Saturday, November 28, 2009

Quantum Computers, Multiverse Theory And Theory Of Everything

Site of the day: http://insecure.org/

The Fabric of Reality by David Deutsch
http://www.amazon.com/Fabric-Reality-Parallel-Universes-Implications/dp/014027541X





David Elieser Deutsch FRS (born 1953 in Haifa, Israel) is a physicist at the University of Oxford. He is a non-stipendiary Visiting Professor in the Department of Atomic and Laser Physics at the Centre for Quantum Computation, Clarendon Laboratory. He pioneered the field of quantum computers by being the first person to formulate a specifically quantum computational algorithm[1], and is a proponent of the many-worlds interpretation of quantum mechanics.

The Fabric of Reality

In his 1997 book The Fabric of Reality, this interpretation, or what he calls the multiverse hypothesis, is one strand of a four-strand theory of everything. The four strands are:

1. Hugh Everett's many-worlds interpretation theory quantum physics, "the first and most important of the four strands".
2. Karl Popper's epistemology, especially its anti-inductivism and its requiring a realist (non-instrumental) interpretation of scientific theories, and its emphasis on taking seriously those bold conjectures that resist falsification.
3. Alan Turing's theory of computation especially as developed in Deutsch's "Turing principle", Turing's universal Turing machine being replaced by Deutsch's universal quantum computer. ("The theory of computation is now the quantum theory of computation.")
4. Richard Dawkins's refinement of Darwinian evolutionary theory and the modern evolutionary synthesis, especially the ideas of replicator and meme as they integrate with Popperian problem-solving (the epistemological strand).

His theory of everything is (weakly) emergentist rather than reductive. It aims not at the reduction of everything to particle physics, but rather mutual support among multiverse, computational, epistemological, and evolutionary principles.

Views

Politically, Deutsch is known to be sympathetic to libertarianism, and was a founder, along with Sarah Fitz-Claridge of the Taking Children Seriously movement. He is also an atheist.

Awards

He was awarded the Dirac Prize of the Institute of Physics in 1998[2], and the Edge of Computation Science Prize in 2005[3]. The Fabric of Reality was shortlisted for the Rhone-Poulenc science book award in 1998[4].

Forthcoming publications

Deutsch is currently working on a book entitled The Beginning of Infinity, which he hopes to finish in 2009.The book should be printed by Penguin Books Ltd. Amazon.com is reporting it as already printed as of January 29th but not yet available to the public.Such a possibility seems to be a mistake from either the publisher or Amazon.com.

See also: Deutsch-Jozsa algorithm

Notes and References

1. Deutsch, David (July 1985). "Quantum theory, the Church-Turing principle and the universal quantum computer". Proceedings of the Royal Society of London; Series A, Mathematical and Physical Sciences 400 (1818): pp. 97–117. doi:10.1098/rspa.1985.0070. http://web.archive.org/web/20030915061044/http://www.qubit.org/oldsite/resource/deutsch85.pdf. Also available here. Abstract available here.
2. Dirac prize award
3. Edge of Computation Science Prize
4. Rhone-Poulenc 1998 shortlist

(http://en.wikipedia.org/wiki/David_Deutsch)

Tuesday, November 24, 2009

Two circulating beams bring first collisions in the LHC

Site of the day: http://wired.com/

Geneva, 23 November 2009. Today the LHC circulated two beams simultaneously for the first time, allowing the operators to test the synchronization of the beams and giving the experiments their first chance to look for proton-proton collisions. With just one bunch of particles circulating in each direction, the beams can be made to cross in up to two places in the ring. From early in the afternoon, the beams were made to cross at points 1 and 5, home to the ATLAS and CMS detectors, both of which were on the look out for collisions. Later, beams crossed at points 2 and 8, ALICE and LHCb.

“It’s a great achievement to have come this far in so short a time,” said CERN Director General Rolf Heuer. “But we need to keep a sense of perspective – there’s still much to do before we can start the LHC physics programme.”

Beams were first tuned to produce collisions in the ATLAS detector, which recorded its first candidate for collisions at 14:22 this afternoon. Later, the beams were optimised for CMS. In the evening, ALICE had the first optimization, followed by LHCb.

“This is great news, the start of a fantastic era of physics and hopefully discoveries after 20 years' work by the international community to build a machine and detectors of unprecedented complexity and performance," said ATLAS spokesperson, Fabiola Gianotti.

“The events so far mark the start of the second half of this incredible voyage of discovery of the secrets of nature,” said CMS spokesperson Tejinder Virdee.

“It was standing room only in the ALICE control room and cheers erupted with the first collisions” said ALICE spokesperson Jurgen Schukraft. “This is simply tremendous.”

“The tracks we’re seeing are beautiful,” said LHCb spokesperson Andrei Golutvin, “we’re all ready for serious data taking in a few days time.”

