Modeling Fighters and Drones Using System Modeler

Hello everyone.

Thank you for attending this talk. Modeling fighters and drones using System Modeler My name is Jan Brigod. I'm the CEO of Wolfram Math, core developers of System Modeler. And in this talk to our interns, Atefe Ismailicert, Esmail Sade and Erik Espinosa will present on a topic related to the new release of the aircraft library. So let me hand over to Atefe.

Thanks.

Well, with the recent development of the aerospace technology, now we know that the gravity doesn't quite hold us down. Where the sky is not the limit, but merely a starting point. And where the technology meets the adventure. And in the most accelerating way. Among aerospace vehicles, quadrotors are now widely used in many different areas and have found their place in various industries and applications even beyond Earth for space purposes. They came a long way starting from 1922 with the Bazzet helicopter with the huge rotor blade of around 5 meter to the current nano quadrotors. But what is behind this widespread use? I'm Atefe Smileizadev, a control system intern@wolfram ASCR. Today I invite you to join me on a quick overview of the quadrators through the aircraft library of the Wolfram System Modeler. Let's start with the quadrotor dynamics. The ingenious part of the quadrator design is the arrangement of the propellers to control the drone in six degrees of freedom. Although it just has four actuators that are actually forces coming from the rotation of the propellers. As you can see in this slide you have different colors for the propellers in the diagonal that shows the different rotation spin. So here you can see that the yellow ones rotating counterclockwise and the green one rotating clockwise. This arrangement benefits from canceling out the net moment generated by rotors and prevent quadrotor to spin. Furthermore, it allows decoupling of the angular motion following the rotation arrangement. A positive roll motion as you can see here, And the same amount of the decrement of the rotation speed of the other two propellers. And a positive pitch results from the generating a positive lift increment which is the result of a faster rotation speed and negative of the front propellers and the negative one for the back propellers. And finally, yaw motion comes from the faster rotation in one diagonal pair and a slower rotation of the other diagonal pair. These changes in the rotation speeds are commanded by the control system to quadrotor. Now I think that you can guess the reason behind the popularity of the quadrotors. Well, the dynamics seems relatively simple. However, the challenge lies in the controller design and how to make the quadrature more stable, precise, efficient and less human Interactive Wolfram System Modeler gives you the opportunity to test and create your own quadrature. And let's begin with an example in System Modeler. This example integrates the quadrotor body as you can see here, connected to a controller. And you have the reference inputs which are the X, y, z positions and yaw angle that is commanded to the controller. We can run this simulation and also you have the possibility to select the reference trajectory type which we go with the infinity trajectory. And let's see the result. This video shows the front view and top view of the infinity motion of the quadrotor. The pink sphere shows the reference trajectory. And we added a one second leg. So you can see how the quadrotor tries to catch the reference trajectory. All right. If you remember I mentioned that the challenge lies in the control system design. In the next example that we see, we compare two different control structure for the same quadrotor and same input. So you can see here in quadrotor number two we connected it to a controller in which we fed back the angles and positions. While for the quadrotor number one we also fed back the angular rates and velocities in addition to the position and the angles. So spoiler alert. Just remember the fast and slow quadrature. And now let's see the difference in the results. Here you can see the plot of the X position versus time. So here you can see the reference which is shown by the green line. And the fast one tries to react to the chains faster and tries to follow the path closer to the reference trajectory. That's because it has more information of the quadrature which we fed back the velocities and angular rates, while the other one responds slower, but it's more smooth and it's with less oscillation. So depending on the application, it's a trade off to select which type of the controller. For example, for the photography you may need something to follow the path smoother and slower. While for the search and rescue you may need a high performance path quadratures. And the multi rotor package is not limited to the quadrotors. You can you have all the tools to model multirotor vehicles. This is an example of the 76 rotor vehicle which has been implemented using the multi rotor package of the system modeler for a customer from aerial industry companies. For the animation we use simple objects. Here you can see the spheres and the cylinders. So it's been used for the initial stage of the design. Of the vehicle. That's why we have them in a simple object. And the cylinders on the propeller are presented here for the color coding of the propellers for the efficient and smart control mechanism. So let's see the motion of this vehicle. Here you can see the takeoff spin and lateral and forward motion. With this, I conclude the drone part. Thank you for your attention. Now I'd like to open the floor for my colleague. Feel free to hold on your curiosity, Write down your question, and I'll be more than delighted to address them during our upcoming question and answer session. Thanks.

