@@bakersbread104 Integral part is for eliminate the error of proportional part and make the transition faster in time. The more time the error signal exists, the bigger the effect of the integral part to compensate this. Let's consider we have a PI: proportional tag by itself cannot eliminate the error value, the bigger the proportional coefficient the less error you have, but the more unstable can the system be. Let say we have an error value which cannot be compensated by the proportional tag: f(x)=-1. Try to integral this in time and summ the two function together: f(f)+F(x) = -x-1. You can see if you check the integral value on the for example t=[0,2] domain, at t0=0 the error value is -1, meanwhile t1=2 the error value is -3. I think i did not make any mistake here but correct me if i have done :)
This is the best explanation of a PID controller I've ever seen, and even shows an excellent breakdown of its implementation. I've been using PIDs for many years but never really thought much about how the math works. Your implementation is actually much more robust than the one I use and addresses some issues I've noticed using mine over the years.
Just when I had given up hope of ever understanding pid controllers, along comes you and explains it with a minimum of algebra and a maximum of understandability.
to calculate a phyisical turret you could predict the targets position instead = cause a bullet got traveltime as well. step 1: grab the target position and store it as a vector3 and give it a fancy name like "oldTargetPosition" step 2: grab the distance towards the target starting from the firepoint(barrelEnd) and use it to calculate the time the bullet would travel step 3: wait for as long as the bullet would take to travel towards the target step 4: grab the "current target position" again and "substract" it from the "old position" to get the difference between both position and call it Vector3"DistanceMoved" step 5: create a new Vector3 and call it somting like "predictedTargetLocation = currentTargetPosition + DistanceMoved" step 6: if the bullet is a victim of gravity (like in RL) -> calculate the bullet falloff from its "traveltime(step2)" towards the target and store it in a Vector3 called "bulletFalloff" step 7: add "bulletFalloff" to "PredictedTargetLocation" step 8: now if the target keeps moving at a more or less constant pattern the turret would precalculate the point where the bullet would connect with the target. if this would be connected to an AI that has stored targetspecific information about manouverability weakspots etc. , then it could use those informations and add them into the equation.
I have tried a little bit to understand PID controllers in the past but failed. This video explains it so well, and it's very easy to follow along. The explanations and pacing are good and it follows through everything without too much or too little detail. Very well done! The explanation of each term, why they're needed, and how they affect the result is such a good way to understand it.
This video is actually really good. I had classes on PID controllers, but this is really well explained, and the demo and code makes it super usefull. Thanks a lot, great job !
This is one of the best explanations of PID that I've seen. As a simulations engineer, seeing this work in Unity was also incredibly helpful. Thank you sir!
Absolutely invaluable for those who implement advanced control systems in flight simulators of any kind. Thank you for introducing PID controllers to game developers since this topic is mostly covered only in the engineering context.
Big kudos for pointing out that PID systems are a simple starting point, rather than a perfect solution. And great explanation overall! Only criticism is that the suggestion of starting with 1 as a starting point for the integration saturation is a bit weird, as the units of storedIntegration (and, therefore integrationSaturation) are unit-seconds. Hence the max possible response time of the system (as measured in Hertz/seconds) has to be a factor -- even if the inputs and outputs are -1 to 1, a servo motor vs a oven require very different values. I think better advice would have been to inspect what the largest storedIntegration value encountered in the strongest wind/gravity scenarios are, and then setting integrationSaturation just a little bit bigger than that.
@@Joe-zw9ep Depends entirely on what you're optimizing for: shortest time to tracking, lowest fuel consumption, smoothest ride, or some tradeoff between those. I don't want to be that guy, but there's a reason that there are entire university courses on control systems engineering! But one example of a compromise between lowest fuel consumption and short time would be a suicide-burn-style controller (look up KSP suicide burn or SpaceX suicide burn if you're not familiar with the term). I.e., full thrust toward the target for a bit, and then coast for a while, and then full thrust away from the target initiated at just the right time so that velocity and error reach zero and the same instant, at which point the engine turns off. Another perspective on the same basic idea is to do regularly a cheap simulation going in to the future to figure out when the perfect time to start the braking burn is; the same principle can be used for any control system (and the simulation model can incorporate inconsistencies in the landscape, nonlinearities, and all sorts of stuff like that that is way beyond the understanding of a PID controller). Anyway, that's just one specific example.
@@TheHuesSciTech I am familiar with KSP and the suicide burn! Sorry my question was not really up to par but I don't know much about control theory. Don't worry you're not "that guy" it is all interesting, I know there are things beyond PID :)
This is EXACTLY what I needed for my game! I managed to make the P part, but I was struggling with oscillations. I knew I'd have to incorporate a derivative in there somewhere, but I didn't know how. Thank you!!!