These developments come just three days after the LHC restart, demonstrating the excellent performance of the beam control system. Since the start-up, the operators have been circulating beams around the ring alternately in one direction and then the other at the injection energy of 450 GeV. The beam lifetime has gradually been increased to 10 hours, and today beams have been circulating simultaneously in both directions, still at the injection energy.

Next on the schedule is an intense commissioning phase aimed at increasing the beam intensity and accelerating the beams. All being well, by Christmas, the LHC should reach 1.2 TeV per beam, and have provided good quantities of collision data for the experiments’ calibrations.

(http://press.web.cern.ch/press/PressReleases/Releases2009/PR17.09E.html)












Wednesday, November 18, 2009

Neural Stem Cells In Mice Affected By Gene Associated With Longevity

Site of the day: http://forums.digitalpoint.com/

ScienceDaily (Nov. 5, 2009) — A gene associated with longevity in roundworms and humans has been shown to affect the function of stem cells that generate new neurons in the adult brain, according to researchers at the Stanford University School of Medicine. The study in mice suggests that the gene may play an important role in maintaining cognitive function during aging.

"It's intriguing to think that genes that regulate life span in invertebrates may have evolved to control stem cell pools in mammals," said Anne Brunet, PhD, assistant professor of genetics. She is the senior author of the research, which will be published Nov. 6 in Cell Stem Cell.

Unlike your skin or your intestine, your adult brain doesn't make a lot of new cells. But those it does are critical to learning, memory and spatial awareness. To meet these demands, your brain maintains two small caches of neural stem cells, which can both self-renew and give rise to neurons and other cells known as oligodendrocytes and astrocytes. Properly balancing these functions allows you to generate new nerve cells as needed while also maintaining a robust neural stem cell pool.

As mice and other organisms age, the pool of neural stem cells in the brain shrinks and fewer new neurons are generated. These natural changes correlate with the gradual loss of cognitive ability and sensory functions that occur as we approach the end of our lives. However, the life span of some laboratory animals can be artificially extended by mutating genes involved in metabolism, and some humans outlive their life expectancy (about 70 years for someone born in 1960) by decades. Brunet and her colleagues wanted to know why.

The researchers studied a family of transcription factors called FoxO known to be involved in proliferation, differentiation and programmed cell death. FoxO genes are required for the extreme longevity seen in some strains of laboratory roundworms, and a single mutation in the FoxO3 gene has recently been associated with long life in Japanese, German, American and Italian populations.

"We wanted to know if FoxO3 could be involved in regulating the pool of neural stem cells," said Brunet. To do so, the researchers examined laboratory mice in which the FoxO3 gene was knocked out. While mice can live without FoxO3, such mice usually die from cancer between 12 and 18 months after birth. The normal life span of a laboratory mouse is about 30 months.

Brunet and her colleagues used mice of three different ages, both with and without the gene: 1-day-old (newborns), 3-month-old (young adult) and 1-year-old (middle age). They found that, overall, adult and middle-aged mice without FoxO3 had fewer neural stem cells than did age-matched mice with this regulatory protein. There were no significant differences between the newborn mice with and without FoxO3, suggesting that FoxO3 loss only affects adults.

The researchers also discovered that the few stem cells found in the adult mice without FoxO3 more rapidly churned out neural cell precursors -- those cells destined to become new neurons -- than did the mice with normal FoxO3 levels. In fact, the brains of the mice that lacked FoxO3 were heavier than the control group, perhaps because they were burning through their pool of neural stem cells by making too many new nerve cells.

When the researchers looked at the neural stem cell in a laboratory dish, they found that those from young and middle-aged adult mice lacking FoxO3 -- but not those from newborn mice -- seemed to be compromised in their ability to self-renew and to generate the three types of nerve cells. Further investigation bolstered their findings when they discovered that the FoxO3 protein regulates the expression of genes involved in quiescence and differentiation in cells.

The researchers concluded that FoxO3 may be needed for the stem cells to re-enter a waiting state called quiescence that normally occurs after dividing. Cells that are unable to enter quiescence are less able to self-renew and may lose their ability to become any of the three nerve cell types.

Together, the research results suggest that FoxO3 is important to regulate the pool of neural stem cells in the adult brain.

Although the researchers studied mice of varying ages, from birth to about one year, Brunet stressed that their current study does not address changes that might occur in FoxO3 levels or activity over time -- a technically difficult endeavor they are now pursuing.

"We suspect that indeed there will be some changes," said Brunet. "But they will be relatively subtle. We know that the level of FoxO3 doesn't vary drastically, but it's possible the protein becomes less active over a mouse's life span. Or perhaps it simply becomes overwhelmed by the accumulated molecular changes of aging."

Brunet and her colleagues, along with collaborators at the University of Arkansas, are working on creating a mouse in which FoxO3 levels are artificially elevated. If their theory about the function of the protein in the brain is correct, it's possible that the neural stem cell pools of these mice will be protected from the ravages of time.

