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Hmmm.... what about your actuator pole? If it's too slow then it can cause instability at low gain.

​@@LearnGandC Hi Ben, the actuator pole is at the same place (s=-4) as indicated in the video

Hey there, it's great to hear the lesson is coming in handy! Thanks for watching

Thank you! I'd recommend Blakelock, Automatic Control of Aircraft and Missiles. The 1st edition is fine and much cheaper, but the 2nd edition is better if you can find it.

Hello Sankalp, as you have found, you can access the code from my Patreon page. Thank you for subscribing!!!

Ah, because the left answer would provide a negative tgo estimate. Examine the numerator terms to observe this.

@@LearnGandC First of all, thank you so much for your posts and videos. They are incredibly informative and a true pleasure to watch! but i dont get why t_go is negative on the left. for example v=-10 A=1 R=32 the sqrt((-10)^2-2*1*32)=sqrt(36)=6 in this case the left value is -(-10)+6=16 and the right value is -(-10)-6=4 both postive

Of course, glad you like the content! Note closing velocity is positive when the bodies are approaching each other. Also, while there are exceptions as you may have found, that solution provides negative values for a relevant range of parameter values.

No problem! Thanks for watching!

Ok, had to do a little investigation. It's to make a steady state gain of 1, but the transfer function is not correctly listed. It actually has a pole at 1.5. You can find this on my Patreon post (thanks for subscribing) at the link below. Go into the driver PI_Control_of_Airspeed and then look at Part G where the lead compensator is specified. Thanks for watching and the question! www.patreon.com/posts/airspeed-control-85847981?Link&

@@LearnGandC OK now I understand. The gain of 7.5 is for the pole at 1.5 that you showed as a compromise after the pole at 4 required too much control effort (risk of thrust saturation).

Thanks for the suggestions! I agree and will update the playlist.

Ah thanks for catching that. I plan to update the lesson in the near future as a second revision.

I'd recommend Paul Zarchan's book. You can find it on my list of recommended texts: learngandc.com/recommended-texts

Not necessarily. For example, linear analysis and application of linear control methods has been effective in aircraft control for decades!

I don't believe this is a general conclusion that can be drawn (Pure requires more ap than True). Pure ap is proportional to Vp while True is proportional to Vc. In this example, Vc > Vp, and I believe this is in part why for a given N, ap-True < ap-Pure. I don't know why Zarchan focused on TPN. His book is already long enough, actually now two volumes, so perhaps it's a brevity thing.

Thanks, based on your comment, I've reordered the playlist so they are now in order 2.1 to 2.6!

Yes, you are correct. Thanks for pointing this out. I'll update the errata in the description. Although the name should be w_over_u, it's actually implemented correctly.

Thanks. Not to my knowledge, I was able to verify against the check cases. Are you sure your initial conditions are consistent? Note, pitch angle is set to -90 degrees so that the brick accelerates in the positve x-direction.

My pleasure! Thank you!

Your welcome! One set of gains at all conditions will be better than no gains, but it's not ideal. About any flight condition, there will be a set of gains that produces the ideal behavior. So, the pilot can adjust with knobs. A gain-scheduled SAS would be the next step. For integral control, it could certainly by used a in control augmentation system (CAS) where there's an outer loop to enforce tracking of the pilot-commanded variable. Derivative control could help dampen rates more quickly, but of course there's the risk of amplifying noise through the derivative. Proportional control is a simple solution that apparently met requirements based on the number of successful flights. So from an overall experimental space plane program perspective, it's possibly the best approach for its purpose.

Yes, that's correct! I did a poll and people wanted insight into the issues found when developing the simulation.

@@LearnGandC got it, thank you. I definitely appreciate that insight, it is consistent with my own experience, I must say, quite unfortunately. I asked because I wasn't sure if I was supposed to look deeper into the plots to see minuscule differences between lines in the plot. Great job by the way, I'm enjoying those videos a great deal.

Hello there. Unfortunately I don't have specific insight into Boeing or Airbus autopilot architecture. However, pitch command tracking controllers have fundamental PI architectures. For example, one could implement integral control on pitch angle error and proportional control on pitch rate for artificial damping. This makes use of navigation and IMU data which should be part of the avionics of modern aircraft. My series on longitudinal flight control (see www.learngandc.com) covers the architecture and tuning of basic controllers like the pitch tracking controller.

It's a valid approximation for aircraft modeling and simulation when speed and distance is limited. For accurate prediction of aircraft flight at high speed or over longer distances, we must account for the oblate and rotating earth.

Hello, at least two more. There's one about initial model development (coming soon) and the one where a more comprehensive model is developed. Over time, new parts of the simulation will likely be added and this simulation will be used for flight control lessons in other series.

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

Thanks for letting me know! If I have not added it to the errata, I will do so.

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!!