Відео

Haha, true. More lessons coming soon.

Thank you!

That's great feedback, thank you! It's been a while, but the content for my next lesson is coming to fruition. It's derving a flight dynamic model of the X-15 spaceplane from the literature and simulating its dynamic response. Be sure to check out the errata of this lesson (and my other lessons) in the description below. How many bugs/errors are left after one is found? n-1

Haha, you're welcome.

Great, that issue has plagued us all at some point.

Good catch! Yes, this actually carried over to my sim and caused me several hours of troubleshooting before I found it. I'll post an errata for this lesson. Thanks for watching!

Yes, it's particularly useful when we have a continuous time simulation.

Glad you like it! Thanks!

Thanks for watching! Yes, you are correct. Unfortunately, this is an error. I'll add an errata list to the description. Thanks for catching this mistake.

Hello, I do not have lateral control videos but Stengle has an open online course that may cover it. You can access it at www.learngandc.com. Navigate to Resources/Courses then scroll down. Thanks for watching.

@@LearnGandC thank you!

It's my pleasure. Could you be more specific? For example, the time of the video and the equation with the error in it? Thank you

@@LearnGandC The time is 22:56. When i compare the equation of yaw and code (117 to 120), i notice that there may be a sign discrepancy. In other words, comparing the code and my opinion: dx[5] = -->(in video) ((Jxx_b_kgm2 * (Jxx_b_kgm2 - Jyy_b_kgm2) + Jxz_b_kgm2**2) * p_b_rps * q_b_rps + \ Jxz_b_kgm2 * (Jxx_b_kgm2 - Jyy_b_kgm2 + Jzz_b_kgm2) * q_b_rps * r_b_rps + \ Jxz_b_kgm2 * l_b_kgm2ps2 + \ Jxz_b_kgm2 * n_b_kgm2ps2)/Den -->(photo of formula (my opinion)) ((Jxx_b_kgm2 * (Jxx_b_kgm2 - Jyy_b_kgm2) + Jxz_b_kgm2**2) * p_b_rps * q_b_rps - \ Jxz_b_kgm2 * (Jxx_b_kgm2 - Jyy_b_kgm2 + Jzz_b_kgm2) * q_b_rps * r_b_rps + \ Jxz_b_kgm2 * l_b_kgm2ps2 + \ Jxz_b_kgm2 * n_b_kgm2ps2)/Den

Most welcome!

Yes, you can directly translate it to flight path angle rate but I have not tried to convert to pitch rate. You may be able to make a PI-coupler between acceleration and q.

A lot of the research I have done into trying to figure this out tells me that omega is the input frequency, but if I am not using discrete time-steps or I just need to figure out what s is when time = 0, I have no idea what I could use to find that value

Hello there, for our purposes s=jw where w is frequency and j is the imaginary number is sufficient, although there is deeper discussion to be had for sure. Note, the frequency domain analysis assumes that the dynamics are only driven by the oscillatory input and that the transients due to a nonzero initial condition have decayed to where they are negligible. The system output is independent of the initial condition at t=0.

@@LearnGandC Thank you, this helps my understanding somewhat, but a more specific question. How exactly do I calculate the frequency based on a control input? Also, how would I go from finally building my P controller to actually being able to simulate the flight of my model over time?

@@LearnGandC Also, is there a way I can access the Octave code that you wrote to do all of this and generate your plots?

For controller tuning and analysis, we often use a combination of frequency and time domain methods. However, for simulation of the controller in the loop with the plant, it's done completely in the time domain.

Cool, I hope you enjoy it. This largely maps to Chapter 2 in Zarchan, but with a lot more details.

@@LearnGandC that makes sense, I’m into the optimal control stuff now but still interested in the basics as its been a little while since i had time to make good progress lol

You are correct, this is a known error. I'll add it to errata in the description if I have not already. Thank you

Hello, to resolve the acceleration command in the body coordinate system, we must transform with the direction cosine matrix that is based on the line of sight angle. See the discussion starting at 12:50.

That's awesome. Glad you like the video! You can access my whole library for free at www.LearnGandC.com

Thanks so much!

We stand on the shoulders of many smart people who came before us!

Hello there, codes are available through Patreon. The guidance codes are all the way at the bottom of the list of posts. www.patreon.com/user?u=86359827

You are correct! I'll update the errata in the description. Thanks for catching that.

18:14 I also noticed that in the flight control section it should be -e i think.

Is there also any way to get s more explicit view of how you did some parts of the process/ calculations. For example when you showed us the equations of motion I wasn’t sure if to treat α as a variable or a constant (trim condition) and if α_T was a variable or constant. I also don’t know what exactly you used as inputs for the Moment/Torque in 7:10. The video is magnificent but some things were skipped such that it is quite hard for me (an enthusiast) to follow/ model by myself with the use of Matlab.