"We're very interested in understanding how everything unravels during the aging process," said Brunet.

In addition to Brunet, other Stanford researchers involved in the work include postdoctoral scholars Valérie Renault, PhD, Dervis Salih, PhD, and Ashley Webb, PhD; graduate students Victoria Rafalski, Alex Morgan and Saul Villeda; undergraduates Jamie Brett and Camille Guillerey; research assistant Pramod Thekkat; assistant professor of radiation oncology Nicholas Denko, MD, PhD; associate professor of neurosurgery Theo Palmer, PhD; and assistant professor of medicine and of pediatrics Atul Butte, MD, PhD.

The research was funded by the National Institutes of Health, the California Institute for Regenerative Medicine, the Brain Tumor Society, the Esther A. & Joseph Klingenstein Fund Inc., the American Federation for Aging Research, the National Science Foundation, the Lucile Packard Foundation for Children's Health and the National Library of Medicine.

(http://www.sciencedaily.com/releases/2009/11/091105132450.htm)

Researcher Discovers Key to Vital DNA, Protein Interaction


Site of the day: http://forums.digitalpoint.com/

ScienceDaily (Nov. 13, 2009) — A researcher at Iowa State University has discovered how a group of proteins from plant pathogenic bacteria interact with DNA in the plant cell, opening up the possibility for what the scientist calls a "cascade of advances."

Adam Bogdanove, associate professor in plant pathology, was researching the molecular basis of bacterial diseases of rice when he and Matthew Moscou, a student in the bioinformatics and computation biology graduate program, discovered that the so-called TAL effector proteins injected into plant cells by strains of the bacterium Xanthomonas attach at specific locations to host DNA molecules.

They found that different proteins of this class bind to different DNA locations, and particular amino acids in each protein determine those locations, called binding sites, in a very straightforward way.

"When we hit on it, we thought, 'Wow, this is so simple, it's ridiculous,'" Bogdanove said. Bogdanove's research will be published in an upcoming issue of the journal Science and is highlighted in last week's Science Express, an early online edition for research the Science editors feel is particularly timely and important. The paper is being published alongside a study from another research team that arrived at the same conclusions independently.

In his research, Bogdanove was examining how Xanthomonas uses TAL effectors to manipulate gene function in plants in ways that benefit the pathogen. Bogdanove was specifically interested in how different TAL effector proteins are able to activate different corresponding plant genes.

Over the past decade, understanding of this unique class of proteins has grown in leaps and bounds, according to Bogdanove.

Researchers in Germany, at Kansas State University, Manhattan; and here at Iowa State (Bing Yang, assistant professor in genetics development and cell biology) had previously shown that these proteins bind host DNA and activate genes important for disease, or in some cases defense against the bacteria. But no one yet understood how different TAL effectors recognized different parts of the DNA in order to attach and turn on the different genes at those locations.

Through computer analyses, Bogdanove and Moscou discovered that pairs of amino acids distributed throughout a TAL effector protein each specify a particular nucleotide, one of the bases in DNA abbreviated as the letters G, A, T, or C. The complete set of these pairs directs the protein to a matching string of Gs, As, Ts, and Cs in the DNA.

"This simple relationship allows us to predict where a TAL effector will bind, and what genes it will activate. It also makes it likely that we can custom engineer TAL effectors to bind to virtually any DNA sequence," says Bogdanove.

According to Bogdanove, being able to predict TAL effector binding sites will lead quickly to the identification of plant genes that are important in disease. Natural variants that lack these binding sites are a potential source of disease resistance.

Another potential application is adding TAL effector binding sites to defense-related genes so they are activated upon infection.

The possibilities for this new technology extend beyond plant disease control, according to Bogdanove.

"We might be able to use TAL effectors to activate genes in non-plant cells, possibly even in human stem cells for gene therapy. Or we might be able to use them to modify DNA at specific locations and help us study gene function. This could apply in many areas, including cancer research, for example," he said.

Bogdanove said the simplicity of the results surprised the research team.

"A predictable and potentially customizable kind of protein-DNA binding has been hard to find in nature. As Matt and I talked about the possibilities, we got excited and one of us said -- I don't remember who -- 'We've got to submit this to Science, dude,'" said Bogdanove.

Moscou investigated TAL effector DNA binding with Bogdanove through his participation in the Bioinformatics and Computation Biology (BCB) Lab, a student-run organization that provides assistance with computational analyses for life science researchers on campus. Moscou is a founding member of the BCB Lab, which is supported by a training grant to the BCB graduate program from the National Science Foundation. Moscou is doing his dissertation research on a plant pathogenic fungus under Roger Wise, professor in plant pathology.

Research in the Bogdanove laboratory is supported by funding from the NSF Plant Genome Research Program and from the United Stated Department of Agriculture -- Agricultural and Food Research Initiative program.