Thank you very much. Atefe and. Okay. Good morning, dear passengers, this is your captain speaking. We ask you to please fasten your seat belts and secure all baggage underneath your seat as we approach supersonic speeds. My name is Eric Espinosa, systems engineer intern at Wolfram Math Corps, and will be presenting the modeling of supersonic aircraft. Even if the term supersonic reminds us of modernity, technology and achievement, it's been with us since long time ago. The flash before the thunder or the characteristic hoopa sound from the leash, They've been present here forever. Nevertheless, millennia of development would have been needed in order for the Concorde to take off and cruise at Mach 2 and break the sound barrier. Now, the term sound barrier does not come for free. Even During World War II, trained engineers and physicians believed that large objects such as an airplane would not be able to break the speed of sound. The reason for this is drag. Drag is the force that opposes movement in the air. And it's the one that as a kids, we experience when we get our hand out on a moving car. The airplane experiences the same and it again opposes its movement. And they had reasons to believe. So if we can see both the predictions, mathematical predictions, and the experimental data seem to show that there was an asymptote that it went to Infinity on Mach 1.0. As we can see in this graph, on the X axis we have the Mach, and on the Y axis we have the parasite drag, which measures this drag force. In a way, it went to infinity. So they had the reasons to believe so. Nevertheless, they were wrong. And on October 14, 1947, Captain Charles Chuck Yeager broke the speed of sound on board his Bell X1 in this beautiful orange color. And. And you can see how it's actually shaped like a bullet, because engineers back then knew that the bullet was stable at supersonic speeds. But before we continue, we should speak a bit. What is Mach? Just this technicality. Mach is not really the velocity of the airplane by itself, But Rather a ratio between this velocity of the airplane and the local acoustic speed, which is actually temperature dependent, so it changes. And what's very special about it, that if the airplane starts to travel faster than the speed of sound, the sound waves, as we can see on the image, will start to stack on front of it, eventually generating a shock wave here on red. Now, what is really complex about modeling supersonic and especially transonic? Well, like everything that involves fluids, they are capricious. So you have apparition and disappearances of shock waves almost randomly and chaotically along the aircraft wing because they depend on the local velocity. Therefore, it's very, very complex to model even for the most powerful computational fluid dynamics softwares. So how are we going to do that with Sifton modeler? Well, thankfully we have some experimental information from the U.S. air Force and the NASA, especially from some aircraft from the 50s and the 60s. And also this work is based on some work from Professor Peter Cruz from Lynn Shopping University, where I study. We can see on this graph that again, on the X axis we have the Mach number. And on the Y axis, again the parasite drag, we can see how it behaves for different aircraft. And in this way, from the subsonic, before achieving the speed of sound, it's quite low. When it's transonic, we see the steep change, which is the one that used to confuse engineers. Nevertheless, it reaches a peak and then it becomes supersonic and it goes back down a little bit more.

Now.

