Costa Concordia: Mathematical Model of the Submarine

Hopefully the Costa Concordia won’t become a submarine, but the only ready control system design document that I could find easily was from MIT.

Multivariable control system design for a submarine

The copy isn’t printable since the document was generated in 1976, here is the diagram of the submarine. 

Reference frame:

When doing design, even for the Windows Phone 7 you need to consider reference frames.


The State Variables

When the article was publshed the state variables had to be converted to symbols the computer doing the simulation could handle, which would still be required in today’s computers.



In the real world, pressure and forces

Here are forces that contribute to the model




What are the control inputs for the submarine?

There are three control variables, rudders, stern planes and fairwater planes, which in comparison to a cruise ship is surprising comparable because of the stabilizers and side thrusters used to maneuver the ship.




What are these Control Surfaces?



The machine doing the simulation (it was 1976)

A VAX 11-780 with a graphics display workstation! is used to do the simulation, and a Joystick was used to input commands. 

The software used was FORTRAN 77 using the Microsoft Compiler for FORTRAN 77 (wonder if this is still available)

This is interesting since the 11-780 likely had far less computation power than your cell phone.   Now that I said that, what should I do?  Ignore my own statement, is it possible to take the simulation program and put it on the phone?  Seriously?

Where do we go from here?

In the next blog, we will take a look at the control system analysis tools