(http://www.sciencedaily.com/releases/2009/11/091110171654.htm)

Saturday, November 7, 2009

Looking At The Compact Disc

Site of the day: http://molecularstation.com/

All human DNA information can be written on two CDs
Oh yeah, humans are limitless ;).
Moreover, only small part of it is utilized in protein synthesis.

Kolmogorov Complexity

Site of the day: http://molecularstation.com/

Wikipedia - Kolmogorov complexity
http://en.wikipedia.org/wiki/Kolmogorov_complexity

Graph Theory

Site of the day: http://molecularstation.com/

Wikipedia - Graph Theory
http://en.wikipedia.org/wiki/Graph_theory

Formal Languages

Site of the day: http://molecularstation.com/

Wikipedia - Formal language
http://en.wikipedia.org/wiki/Formal_language

Wednesday, November 4, 2009

Organ Regeneration In Zebrafish: Unraveling The Mechanisms

Site of the day: http://forums.digitalpoint.com/

ScienceDaily (Nov. 2, 2009) — The search for the holy grail of regenerative medicine -- the ability to "grow back" a perfect body part when one is lost to injury or disease -- has been under way for years, yet the steps involved in this seemingly magic process are still poorly understood.

Now researchers at the Salk Institute for Biological Studies have identified an essential cellular pathway in zebrafish that paves the way for limb regeneration by unlocking gene expression patterns last seen during embryonic development. They found that a process known as histone demethylation switches cells at the amputation site from an inactive to an active state, which turns on the genes required to build a copy of the lost limb.

"This is the first real molecular insight into what is happening during limb regeneration," says first author Scott Stewart, Ph.D., a postdoctoral researcher in the lab of Juan Carlos Izpisúa Belmonte, Ph.D., who led the Salk team. "Until now, how amputation is translated into gene activation has been like magic. Finally we have a handle on a process we can actually follow."
Their findings, which will be published in a forthcoming issue of Proceedings of the National Academy of Sciences, U.S.A., help to explain how epimorphic regeneration -- the regrowing of morphologically and functionally perfect copies of amputated limbs -- is controlled, an important step toward understanding why certain animals can do it and we cannot.

"Our experiments show that normal development and limb regeneration are controlled by similar mechanisms," explains Izpisúa Belmonte, a professor in the Gene Expression Laboratory. "This finding will help us to ask more specific questions about mammalian limb regeneration: Are the same genes involved when we amputate a mammalian limb? If not, what would happen if we turned them on? And if we can affect these methylation marks in an amputated limb, what effect would that have?"

The Belmonte lab uses zebrafish, a small fish from the minnow family, to study limb regeneration. "If you amputate the tail of the zebrafish, it regenerates in about a week, seemingly with no effort and leaving no scar," explains Stewart. "What's more, it regenerates a perfect copy and -- like growing grass -- it will do this over and over again."
Since regeneration recapitulates in broad strokes embryonic development, during which a complex multi-cellular organism develops from a handful of embryonic stem cells, the researchers began by comparing gene expression patterns between the two processes. During development, genes within specific cell types are turned on and off to trigger the necessary expression patterns that create a whole animal. Once their job is done, they lie silently till they are turned on once again following amputation.

Based on these similarities, Stewart reasoned that genes involved in regeneration may share silencing mechanisms with the ones active in embryonic stem cells. Embryonic stem cells are maintained in a ready-to-go state, "poised" for action to become whatever cell type is needed. The key to this "poised" state are histones, DNA packaging proteins that are also used as carriers for chemical modifications, such as methylation and acetylation. These chemical marks serve as "on" and "off" switches for specific genes.

Stewart discovered that the histone modifications that poise embryonic stem cell-specific genes for activation are also found on the histones near genes involved in regeneration, putting them into a ready-to-go state. "This suggests that two different gene expression programs may exist; one for normal cellular activity and one for regeneration," explains Stewart. To test this hypothesis, the team looked at the histone marks during regeneration. As suspected, they saw a reduction in "off" switches and an increase in "on" switches in regenerating tissue, tipping the balance toward gene expression.

Delving deeper, the researchers found that enzymes that remove the "off" mark, so-called demethylases, are present in high levels in regenerating tissue. One enzyme in particular, called Kdm6b.1, is found exclusively in cells that are undergoing the regeneration process. Without Kdm6b.1, zebrafish failed to regenerate amputated fins, meaning removal of the "off" mark is a prerequisite for fin regeneration.

In the long term, the Salk researchers hope that these findings will help them understand whether we can affect the outcome of mammalian limb regeneration. In the more immediate future, the team plans to use global approaches to identify all the targets of Kdm6b.1 during regeneration, and to find out what gives the signal to turn these genes off when regeneration is complete.

