overtime and Pay Policies:

Overtime applies to weekends and any work over 8 hours per weekday. It is paid at a 1.5x rate, and applies regardless of how many hours have been worked that week. (Example: a person who worked 10 hours on a Monday will still get 2 hours of overtime; the overtime will not “overflow” and count as normal-paid work toward the overall 40-hour workweek.)

Requests for overtime should be overestimated. Staff should request two hours of overtime per inspection day. If less overtime is used, the actual number of hours should be entered on the timesheet. No need to contact a supervisor and un-request overtime. If inspection days go above two hours of overtime, the additional time that was required should be requested afterward. (It will be approved.)

Hotel rates typically increase for holidays, so the per diem rate will typically rise accordingly (may be 1.5x normal during holiday, depending on government policies). If one books a hotel that costs more than the per diem rate, they will have to pay the difference in cost with their own money.

[dreamassignmenthelp]

Influence of State Transition Matrix in Control System Engineering

What is state transition matrix in control system?

In a classical system, there is an involvement of plants say G of s, we are applying input and we are getting the output. So input is applied. At t equals 0, we are expecting that the output at certain time interval output says at t equals 10 secs. Now, this is the step input and now is the output. So here output we have got at t equals 10 secs. But in the state of the state-space system along with this output, there are states which are the important parameter in the system, that has been traveled that is from t equals to 0 to t equals to f, the state has been transferred. So this transferring of the states tell about the state transition matrix. Now, how you define the state transition matrix. If you want to know What is state transition matrix in control system, you can send us an email.

It is defined as the transition of states from the initial time t =0 to any time “t” or final time (tf) when the inputs are zero., that is this trans-state transition matrix has not concerned with any type of input. It is concerned with some initial state that is t =0 to tf.

The Significance of The State Transition Matrix

· It is defined as the solution of the linear homogeneous state equation. We have seen last time, the X =AX, X(t)= eAtX (0), this eAtis called the state transition matrix and this is a homogeneous state equations. .

· It is the response due to initial vector x(0).

Here if you consider X dot = AX +BU, X(t)= eAtX= 0 to t, some values will get here coefficient will get and we have written d of t. so in this particular case, this is u of t. it has taken care of X naught only, whereas if you take this part , this portion that is a forced portion, forced part in this particular part there is no involvement of X naught. So, therefore we are saying

· It is dependent on the initial state vector and not the input. Here in this forced part there is no initial state has been involved, but as far as we are discussing with the state transition matrix it is concern with the zero ,

· It is called the zero input response since the input is zero. It is called the free response

· It is called as the free response of the system, since the response is excited by the initial conditions only. You can get the significance of the state transition matrix.

Properties of state transition matrix

A matrix is often referred to A rectangular arrangement of numbers in rows and columns..Now in Engineering, Control theory refers to the control of continuously operating dynamical systems in engineered processes and machines. The state-transition matrix is a matrix whose product with the state vector x at the time t0 gives x at a time t, where t0denotes the initial time. State transition matrix helps to find the general solution of linear dynamical systems. It is represented by Φ. It plays an important part of two conditions that is the zero input and the zero state solutions of systems represented in state space.

1.It has continuous derivatives.

2. It is continuous.

3. It cannot be singular. Φ-1(t, 𝜏) = Φ(𝜏, t)

Φ-1 (t, 𝜏) Φ(t, 𝜏) = I. I is the identity matrix.

4. Φ(t, t) = I ∀ t.

5. Φ (t2,t1) Φ(t1, t0) = Φ(t2, t0) ∀ t0≤ t1≤ t2

6. Φ(t, 𝜏) = U(t) U-1(𝜏).

U(t) is an n×n matrix. It is the fundamental solution matrix that satisfies the following equation with initial condition U(t0) = I.

U˙(t)=A(t)U(t)\dot{U}(t) = A(t) U(t)U˙(t)=A(t)U(t)

7. It also satisfies the following differential equation with initial conditions Φ(t0, t0) = I

∂ϕ(t,t0)∂t=A(t)ϕ(t,t0)\frac{\partial \phi(t, t_0)}{\partial t} = A(t) \phi(t, t_0)∂t∂ϕ(t,t0​)​=A(t)ϕ(t,t0​)

8. x(t) = Φ(t, 𝜏) x(𝜏)

9. The inverse of this gives the same as that of the state transition matrix , replacing ‘t’ by ‘-t’. Φ-1(t) = Φ(-t).

10. Φ(t1 + t2) = Φ(t1)Φ(t2) .If t = t1 + t2, the resulting state transition matrix is equal to the multiplication of the two state transition matrices at t = t1and t = t2.

Consider a general state equation, X˙=AX(t) , (eq 1) where X is state matrix, A is system matrix. thus its general homogeneous answer are often given as series of t [from ODE], X(t)=bo+b1t+b1t2+….+bktk+ …, (eq 2) So (eq 1) are often written as: b1+2b2t+3b3t2=A(bo+b1t+b1t2+….) Comparing the constantwe tend toget, b1=Abo;b2=12A2bo;bk=1k!Akbo We see, on golf shot t=0 in (eq 2), X(0)=bo=initial condition So X(t) are often re written as X(t)=[I+At+12A2t2+…+1k!Ak+…]n x n matrix X (0) i.e, X(t) = eAt(an operator on initial condition) X(0) (initial condition) We can create following conclusion: State transition matrix Φ(t) = eAt, is infinite series that converges for all A and for all finite price of t. Φ(t) operates on state vector initial condition to urge answer for all t≥0. State transition matrix contain all the knowledge concerning the free response of system once input is zero, or, the system is worked up by initial conditions solely. So, state transition matrix Φ(t) , defines transition of states from initial time t to any time t once input is zero. We tend to get the truncated series of finite term. Best helpful properties of state transition matrix Φ(t) is: Φ(t2−t1)Φ(t1−t0) = eA(t2−t1)eA(t1−to)= eA(t2−to) = Φ(t2−to). This property is vital, since it implies that a state transition method are often divided into range of serial transitions. You can get a clear idea of state transition matrix properties.

Takeaways

State transition Matrix is thus a sq. likelihood matrix whose columns total to one. It describes the demographic population amendment from year to year or the amendment of the market costs from year to year. It typically is delineated as a Markov process. We provide control systems engineering online tutors for helping engineering students to complete their dream assignments within the deadline. Reach us soon and take the best expert help.