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Fractals, Chaos, and Control Systems on Rails


Control Systems 102: GNC, Control

Posted by Harry Seldon on May 04, 2009

This post is part of a series about Guidance, Navigation and Control. See the table of contents here.

Stability and Control

Control answers the question ”How can the vehicle be stable?”. For an aircraft, it means “how can the aircraft accomplish basic moves such as flying straight, climbing, descending?”. A more technical definition of stability would be “the tendency of the vehicle to maintain or deviate from an established flight condition”. Control is the ability of the vehicle to be manoeuvred or steered from one flight condition to another.
It is very important to notice that questions regarding the stability (as opposed to a crash) are mainly addressed by the control and not the guidance nor the navigation. That is why one often speaks about Stability and Control System (SCS) and not only Control System.
The SCS is made of two parts: Stability Augmentation System (SAS) that stabilizes the aircraft (if it is naturally unstable) and improves its handling qualities. Then, the Control Augmentation System (CAS) typically allows the vehicle to maintain its altitude or heading. These functions are called altitude hold and heading hold modes in the AutoPilot (AP). The SCS creates the low level orders directly sent to the actuators (ailerons, rudder, elevator, engines, etc.). It is also sometimes called the Piloting System, meaning piloting is associated to low level, stabilization work.
Thus, how to fly is known by the control. Once it is done, higher level objectives can be achieved such as following a trajectory, that is going from a point A to a point B. High level orders will be sent by the guidance system.


Next chapter will be about Guidance.

Stability and Control
About GNC written GN&C or GCN written GC&N
About the human pilot
About control loops

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Control Systems 102: GNC, Navigation

Posted by Harry Seldon on April 27, 2009

This post is part of a series about Guidance, Navigation and Control. See the table of contents here.


Navigation (Nav) refers to the question ”where is currently the vehicle?”. A Navigation System (NS) aims at giving you your position. Nowadays the main sensor associated to navigation is definitely a GPS (Global Positioning System) sensor. More generally the Nav collects all the data from the sensors and processes them to make a precise, smooth and high frequency information about position and speed.
The main control theory tool for navigation is probably the Kalman filter. Typically, embedded on board an aircraft, the navigation will combine GPS data, air data, inertial data and the aircraft dynamical model into a Kalman filter.


Next chapter will be about Stability and Control.

Stability and Control
About GNC written GN&C or GCN written GC&N
About the human pilot
About control loops

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Control Systems 102: GNC, Guidance, Navigation and Control, Introduction

Posted by Harry Seldon on April 27, 2009

Guidance, Navigation and Control are often together. It makes perfect sense because all three of them depend on control theory and because they are the components of the software part of a Control System. But do you clearly know the differences between Guidance, Navigation and Control? I am going to explain them taking the example of an aircraft. In future posts I will take other examples such as a company, a country government or the go game. This series of posts is a follow up of Control Systems 101.


This post was quite long so I decided to cut it in several parts. Even cut in several parts, the point remains to consider GNC as a whole, it is not to make extensive explanations on each topic. Wikipedia would be fine for this, whereas it is not so good as far as the GNC topic is concerned. According to your comments, I may update Wikipedia with the little work made here.

The first chapter presents the Navigation System.

Here is the Table of Contents (TOC):

Stability and Control
About GNC written GN&C or GCN written GC&N
About the human pilot
About control loops

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There will be war, or, how to prevent it

Posted by Harry Seldon on February 27, 2009

For some time, I have wanted to post about “crises are natural preludes to wars”. I am definitely not that qualified to say that, so I am glad these guys (LEAP experts) are. They predicted quite well the crisis, they invented the word “global systemic crisis” back in 2006. What they say is very scary. Even if they do their best not to mention “war”, they speak about “global geopolitical dislocation”, “tragic consequences” and say “the world will look more like Europe in 1913 rather than our world in 2007”. However, as I am an optimistic guy, let me remind you that I have good news about the crisis and that controls and that genius can save us.

In case I am not clear about why controls can save the world, here is the short version: uncontrolled systems, like natural systems are almost always unstable and chaotical. Chaotical systems (1) are ‘worse’ than unstable because they look like they are stable, like they are converging to a limit but actually at about any time they can diverge. So nothing is worse than “no control”. At worst a bad control leaves us in an uncontrolled situation.
Therefore, the world needs more control at all scales from “personnal self-control” to “World control” going through cities, regions, states, or countries control systems. In case you wonder, I am really not speaking of some kind of a Big Brother, fascist, centralized control system. I am more speaking of a democratic, distributed (decentralized) control system. If you are a computer scientist think about the Git Distributed Version Control System, (intro to git here, graphical explanation here). I will explain more in details what I am thinking about in a later post. Remember my point for today. There is no real choice it is either control or war. War, being the expression of the natural divergence of an uncontrolled human system; WWIII would be a ‘game over’ for the world. However, once you choose control, there are plenty of possibilities, stay tuned.