In addition to Stewart and Izpisúa Belmonte, Zhi-Yang Tsun, also contributed to the study.
The study was funded in part by the California Institute for Regenerative Medicine, the Fundacion Cellex, the G. Harold and Leila Y. Mathers Charitable Foundation, the Ipsen Foundation, and the National Institutes of Health.

(http://www.sciencedaily.com/releases/2009/11/091102171419.htm)

Systems Theory

Site of the day: http://forums.digitalpoint.com/

Wikipedia - Systems theory
http://en.wikipedia.org/wiki/Systems_Theory

On Control Theory

Site of the day: http://forums.digitalpoint.com/

Well, in fact control theory worth learning only in cases, when you are going to construct or analyze complex automatical systems. Otherwise, it's like wasting time.

Control theory

Site of the day: http://forums.digitalpoint.com/


Control theory is an interdisciplinary branch of engineering and mathematics, that deals with the behavior of dynamical systems. The desired output of a system is called the reference. When one or more output variables of a system need to follow a certain reference over time, a controller manipulates the inputs to a system to obtain the desired effect on the output of the system.


Contents
1 Overview
1.1 An example
2 History
3 People in systems and control
4 Classical control theory
4.1 Closed-loop transfer function
4.2 PID controller
5 Modern control theory
6 Topics in control theory
6.1 Stability
6.2 Controllability and observability
6.3 Control specifications
6.4 Model identification and robustness
7 System classifications
7.1 Linear control
7.2 Nonlinear control
8 Main control strategies


Overview

Control theory is
a theory that deals with influencing the behavior of dynamical systems
an interdisciplinary subfield of science, which originated in engineering and mathematics, and evolved into use by the social sciences, like psychology, sociology and criminology.

An example

Consider an automobile's cruise control, which is a device designed to maintain a constant vehicle speed; the desired or reference speed, provided by the driver. The system in this case is the vehicle. The system output is the vehicle speed, and the control variable is the engine's throttle position which influences engine torque output.
A primitive way to implement cruise control is simply to lock the throttle position when the driver engages cruise control. However, on mountain terrain, the vehicle will slow down going uphill and accelerate going downhill. In fact, any parameter different than what was assumed at design time will translate into a proportional error in the output velocity, including exact mass of the vehicle, wind resistance, and tire pressure. This type of controller is called an open-loop controller because there is no direct connection between the output of the system (the vehicle's speed) and the actual conditions encountered; that is to say, the system does not and can not compensate for unexpected forces.
In a closed-loop control system, a sensor monitors the output (the vehicle's speed) and feeds the data to a computer which continuously adjusts the control input (the throttle) as necessary to keep the control error to a minimum (that is, to maintain the desired speed). Feedback on how the system is actually performing allows the controller (vehicle's on board computer) to dynamically compensate for disturbances to the system, such as changes in slope of the ground or wind speed. An ideal feedback control system cancels out all errors, effectively mitigating the effects of any forces that may or may not arise during operation and producing a response in the system that perfectly matches the user's wishes.

History

Although control systems of various types date back to antiquity, a more formal analysis of the field began with a dynamics analysis of the centrifugal governor, conducted by the physicist James Clerk Maxwell in 1868 entitled On Governors.[1] This described and analyzed the phenomenon of "hunting", in which lags in the system can lead to overcompensation and unstable behavior. This generated a flurry of interest in the topic, during which Maxwell's classmate Edward John Routh generalized the results of Maxwell for the general class of linear systems.[2] Independently, Adolf Hurwitz analyzed system stability using differential equations in 1877. This result is called the Routh-Hurwitz theorem.[3][4]
A notable application of dynamic control was in the area of manned flight. The Wright Brothers made their first successful test flights on December 17, 1903 and were distinguished by their ability to control their flights for substantial periods (more so than the ability to produce lift from an airfoil, which was known). Control of the airplane was necessary for safe flight.
By World War II, control theory was an important part of fire-control systems, guidance systems and electronics. The Space Race also depended on accurate spacecraft control. However, control theory also saw an increasing use in fields such as economics.

People in systems and control


Main article: People in systems and control

Many active and historical figures made significant contribution to control theory, including, for example:
Alexander Lyapunov (1857-1918) in the 1890s marks the beginning of stability theory.
Harold S. Black (1898-1983), invented the concept of negative feedback amplifiers in 1927. He managed to develop stable negative feedback amplifiers in the 1930s.
Harry Nyquist (1889-1976), developed the Nyquist stability criterion for feedback systems in the 1930s.
Richard Bellman (1920-1984), developed dynamic programming since the 1940s.
Andrey Kolmogorov (1903-1987) co-developed the Wiener-Kolmogorov filter (1941).
Norbert Wiener (1894-1964) co-developed the Wiener-Kolmogorov filter and coined the term cybernetics in the 1940s.
John R. Ragazzini (1912-1988) introduced digital control and the z-transform in the 1950s.
Lev Pontryagin (1908-1988) introduced the maximum principle and the bang-bang principle.