How can we actually do that with this implementation, with the Worldram language, it's pretty easy, especially because of the sliders. Once that we introduce a modified version of Petr Cruz's equation, then we can actually use the sliders to tune it so that they look exactly or very close to us, the experimental data that we want to achieve without actually having to get into the core mathematics of what these shaping variables represent. Super easy to do, super effective. We can even go one step further and consider for the wing sweep. The wing sweep is this angle that forms between the wing and the lateral plane, basically how much the airplane looks like an arrow. For example, if we check at zero degrees, which is like this Bell X Ray one, the one that Chuck Yeager used to break the speed of sound. The change in drag, again, Mach versus drag, is really steep. Nevertheless, if we give some angle to it, let's say 20 degrees, we have a lot less of an increase. If we go to 45 degrees, like in the case for this thunderchief, it doesn't get that much better, but it's still a longer decrease of drag than with 0 degrees. If we go full delta, like this delta dagger 60 degrees, then we can see that the increase of drag is so much lower. That is why the airliner in which you travel has some sweep. Not because it's going to cross the speed of sound like the Concorde, but because it's actually flying really close to it, about Mach 0.7. It's because of this. Now, the same methodology was followed for the other variables that are changing, let's say, the slope of the lift against the angle of attack, like in this graph over here. From there we can actually generate a nice 3D graph which relates the lift coefficient with the map and with the angle of attack. These kind of graphs give a huge insight not only to students or developers, but also to engineers. And they are not that easy to be found on a textbook, at least the ones that I've seen so far. So how do we actually make the simulation of this first supersonic flight? It looks rather simple. We have the airplane in the center and we're going to control constant control. We're going to connect constant control inputs to this airplane. So no pilot on board, probably Chuck Yeager, is going to have a rather bumpy ride today. Now, if we check inside of this aircraft, we're going to see its main components named propulsion body and its control surfaces. How is the drag modeled? Using a simple world force. Here it has the input that have all the mathematical modeling that comes from the modifications from Petr Cruz's work. And as you see at that we have modeled the supersonic aircraft. Now the only thing left to do the link between Mathematica and System Modeler is that we get these parameters that we got from tuning the curves and we introduce them as parameters for the simulation. And with that, dear passengers, we are ready to break the speed of sound. So buckle up as we see the results of this simulation. If we check it over here. First, let's see that it is behaving as we want it to behave. Again, on the X axis we have the Mach. And on the Y axis we have the drag coefficient. Here, the wave drag, which is a supersonic dragon, it does exactly what experiments say it does. There is a steep increase, then it reaches a maximum and then it starts to go down as the airplane is accelerating. Know that this is very counterintuitive here. The maximum is not reached at exactly Mach 1.0. This is because of some angle of attack variations. Now, if we take a look to the drug coefficients, the drug is made out of a lot of things, the parasite drug is the one that we feel when we put our hands outside. And the wave drag is the one that is being generated because of supersonic airspeed. So if you see the drag coefficient of the wave, it's actually the supersonic drag. We can see how at the beginning, it's the parasite drag, the one from the hand that is the main contributor to the total drag. Nevertheless, as the airplane is approaching speed of sound, we can see here plotted the mach, it reaches a maximum. Nevertheless, as said before, as the airplane keeps accelerating, it goes down, even if the Mach goes up. Then as the airplane starts to decelerate, it peaks again at Mach 1.0. And then as it reaches subsonic airspeeds, it goes way down. So moral of the story, don't fly at transonic airspeeds. You either fly subsonic, very fast, but subsonic, which is the way that airliners do, or you cruise at supersonic airspeeds, which is what the Concorde did, which is what the fighter aircraft that cruise at supercruise can do. And with this, we can actually check the simulation. And here we see the bell x1 traveling. This is the time scale to 10 times more, as it should do. And you can see that there's nothing really interesting happening to the naked eye. Well, because shock waves are invisible to the human eye. Also, we don't see the condensation cone that we see on Internet pictures. That's because the humidity at the altitude at which Chuck Yeager broke the speed of sound in is not really a lot. What we can see is some oscillation. And this. I would like to ask the question for the audience, why is this oscillation happening? I give you a clue. It has to do that there is not a pilot present. And with that, dear passengers, we have reached our destination of supersonic flight and drone modeling. We open the floor for questions and we invite you to come to the Wolfram System Modeler digital booth. Thank you.

I hope people enjoyed it. And this is the work done with the aircraft 2.0 library, which will be released with the next release of System Modeler.

We have a question, Jan. Sorry, from Randy Junk. Do you have any handouts? Yes, it will be uploaded soon after the conference. Thanks.

Yeah, as soon as possible. As soon as they will. They will be available soon for you.

Awesome.

Then I think that's it. It was a quick flight.

Hope you enjoyed. Thank you.

Thank. You.