Thanks so much! I'm looking forward to getting the next lesson out.

That's awesome! Thanks for watching!!

You're welcome! Thanks for watching.

Welcome Braulio! It's great to learn of your background and that you enjoy the course content. The next lesson will appear tonight if all goes to plan!

Hey Joseph, q is pitch rate and qbar is dynamic pressure. Correct on z_e. Thanks for watching!

Hello there! Yes, folks can access the code through support of the channel on Patreon. It's 5 bucks a month and you get all codes, as well as additional content that helps explain the codes. www.patreon.com/user?u=86359827

Right, L means you have a linear problem. You can get a solution for a nonlinear problem statement but you may have to resort to numerical results, as opposed to an analytical solution.

Thank you! I'm glad you like them.

You got it, more coming soon!

Thanks!

Hey Kevin, the basis is that zero los rate means the target is at a constant lead angle relative to the pursuer so that if the closing velocity is positive, there will be a collision. If the los rate is nonzero, then one body will pass the other. The exception is if the target constantly maneuvers. Then there will be necessary a changing los rate for intercept, up to intercept.

Thanks for catching those bugs!

Hi there, absolutely! Tabular drag data for a body is often given as a function of Mach number. To find the data, you'll have to search in reports, journal articles, or conference papers through your favorite search engine. As I find good resources for aerodynamic data, I'll link to them on the webpage, www.learngandc.com.

Doing some research for an upcoming video, I found this report that you may find helpful: ntrs.nasa.gov/api/citations/20110016614/downloads/20110016614.pdf

@@LearnGandC thank you. It seems that best fit curves for Cd across a range of Mach numbers are usually derived from a collection of drop test results. I wonder if someone has devised a mathematical approach of getting Cd values based on object dimensions.

Yes, the dimension comes in from computing drag from the drag coefficient as the reference area is involved. In addition, there is the transition to turbulence, a Reynolds number effect, which is based on diameter.

No problem! Thanks for watching!

@@LearnGandC why not animating the results next time with matplotlib it would give a huge value and better understanding of what is happening when running the simulation 🙋🏻

Yes, eventually I will do this. Further, I plan to interface with Flight Gear to really bring things to life. All in time.

@@LearnGandC that's great and more comprehensive, thank you sir 😊🙏🏻

There are a lot of topics in this one for sure! It's great to know you appreciate it. Thanks

You're welcome. I made this series after I found very limited explainations of the principles of guidance and also in response to the silly "the missile knows where it is..." video.

​@@LearnGandC doesn't mean anything to me or maybe I'm too dumb to understand the missile knowing where it is in that video.

@@w花b It's a really bad attempt at explaining how a missile is guided, if I recall correctly it was a training video

It was determined from the inverse tangent of the crossrange over downrange from the relative position vector at t(i+1). These positions were literally measured on the diagram to determine lambda(i+1).

You are correct! Another viewer also found this error a couple years ago. I have a list of errata in the video description. Thanks for watching!

Thanks for catching that! I take it you meant great course as opposed to great curse haha

Hello, Codes are available to Patreon subscribers ( www.patreon.com/user?u=86359827 ). The model is in its early stages of development, but once completed, it absolutely could be used as a RL agent.

Absolutely! Trim is a question of whether an aircraft can hold an equilibrium at a flight condition. About that equilibrium condition, the system can be stable or unstable.

@@LearnGandC I have a nonlinear aircraft model. When I trim the aircraft for stable case (Cg ahead of the neutral point) there is no problem, but when I move Cg behind the neutral point again I can find a trim point but aircraft cannot maintain its trim condition. Even I run the simulation for 1-2 seconds, aoa increases by 2-3 degrees for example (system has no disturbance or perturbation). Also, I used simulink for this simulation. Do you have any idea what should be the reason sir?

Yes, what you are experiencing is normal and expected. First, note that you have an unstable dynamic system. Second, note that you are attempting to simulate that system with an initial condition about its equilibrium point. However, ask yourself, do you know exactly the equilibrium (trim) condition? If your system diverges its because your off the equilibrium condition. The difference between your approximated trim condition and the exact trim condition may be small, but that small difference will grow according to the severity of the instability.

@@LearnGandCI understand what you mean. Thank you very much for your answer and videos.

You're welcome

Thanks very much! I've just started developing the next lesson.

@@LearnGandC Can't wait. One thing I would love to see here is how can we use this simulation, to spec out our actuators? I know we need more information regarding flight path and conditions, but that would be fantastic. Cheers.