Classical control theory

To avoid the problems of the open-loop controller, control theory introduces feedback. A closed-loop controller uses feedback to control states or outputs of a dynamical system. Its name comes from the information path in the system: process inputs (e.g. voltage applied to an electric motor) have an effect on the process outputs (e.g. velocity or torque of the motor), which is measured with sensors and processed by the controller; the result (the control signal) is used as input to the process, closing the loop.
Closed-loop controllers have the following advantages over open-loop controllers:
disturbance rejection (such as unmeasured friction in a motor)
guaranteed performance even with model uncertainties, when the model structure does not match perfectly the real process and the model parameters are not exact
unstable processes can be stabilized
reduced sensitivity to parameter variations
improved reference tracking performance
In some systems, closed-loop and open-loop control are used simultaneously. In such systems, the open-loop control is termed feedforward and serves to further improve reference tracking performance.
A common closed-loop controller architecture is the PID controller.



Closed-loop transfer function


The output of the system y(t) is fed back through a sensor measurement F to the reference value r(t). The controller C then takes the error e (difference) between the reference and the output to change the inputs u to the system under control P. This is shown in the figure. This kind of controller is a closed-loop controller or feedback controller.
This is called a single-input-single-output (SISO) control system; MIMO (i.e. Multi-Input-Multi-Output) systems, with more than one input/output, are common. In such cases variables are represented through vectors instead of simple scalar values. For some distributed parameter systems the vectors may be infinite-dimensional (typically functions).



If we assume the controller C, the plant P, and the sensor F are linear and time-invariant (i.e.: elements of their transfer function C(s), P(s), and F(s) do not depend on time), the systems above can be analysed using the Laplace transform on the variables. This gives the following relations:



Solving for Y(s) in terms of R(s) gives:


The expression


is referred to as the closed-loop transfer function of the system. The numerator is the forward (open-loop) gain from r to y, and the denominator is one plus the gain in going around the feedback loop, the so-called loop gain.

If


i.e. it has a large norm with each value of s, and if
then Y(s) is approximately equal to R(s). This means simply setting the reference controls the output.

PID controller



The PID controller is probably the most-used feedback control design. "PID" means Proportional-Integral-Derivative, referring to the three terms operating on the error signal to produce a control signal. If u(t) is the control signal sent to the system, y(t) is the measured output and r(t) is the desired output, and tracking error e(t) = r(t) − y(t), a PID controller has the general form
The desired closed loop dynamics is obtained by adjusting the three parameters KP, KI and KD, often iteratively by "tuning" and without specific knowledge of a plant model. Stability can often be ensured using only the proportional term. The integral term permits the rejection of a step disturbance (often a striking specification in process control). The derivative term is used to provide damping or shaping of the response. PID controllers are the most well established class of control systems: however, they cannot be used in several more complicated cases, especially if MIMO systems are considered.


with the PID controller transfer function


Modern control theory

In contrast to the frequency domain analysis of the classical control theory, modern control theory utilizes the time-domain state space representation, a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations. To abstract from the number of inputs, outputs and states, the variables are expressed as vectors and the differential and algebraic equations are written in matrix form (the latter only being possible when the dynamical system is linear). The state space representation (also known as the "time-domain approach") provides a convenient and compact way to model and analyze systems with multiple inputs and outputs. With inputs and outputs, we would otherwise have to write down Laplace transforms to encode all the information about a system. Unlike the frequency domain approach, the use of the state space representation is not limited to systems with linear components and zero initial conditions. "State space" refers to the space whose axes are the state variables. The state of the system can be represented as a vector within that space.


Topics in control theory


Stability


The stability of a general dynamical system with no input can be described with Lyapunov stability criteria. A linear system that takes an input is called bounded-input bounded-output (BIBO) stable if its output will stay bounded for any bounded input. Stability for nonlinear systems that take an input is input-to-state stability (ISS), which combines Lyapunov stability and a notion similar to BIBO stability. For simplicity, the following descriptions focus on continuous-time and discrete-time linear systems.
Mathematically, this means that for a causal linear system to be stable all of the poles of its transfer function must satisfy some criteria depending on whether a continuous or discrete time analysis is used:
In continuous time, the Laplace transform is used to obtain the transfer function. A system is stable if the poles of this transfer function lie strictly in the closed left half of the complex plane (i.e. the real part of all the poles is less than zero).
In discrete time the Z-transform is used. A system is stable if the poles of this transfer function lie strictly inside the unit circle. i.e. the magnitude of the poles is less than one).
When the appropriate conditions above are satisfied a system is said to be asymptotically stable: the variables of an asymptotically stable control system always decrease from their initial value and do not show permanent oscillations. Permanent oscillations occur when a pole has a real part exactly equal to zero (in the continuous time case) or a modulus equal to one (in the discrete time case). If a simply stable system response neither decays nor grows over time, and has no oscillations, it is marginally stable: in this case the system transfer function has non-repeated poles at complex plane origin (i.e. their real and complex component is zero in the continuous time case). Oscillations are present when poles with real part equal to zero have an imaginary part not equal to zero.
Differences between the two cases are not a contradiction. The Laplace transform is in Cartesian coordinates and the Z-transform is in circular coordinates, and it can be shown that