For French readers, I learnt about that article from the LEAP reading this on yahoo news and that article is itself directly taken from Le Monde.

(1) Climate or Volcanoes are good examples of chaotical systems. For a long time they look quiet, and all of a sudden they explode. So yes, they should be controlled. CO2 control is an attempt for climate. Not sure it will work, not sure it is really useful but it is definitely worth trying it. I have a humoristic post about a volcano control system in preparation.

PS If you are interested in controls questions, please join the control theory group on Facebook.
PPS If you wonder what ThinkoSphere is doing in all that, I will speak about it in a later post. But you are definitely right, it is related.

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Facebook's Control Theory group, you know you are a Control theorist when

Posted by Harry Seldon on February 26, 2009

You will want to join the Control Theory group on Facebook if, or you know you are a Control theorist when:

  • For you, Vibration Control is not only a Sex toy.

  • Finding the good frequency is not only the problem of your girlfriend.

  • “Slower, Faster, now it is good” reminds you your work.

  • You see everything as a control system. (which is called being controlphrenic)

  • You have already thought “laws are way too complex, a PID would do the job”.

  • You have already said to your lawyer “Don’t tell me about laws, I am designing them all day”.

  • Every 10 words you say is either feedback, stable, unstable, transient, control or state.

  • Kalman is some god.

  • Navigation is for you another word for Kalman filter.

  • You know the difference between guidance, navigation and controls.

  • For you, airplanes, rockets, cars, finance, politics, trains, teams should be controlled with some good sensors, good actuators and good controls.

  • “Everything is under control” means something to you.

  • Socrates should have said “control yourself” instead of “know yourself”.

  • Every Pilot should be an “Automatic Pilot”.

  • But actually, you do not enter an automatic vehicle ,”you know too much” ;-)

  • ‘Chaos’ does have not the same meaning as for anybody else.

  • Control theory can save the world

Feel free to complete the list in the comments!

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Yes, he can save the world !

Posted by Harry Seldon on February 23, 2009

He is from a minority. He is American, lives in the US but has a dual culture. He studied in the best universities. He is one of the smartest guys on Earth. He had many awards for his outstanding work along his long and brilliant career. He has always fought received ideas. He is not afraid of complexity but knows to recognize simplicity in the middle of intricated systems that most people consider as infinitely complex. He is not afraid of telling people when they are wrong. He is not afraid of telling them what to do. He does not hesitate to fight alone against the majority but definitely prefers to be with the majority. If listened to earlier, many casualties would have been avoided. He wants to change the world and he has a plan.
No, I am not speaking about Barack Obama. Let me continue. He is Franco-American. He studied aeronautics. He deserves a Nobel prize in all categories: economy, physics, medecine (biology), chemistry, and even litterature and peace, because his work helped describing and understanding the geometry of nature. His work can indeed be applied to stock market, natural borders, lungs description, fluid mechanics, animal population evolution, clouds. He wrote many inspiring books. If more listened to the world would be way more peaceful because better understood and less submitted to crisis.
Yes, I am speaking about Benoit Mandelbrot and the good news is: his work on finance is slowly being recognized by the media and by economists.

Listen to Mandelbrot and global warming, crisis and wars will just be bad memories. OK I am exaggerating, but I am not sure how much ;-).

PS If you know which conferences Mandelbrot is going to attend this year, please let me know in the comments because he is definitely the celebrity I would love most to meet.
mandelbrot antenna

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Good news from the combat against the crisis

Posted by Harry Seldon on February 22, 2009

Julia island
In my 2009 wishes, I wished that people better understand the world. For this purpose, I suggested they read The (Mis)behaviour of Markets: A Fractal View of Risk, Ruin and Reward by Benoit Mandelbrot.
Actually, for one year and a half we have been inside this growing up crisis I have been appalled by the small number of articles in the media about Mandelbrot’s work on Finance and more generally by the small number of articles about chaos theory and economy. Indeed more than ten years ago, Mandelbrot explained why the finance world was walking on its head. To make it short, it is because financial theory fundamental principles are wrong and over-optimistic. These principles state that the hazard involved in the market theory is regular enough to be smoothed by the big numbers law. This hazard is “benign”. Basically, with the standard theory, crisis can’t happen. So yes, you must be dreaming, there is no crisis, unless you listen to Mandelbrot that tells you that the hazard is actually “savage” and potentially leading to a collapse of the market: a crash.

