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Benoit Mandelbrot, father of the fractal theory, has just died

Posted by Harry Seldon on October 17, 2010

Benoit Mandelbrot is leaving us way too soon, even at 86. There is still so much to do to educate people about fractals.

I got the incredible luck to speak to him on the phone almost exactly one year ago (on the Sunday 24th of October 2009). He was still in good shape and he had quite a lot of projects. Among them, he was preparing a book of his memories. I hope he had the time to finish it.

I am shocked by this news.
All my thoughts go to his familly.

In an interesting but sad coincidence that life can do, I met this current week Nassim Nicholas Taleb who is, in some sort, Mandelbrot’s disciple.

The king is dead. Long live the king.
Mandelbrot is dead. Long live Taleb.

For more information, see the links given by the message sent by the Finance and Mandelbrot Facebook group :

Philippe Herlin October 17 at 10:01am R.I.P. BENOIT MANDELBROT, 1924-2010


Finance & Mandelbrot
http://www.facebook.com/group.php?gid=53108760302

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Simplexity: Things are a lot simpler than they seem and vice versa

Posted by Harry Seldon on October 20, 2009

Have you ever heard of simplexity ?

Some systems are a lot simpler than they look like. For instance, let’s consider the shape of a tree. It looks complex, especially if you compare it with a straight line. However, if you have read Mandelbrot or heard of fractals, you know that all you need to draw a tree is a 2 lines pattern, which you repeat a big number of times introducing at each step some light randomness. You can model pretty easily this tree shape. At least you can generate at your will tree shapes. That is typically the way used in computer graphics to generate natural virtual 3D scenes. However, this does not mean you can predict the accurate shape of a tree from its seed.

So, is the tree shape complex or simple? Thanks to Mandelbrot we know now that the shape is a lot simpler than it seems. Associating the notions of predictability and simplicity, the converse is also true: it is more complicated than you could think even if you have heard of fractals. Hence this notion of simplexity, contraction of simplicity and complexity.

Here are a few good books on the subject:

If you know about fractals and chaos, you must be already familiar with that fact that simplicity can bring complexity quickly and easily. But you might not know this term of simplexity.
More generally, each time you think “this thing is a lot simpler than I had imagined at first”, you experience simplexity: in fact, you changed your first impression of overall complexity by discovering the underlying simple principles.

While we are at it. There is a field where simplexity shows all its magnificence: it is in finance. International finance looks complex but there are a limited number of principles behind it. You can even fairly easily model a stock chart. (Even if this model has nothing to do with the actual models used by financial analysts). But even with a good model you cannot predict easily the stock chart of a determined company.
For more info, you can have a look at the Facebook group “Finance & Mandelbrot”.

And at last, because I cannot prevent from saying it again, If you want to keep things simple, then regulate them. Contrary to what you could think, you do not need very accurate models to control a system.

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What happened to AF447 Air France Flight?

Posted by Harry Seldon on June 06, 2009

(Not so) Black box

[EDIT 11/12/2011] Change of the picture due to change on the NTSB website.
[EDIT 27/02/2010] A good article by Der Spiegel about the The Last Four Minutes of Air France Flight 447.

When I started the blog post series about autopilots, I did not think flight control systems would become that of a hot subject. And seen the horrible tragedy of Air France flight AF447, I would have preferred it to remain a technical subject for specialist and not something that is in all the media.

As an aerospace engineer, as a control system engineer, as a private pilot, and as a French man, I am especially mourning the loss of all passengers and crew of AF447. All my condolences go to the families and friends of the victims.

This week, like many, I followed the news about AF447 in the media and on twitter. The first obvious element of explanation is weather. Cumulo Nimbus clouds are known to be the nightmare of every pilot. Airplanes are not really supposed to enter one. This includes airliners that are equipped with a weather radar to avoid entering most severe weather zones. So one can wonder if the weather radar really worked. It could have been damaged or victim of shadowing effect (see in the comments). Inside a CuNimb you will find severe turbulences, lightnings, heavy precipitation, hail and severe icing.
An excellent analysis of the weather involved in AF447 tragedy has been made by a former US Air Force meteorologist. Conclusion is “There is a definite correlation of weather with the crash.” It looks much like weather is a main factor but not the only factor. Weather conditions opened many ways of attacking the structure of the airplane and also its sensors and actuators.

As you read my previous posts about flight control systems, you know how fundamental the sensors are. And it happens that Airbus was not so sure of the speed sensors as there was “an ongoing program at the carrier to renew its planes’ speed sensors”. I do not know what Airbus was thinking about these pitot tubes made by Thales but they might have been thought not robust enough for severe weather conditions, the kind of weather conditions AF447 encountered. And indeed the speed sensors seem incriminated by ACARS messages. That is why Airbus published a communication recalling the procedures “in case of unreliable airspeed indication”. Airbus also added they were not blaming the pilots. Fortunately, because it is quite a desperate situation to be in a storm without AP and without speed sensors. Wrong airspeed could lead to a stall. For instance if the indicated air speed is overestimated, the pilot will want to slow down the aircraft to maintain the aimed speed. Notice that the turbulent condition, making the aircraft to jump and pitch could not allow the pilot to simply keep a pitch attitude and then a fixed airspeed. So the actual airspeed would have then reached a value below the stall velocity leading the aircraft to stall and fall like a stone. Then during the fall the aircraft could have dislocated leading to the scene seen by the Spanish pilot in the vicinity at the time reported: “Suddenly we saw in the distance a strong and intense flash of white light, followed by a downward, vertical trajectory which broke up into six segments”. Here I do not really understand how another pilot could see anything if the weather was so bad and thus leading to a low visibility.