-the negative-real part in the Laplace domain can map onto the interior of the unit circle
-the positive-real part in the Laplace domain can map onto the exterior of the unit circle

If a system in question has an impulse response of
then the Z-transform (see this example), is given by


which has a pole in z = 0.5 (zero imaginary part). This system is BIBO (asymptotically) stable since the pole is inside the unit circle.
However, if the impulse response was
then the Z-transform is

which has a pole at z = 1.5 and is not BIBO stable since the pole has a modulus strictly greater than one.
Numerous tools exist for the analysis of the poles of a system. These include graphical systems like the root locus, Bode plots or the Nyquist plots.
Mechanical changes can make equipment (and control systems) more stable. Sailors add ballast to improve the stability of ships. Cruise ships use antiroll fins that extend transversely from the side of the ship for perhaps 30 feet (10 m) and are continuously rotated about their axes to develop forces that oppose the roll.

Controllability and observability

Main articles: Controllability and Observability

Controllability and observability are main issues in the analysis of a system before deciding the best control strategy to be applied, or whether it is even possible to control or stabilize the system. Controllability is related to the possibility of forcing the system into a particular state by using an appropriate control signal. If a state is not controllable, then no signal will ever be able to control the state. If a state is not controllable, but its dynamics are stable, then the state is termed Stabilizable. Observability instead is related to the possibility of "observing", through output measurements, the state of a system. If a state is not observable, the controller will never be able to determine the behaviour of an unobservable state and hence cannot use it to stabilize the system. However, similar to the stabilizability condition above, if a state cannot be observed it might still be detectable.
From a geometrical point of view, looking at the states of each variable of the system to be controlled, every "bad" state of these variables must be controllable and observable to ensure a good behaviour in the closed-loop system. That is, if one of the eigenvalues of the system is not both controllable and observable, this part of the dynamics will remain untouched in the closed-loop system. If such an eigenvalue is not stable, the dynamics of this eigenvalue will be present in the closed-loop system which therefore will be unstable. Unobservable poles are not present in the transfer function realization of a state-space representation, which is why sometimes the latter is preferred in dynamical systems analysis.
Solutions to problems of uncontrollable or unobservable system include adding actuators and sensors.

Control specifications

Several different control strategies have been devised in the past years. These vary from extremely general ones (PID controller), to others devoted to very particular classes of systems (especially robotics or aircraft cruise control).
A control problem can have several specifications. Stability, of course, is always present: the controller must ensure that the closed-loop system is stable, regardless of the open-loop stability. A poor choice of controller can even worsen the stability of the open-loop system, which must normally be avoided. Sometimes it would be desired to obtain particular dynamics in the closed loop: i.e. that the poles have



where λ is a fixed value strictly greater than zero, instead of simply ask that Re[λ] <>

Another typical specification is the rejection of a step disturbance; including an integrator in the open-loop chain (i.e. directly before the system under control) easily achieves this. Other classes of disturbances need different types of sub-systems to be included.



Other "classical" control theory specifications regard the time-response of the closed-loop system: these include the rise time (the time needed by the control system to reach the desired value after a perturbation), peak overshoot (the highest value reached by the response before reaching the desired value) and others (settling time, quarter-decay). Frequency domain specifications are usually related to robustness (see after).
Modern performance assessments use some variation of integrated tracking error (IAE,ISA,CQI).



Model identification and robustness

Main article: System identification

A control system must always have some robustness property. A robust controller is such that its properties do not change much if applied to a system slightly different from the mathematical one used for its synthesis. This specification is important: no real physical system truly behaves like the series of differential equations used to represent it mathematically. Typically a simpler mathematical model is chosen in order to simplify calculations, otherwise the true system dynamics can be so complicated that a complete model is impossible.