So where is the good news ?

It looks like main stream media are slowly understanding Mandelbrot’s work and they are speaking about it. I found yesterday an excellent article in one of the main French financial newspapers about Mandelbrot’s work on finance. The second good news, contained in that article, is that Mandelbrot’s book are being republished. A third good news, is that the author of the previous article, Philippe Herlin is very proactive and has just created a Facebook group called “Finance & Mandelbrot”. I joined immediately ! An instant interest of this group is that Philippe Herlin gives a list of news articles about the subject (given below). Please notice the link called How Fractals Can Explain What’s Wrong with Wall Street which is dated on February 1999. Yep, it is not a typo for 2009 !
Last but not least, there is a significant political news. Mandelbrot showed that the financial system was fractal, exhibiting the same behaviour at all scales. Actually that was the start of his long and brilliant career. Later on he showed the same behaviour for climate, geology, ecology, or biology. Actually about any natural system is fractal and even chaotical. However, there is a good way to smooth the behaviour of a system, it is called control. Our world needs more control (distributed control whenever possible). That is to say, more rules, more ways to enforce them and more ways to measure their efficiency. So the good news is today European leaders backed sweeping new regulations for financial markets. Questions remain, will the rules be good and will they be enforced?

By the way, if you want to understand a little better the whole world, if you want to hear about economy, climate, geology, ecology, or biology in less than 200 pages, just read these two amazing books. Your vision of the world will change and for almost free because these books are quite old (but have never been so fashionnable).

Nostalgia: I was offered these books 13 years ago. I read them then. They are definitely among the best gifts I have ever received. They stand in my bookshelf, one arm away from where I am writing these lines. Believe me these books are far easier to read than the Bible so you can give them to your children. I read them again 2 years ago after completing my studies in Dynamical Systems and Controls. I understood plenty of things I had missed in the first reading. So you can also offer these books to adults. They will learn quite a few things about the nature of our world.


In English

In French

If you know other good links about fractal, chaos theory and economy, please leave them in the comments.
Mandelbrot set

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Launching ThinkoSphere Alpha, an accelerator of democracy

Posted by Harry Seldon on January 24, 2009

I am pleased to announce that the alpha version of ThinkoSphere.com is hereby publicly launched! I have finally integrated the new design. I hope you like it.

What is ThinkoSphere?
ThinkoSphere is a brand new experiment that publicly aims at implementing more Control Systems Philosophy into the democracy. That means I want to give each of you more power in:

  • Giving your opinion
  • Knowing the opinion of others
  • Analyzing thoroughly this data
  • Reacting accordingly to the results of a poll or vote

The Control Systems philosophy is pretty straightforward: you sense, you think, you act. This process is scale independent: it is the same that drives your personnality. It is also the same process that drives the society. So let us make it more transparent.

What is the current state of ThinkoSphere?
Currently, ThinkoSphere might look like a classical polling website. However, ThinkoSphere has 2 great features that are innovative, fun and very useful:

It means that, among the “sense, think, act” parts, the sense and think parts are currently the most developed ones.
To be precise, you can:

What comes next?
Plenty of things: widgets, API, internationalization (i18n), localization (l10n)… But for now, it is time to test in the real word what has already been done. So, what do you think about this project?. You are very welcome to leave your comments here. I am specifically appreciating negative feedback so that I can improve. It is all about control isn’t it?. Moreover, if there are features you want to see added, leave a suggestion here or create a poll.

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Control Systems 101: a Flight Control System example

Posted by Harry Seldon on January 03, 2009

Flight control system
The about page of this blog says this blog is about Linux, Ruby on Rails, Controls and the Thinkosphere project. It is now time to speak about controls.
First things first. What is a control system (CS) ? I am glad you ask because it is not an easy question. A way to answer is to give various examples which I will do in this post and next ones. Right now, I would say that a control system is a set of methods, processes and machines or humans that aims at shifting the state of a system from an initial state to a new determined state while keeping the behaviour of the system inside some bounds. OK, the definition is not very sexy. However, you notice immediately that many systems (if not all) will fall into this definition. That is the point of this blog. I want to show you that control systems are about everywhere. Everything and everybody is either a control system or a part of a control system.

What does a control system consist in ?
A CS is made of actuators, sensors, controllers. Another way to say it is: a CS is made of muscles, perceptors, brains. In order to enter the details of how a control system works I will take the example of an Aircraft Flight Control System (FCS) because it is what I know best as I am a Flight Mechanics and Controls Engineer, and a private pilot.