One more word about flight planning, if I were the BEA (French Bureau of Enquiry and Analysis for Civil Aviation Safety), I would also investigate around the Air France (and airlines in general) flight planning procedures to make sure they take enough margin to avoid the most severe weather and that they do not privilege the fuel cost at the risk of compromising flight safety.

Conclusion

Severe weather and not robust enough speed sensors might be the causes of the crash. Let’s hope the official investigation will be quick enough to find the causes in terms of weather, flight planning, hardware or human errors involved so that they won’t be repeated. It won’t be an easy task but even without the DFDR (Digital Flight Data Recorder) or CVR (Cockpit Voice Recorder) (that is to say the black boxes, not so black as you can see on the image at the beginning of this article), thanks to the ACARS messages and the visual testimony (if it is indeed related…) a detailed analysis can be done. AF447 has unfortunately become the Titanic of the XXIst century with all his mysteries. Hopefully, it won’t take 73 years to localize the wreck.

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Control Systems 102: GNC, Conclusion

Posted by Harry Seldon on May 25, 2009

It’s time to get the conclusion of this Guidance, Navigation and Control post series.

Conclusion

To sum up:

And finally, “do not put the cart before the horse”. The cart is the guidance system, the horse is the control system. A good guidance without a good control is totally useless. A good plan is nothing without a good pilot. I’d rather fly in an aircraft with a good Stability and Control System and a poor Guidance System than the opposite. In the first case you might not reach your wanted destination, in the second case you will crash!
We live in an economic world with a lot of guidance and very little control. That is why the finance world totally collapsed, leading us to the current global crisis. More details in a future post…

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Control Systems 102: GNC and Human Pilot

Posted by Harry Seldon on May 19, 2009

This post is part of a series about Guidance, Navigation and Control. See the table of contents here.
3 parts are in this post because they are shorter:

  • About the human pilot (with fresh news: man in an Unmanned Aerial Vehicle is for “soon”)
  • About GNC wordings
  • About the various control loops

About the human pilot

At the beginning of aeronautics, the human pilot was actually a pilot. That is the person had to stabilize the airplane. He was permanently using the flight stick. This was a full time job and a navigator was required to keep track of the aircraft position. Then thanks to a better Navigation System and thanks to the autopilot, the human pilot became more a navigator and a flight manager giving high level orders (altitude, etc.) to the plane in accordance with the flight plan and the Air Traffic Control (ATC).
The next steps are:

  • Fully automatized flight. The commercial airplane flies autonomously, it receives its orders from the ATC through a radio data link. The captain is responsible for the flight safety and can fly the aircraft in case of emergency. This can be forecast for within 20 years. A passenger will be aboard a small UAV (unmanned air vehicle) in probably less than 10 years.
  • Fully automatized ATC. This can be forecast for within 30 years. Unless videoconference kills aviation before that!

To prove that what I am speaking about is not utopia. Here is a news I learned a few days after writing this article. Boeing has filed a patent for an aircraft that could fly autonomously, with one pilot or two pilots. It seems to be for a helicopter. For the moment, the autonomous mode is meant to work when there is nobody inside the aircraft but the step to an autonomous flight with people on-board is then very small (even if it would be a giant step for mankind). So I tell you it is for sooner than you may expect.

By the way, the world will need more and more Control Systems Engineer. Even today, at this time of crisis, the world (France, UK and US at least) is lacking of such engineers so you can study it safely, you won’t be unemployed.

About GNC written GN&C or GCN written GC&N

The acronym GNC can appear in several variations according to what you want to emphasize. GN&C means you separate the low level stabilization (C) from the higher level orders (G&N). GC&N means you associate G and C which are technically similar and you separate them from the Navigation which uses more advanced tools such as the Kalman filter. Both wordings are then completely justified.

About the control loops

Notice we have a lot of Control Systems working on top of each other in an airplane:

This is something to keep in mind that in order to control a system you need several loops from the low level to the high level. The most important system being the pilot (the Stability and Control System). Once you can safely achieve your basic moves (once you have a stable system), then you can think about making long trips and accomplishing a complete plan.

I am anticipating on the conclusion but never forget that the low level control loops are the most important even in “company control”, else you are going straight to a crash. Our (financial but not only) world has completely forgotten that.

Next part will be the conclusion.

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

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Control Systems 102: GNC, Guidance

Posted by Harry Seldon on May 12, 2009

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

Guidance

Guidance refers to the questions ”where am I going to?”, ”How can the vehicle follow a trajectory?”. The trajectory itself is prepared by the Flight Planning System (FPS) (or Mission Planning System, MPS). During the flight, the Flight Management System (FMS) knows the trajectory and gives the current portion to the Guidance System (GS) . The Guidance System is in charge of converting the high level parameters (trajectory, waypoint positions) into a set of lower level orders that can be understood by the control, typically altitude, heading or directly a load factor, that is an acceleration. In some cases the guidance can have the role to compute a trajectory between 2 points.
It is also in charge of maintaining the trajectory and the other high level parameters. That means the guidance is itself a control loop. Typically the guidance is the Position Control System (PCS).
This is where things become tricky. Piloting and Guidance are essentially similar. The difference to keep in mind is that the pilot is a low level control loop whereas the guidance is a high level control loop. A nice world would be a world where guidance and pilot loops are two independent loops. Unfortunately both are coupled, and designing one, you need to keep the other one in mind.

GNC

Next chapter will be about GNC and human pilot.

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

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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.

GNC

Next chapter will be about Guidance.

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

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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

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.

GNC

Next chapter will be about Stability and Control.

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

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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.

GNC

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):

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

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