System identification

The process of determining the equations that govern the model's dynamics is called system identification. This can be done off-line: for example, executing a series of measures from which to calculate an approximated mathematical model, typically its transfer function or matrix. Such identification from the output, however, cannot take account of unobservable dynamics. Sometimes the model is built directly starting from known physical equations: for example, in the case of a mass-spring-damper system we know that
Even assuming that a "complete" model is used in designing the controller, all the parameters included in these equations (called "nominal parameters") are never known with absolute precision; the control system will have to behave correctly even when connected to physical system with true parameter values away from nominal.
Some advanced control techniques include an "on-line" identification process (see later). The parameters of the model are calculated ("identified") while the controller itself is running: in this way, if a drastic variation of the parameters ensues (for example, if the robot's arm releases a weight), the controller will adjust itself consequently in order to ensure the correct performance.
Analysis
Analysis of the robustness of a SISO control system can be performed in the frequency domain, considering the system's transfer function and using Nyquist and Bode diagrams. Topics include gain and phase margin and amplitude margin. For MIMO and, in general, more complicated control systems one must consider the theoretical results devised for each control technique (see next section): i.e., if particular robustness qualities are needed, the engineer must shift his attention to a control technique including them in its properties.
Constraints
A particular robustness issue is the requirement for a control system to perform properly in the presence of input and state constraints. In the physical world every signal is limited. It could happen that a controller will send control signals that cannot be followed by the physical system: for example, trying to rotate a valve at excessive speed. This can produce undesired behavior of the closed-loop system, or even break actuators or other subsystems. Specific control techniques are available to solve the problem: model predictive control (see later), and anti-wind up systems. The latter consists of an additional control block that ensures that the control signal never exceeds a given threshold.

System classifications

Linear control

Main article: State space (controls)

For MIMO systems, pole placement can be performed mathematically using a state space representation of the open-loop system and calculating a feedback matrix assigning poles in the desired positions. In complicated systems this can require computer-assisted calculation capabilities, and cannot always ensure robustness. Furthermore, all system states are not in general measured and so observers must be included and incorporated in pole placement design.

Nonlinear control

Main article: Nonlinear control

Processes in industries like robotics and the aerospace industry typically have strong nonlinear dynamics. In control theory it is sometimes possible to linearize such classes of systems and apply linear techniques, but in many cases it can be necessary to devise from scratch theories permitting control of nonlinear systems. These, e.g., feedback linearization, backstepping, sliding mode control, trajectory linearization control normally take advantage of results based on Lyapunov's theory. Differential geometry has been widely used as a tool for generalizing well-known linear control concepts to the non-linear case, as well as showing the subtleties that make it a more challenging problem.

Main control strategies

Every control system must guarantee first the stability of the closed-loop behavior. For linear systems, this can be obtained by directly placing the poles. Non-linear control systems use specific theories (normally based on Aleksandr Lyapunov's Theory) to ensure stability without regard to the inner dynamics of the system. The possibility to fulfill different specifications varies from the model considered and the control strategy chosen. Here a summary list of the main control techniques is shown:


-Adaptive control
Adaptive control uses on-line identification of the process parameters, or modification of controller gains, thereby obtaining strong robustness properties. Adaptive controls were applied for the first time in the aerospace industry in the 1950s, and have found particular success in that field.


-Hierarchical control
A Hierarchical control system is a type of Control System in which a set of devices and governing software is arranged in a hierarchical tree. When the links in the tree are implemented by a computer network, then that hierarchical control system is also a form of Networked control system.


-Intelligent control
Intelligent control use various AI computing approaches like neural networks, Bayesian probability, fuzzy logic, machine learning, evolutionary computation and genetic algorithms to control a dynamic system.


-Optimal control
Optimal control is a particular control technique in which the control signal optimizes a certain "cost index": for example, in the case of a satellite, the jet thrusts needed to bring it to desired trajectory that consume the least amount of fuel. Two optimal control design methods have been widely used in industrial applications, as it has been shown they can guarantee closed-loop stability. These are Model Predictive Control (MPC) and Linear-Quadratic-Gaussian control (LQG). The first can more explicitly take into account constraints on the signals in the system, which is an important feature in many industrial processes. However, the "optimal control" structure in MPC is only a means to achieve such a result, as it does not optimize a true performance index of the closed-loop control system. Together with PID controllers, MPC systems are the most widely used control technique in process control.


-Robust control
Robust control deals explicitly with uncertainty in its approach to controller design. Controllers designed using robust control methods tend to be able to cope with small differences between the true system and the nominal model used for design. The early methods of Bode and others were fairly robust; the state-space methods invented in the 1960s and 1970's were sometimes found to lack robustness. A modern example of a robust control technique is H-infinity loop-shaping developed by Duncan McFarlane and Keith Glover of Cambridge University, United Kingdom. Robust methods aim to achieve robust performance and/or stability in the presence of small modeling errors.


-Stochastic control
Stochastic control deals with control design with uncertainty in the model. In typical stochastic control problems, it is assumed that there exist random noise and disturbances in the model and the controller, and the control design must take into account these random deviations.

(http://en.wikipedia.org/wiki/Control_theory)




Tuesday, November 3, 2009

Feedback Control Systems

Site of the day: http://www.johnchow.com/

Feedback Control Systems by Charles L. Phillips, Royce D. Harbor
http://www.amazon.com/Feedback-Control-Systems-Charles-Phillips/dp/0139490906/ref=ntt_at_ep_dpt_2

This combines well with Donald E. Knuth's "Art of Computer Programming"
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John Chow is cool. And he IS a good marketer.