What is the aim of the FCS ?
Basically, nothing else than conducting the flight to move safely the airplane from a Point A to a point B minimizing the cost (Fuel consumption), minimizing the time and maximizing the passenger comfort… Yep quite a lot of things to do ! CS Design is not something very easy.

Actuators act on the system. For a mechanical system actuators apply forces and torques on the system.
For our FCS, actuators are:

  • Engines, they generate the thrust
  • Ailerons, they allow tilting the aircraft towards the left or right (along the roll axis, that is one of wings is higher than the other one) and thus they allow the aircraft to change its heading)
  • Elevator, it allows tilting the aircraft towards the up or down (along the pitch axis, that is the nose will be higher than the queue or the opposite)
  • Rudder, it allows tilting the aircraft (along the yaw axis, towards the left or the right in the plane of the aircraft)
  • Spoilers, slats and flaps to better act on the lift

Actuators receive their orders from the controller.

Some other things that fall into the actuators category: action mean, levers, muscles.

The sensors observe the state of the system. They measure critical parameters. For our FCS, sensors are:

  • Gyroscopes, they measure the angular velocities of the aircraft (roll, pitch, yaw rates)
  • Accelerometers, they measure linear accelerations.
  • Angle of attack probe, it gives the angle between the velocity vector and the pitch attitude angle.
  • Pitot tube measures the velocity with respect to the air.
  • Barometer allows estimating the altitude through the air pressure.
  • GPS to give the aircraft position

The controllers gets information about the system from the sensors.

Some other things that fall into the sensor category: feedback, detectors, observers, measures, references.

The controller gets the high level orders from the pilot (where do you want to go, heading, altitude, etc ?). Then, using the control laws it converts the order to low level electric orders sent to the actuators. Next, it checks that the aircraft does what it told it to do. The small discrepancy between the order and the measure is analyzed by the controller which sends an update to the actuators and the control loop goes on. The frequency of the whole process is typically 8 Hz.
The controller is made of computers and softwares. Softwares themselves are made of quite a lot of different parts, the core part being the implementation of control theory algorithms.
For sake of simplicity I am including the estimators, these algorithms that use several data measurements to filter the measurements or compute not measured data, inside the controller.

Some other things that fall into the controller category: guidance, navigation, control,stability, GNC, brain, think, computer, estimators, software, automatics, algorithms, methods, processes, regulator, commander, boss, manager.

In controls, we often speak about loop and feedback. The scheme at the top of this article is the representation of the order in which the parameters are sent and obtained. The pilot enters the parameters into the flight computer. The computer sends the first orders to the actuators. Actuators act on the aircraft. Sensors measure the state of the system and feed them back to the computer. Then, the computer verifies if everything behaves accordingly with what it expects, otherwise (for instance if there were external perturbations or modelling errors) it sends new orders. And the cycle goes on.
Finally, you should basically understand what a control system, controllers, actuators and sensors are. In future posts, I will explain the differences between Guidance, Navigation, and Control. I will give you more example of CS and what their controllers, actuators and sensors are. Some controlled (or not!) systems I have in mind are Economy, Climate, Politics, Society, Company, etc.
In the mean time, you can play the following game. Whatever you see, ask yourself if it is more a controller, a sensor or an actuator and for which CS. Or just do that for the following things: justice, police, lawyer, economist, trader, SEC, president, soldier, medical doctor, clothes, volcano, and ThinkoSphere.
Playing this game, you will quickly understand this motto I often have in mind: “It’s all about controls”!

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Happy new year 2009! May we better understand the world!

Posted by Harry Seldon on January 02, 2009

I wish you all an excellent year 2009 filled with happiness in your private life as well as in your professional life.
Besides that, I wish you to better understand the world we all live in. For this purpose, here are some subjects that deserve all your attention and about which I will blog soon.

This beginning of the new year will be very busy around here. Indeed, I am going to make a major update for ThinkoSphere.com with the new design and I will start a blogging series about Control Systems. Later on I will blog about the fractal theory applied to finance because it is today the best theory explaining the crisis that I have found so far. I am currently reading the book “fractals, hazard and finance” from Benoit Mandelbrot*, father of the fractal theory. This book is amazing, it is ten years old but it looks like it was written 2 days ago, after the crisis.

Moreover, I also wish you to be better understood by your company, by your mayor, by your government. I wish you more democracy in your environment. This starts by giving more your opinion when you are polled. So I wish you more polls and finally I wish you to find your interest in ThinkoSphere.com.

* I am actually speaking about “fractale, hasard et finance” a book in French. Its equivalent in English is The (Mis)behaviour of Markets: A Fractal View of Risk, Ruin and Reward. This is probably the best quality and best quality/price ratio book about finance you can buy nowadays!

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