52 States in 8 Months

Flatness of Cranes

Posted in Diploma thesis by Ulf on November 12, 2008

I’m currently working on the differential flatness of cranes. Believe it or not, but all cranes I know so far are flat. If this doesn’t make sense for you, you probably don’t know what flatness is. Maybe I’ll explain it later.

EDIT: There actually are a couple of non-flat cranes. They can fly, therefore they can fly away. Then however, they just do what they want which makes them uncontrollable. And uncontrollable systems cannot be differentially flat. In Germany, people call these non-flat cranes “Kranich”.

Today, I was a bit bored all day long. Therefore I created a small simulation for two types of flat cranes: boom cranes and gantry cranes. I also added a visualization (see below). If you like these pictures (I do *g*), I still have some more.

ANOTHER EDIT: To give you just a rough idea of what differential flatness is about: It’s a property of a system that allows me to do perfect feedforward control. In this case, I selected the red trajectory of the load and could calculate the necessary blue trajectory (of the crane) in a very simple way.

gantry1boom2

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4 Responses

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  1. Pingu said, on November 12, 2008 at 11:56 pm

    Nice pictures – I guess that’s all Matlab art? But I’d never paint my payload in such these colors, this just doesn’t look very scientific :-P

    About the other cranes, perhaps you just have to examine them closer to find a suitable input which makes them controllable :)

  2. kueken said, on November 13, 2008 at 4:52 am

    also wenn dir langweilig ist weiß ich ja von ein paar Dingen, die noch unbedingt erledigt werden wollten B-)

  3. ulf84 said, on November 13, 2008 at 9:09 am

    @ Pingu:
    The payload actually was the hardest part of the whole drawing script. The ball always rotates itself in the direction of the rope. Therefore I needed some texture. This is the standard colorset of Matlab. However, you’re right, it looks kind of ugly.

    And about the other cranes, you’re right. There actually is an input. At least locally you can use a shotgun to accelerates them with the force [0;0;-m*g]. This however does not allow you to fully move it in any direction. Therefore, although we found an input, the cranes are still not differentially flat.

    @ Kueken:
    Did I forget something which I should have done? Please tell me about it.

  4. […] On Thursday however, he was quite busy. Then I showed him the results which I had visualized on my Wednesdays posting and finally got my appointment for Friday. So… today we had only some shifts in the time […]


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