I take offense to the fact that someone could dislike such a well made and paced video that delivers complex topics in byte sized chunks. Keep it up :fire:
I can totally see the tweaking of PID parameters as difficulty mode for AI ennemies in a game. 2:00 made me think of Felix Baumgartner jumping from the top of the atmosphere and recover from a hard spinning. Thanks for sharing this interesting topic!
Maybe not as specific as you think, whenever you're animating or moving an object in a game, and you want it to look more natural and less jerky, you'd put in something like this. For instance, a you might have a hitscan turret in your game. Maybe it sometimes shows up in places without cover. If it tracks player position perfectly, there's no way the player can avoid its damage. But if it aims using a PID controller, you can twiddle the values so it's a bit slow or it overshoots, so a skilled player doing rapid strafing motions can avoid most of the shots.
As an electrical engineer who programs these things and use them to balance electrical circuits it's amazingly defined and this 100% is the reason I bookmarked this and will be subbing to you. Without a doubt better than a lot of University teachers are capable of explaining it.
I wish this system had a more intuitive name. As a 3D artist with no engineering knowledge whatsoever, I've been struggling for a couple of years with this problem looking for smooth rotation tutorials that just work off of LERPs and the likes, never touching on physics or the 15° to 345° problem. This entire time I've been thinking "there must be a better solution to this..." but without knowing the name of it, or even the names of the problems I was trying to solve, I had no way to look it up. This video would have saved me dozens of hours of trial and error trying to solve something myself I wasn't qualified for, and which was already solved in the first place. It will still probably save me dozens of hours in the future, so thank you.
After 2 years in university where I had to go through all the Laplace explanations, found this video incredibly useful to explain what a controler is and how it works. Good work
thank u so much, my control systems and advanced controls systems classes for electrical engineering have been completely theoretical and this video has explained so much for me
Great video, thank you! I work with PID controllers every day, but I've never really understood the theory behind tuning the derivative term, and this really helped.
Also glad I found this! XD A long time ago I remember trying to make a hoverboard demo game, but I had such bad oscilation and the thing would always resonate out of control and flip over. This might be what I needed.
Incredible video! you helped me make an autopilot system for my unity game, and I will be using this system to make an autopilot for an RC plane in the future also.
Another great place to learn about pids is a game called storm works, a sandbox game made in unity that works on node based math and logic, they also lets you built vehicles and objects using pids
Love your visualisations and the different dimensions involved, they really help explain the concepts. Blew my mind when I realised how many game AIs probably use it to target me. Text from another video (qKy98Cbcltw)," P: if you’re not where you want to be, get there. I: if you haven’t been where you want to be for a long time, get there faster D: if you’re getting close to where you want to be, slow down. "
like most things, the first time i met PIDs the explanations were poorly understood and expressed. thank you! for imparting your thoroughness of erudition! if society had had an egalitarian attitude (and chatgpt) decades ago, we'd be decades ahead!
wow, ive tried to do something with a PID controller a few months back, but failed due to lack of understanding how to implement one. but now ive found your video and understood it instantly. you earned a sub!
As a sidenote, you can implement very simple motion smoothing to stuff like the camera by putting a proportional controller to handle the error between desired and actual position.
ok this is really helpful, as i was trying to learn how to make AI in Newtonian space, and now that i have knowledge i now know where to start with it.
I was struggling with an issue due to fast changing target position and thanks to you, it's now fixed. Thanks a lot, very good video !! It would be great to see how you adapt your code to work with Vector3 in current and target value. I just did overcharged and change every float in Vector3 but I am sure there is a way of doing it better.
Fantastic video! I've always wanted to build my own quadcopter flight controller, and I will definitely be using this as a reference when doing controller logic. :)
Bit tangential, but you could implement the PID conveniently as a method returning an IEnumerator because the produced "enumerables" are stateful. So you can just keep the previous by iterating through it.
I used something similar to write a 3d flocking program in Blitz3D ( anyone remember that? ) Specifically I was experimenting with Subsumption architecture to produce more complex behaviours
I like this video very much! The calculation of the derivative-measure doesn't need the errorRateOfChange. Always take the negative valueRateOfChange and there is no derivative-kick. If the setpoint stays constant, the negative valueRateOfChange is the same as the errorRateOfChange. Or am I wrong?
This explanation is awesome. I would love it when I was looking into it. Great stuff. BTW I was trying to create a perfect stop thruster (as in thruster that will stop the fall at the exact target height... also known as suicide burn). I was only able to implement it with gravity/drag calculations, not with PID, because with PID it was either falling slower than possible, or overshooting (therefore crashing). Since you seem to know your engineering, how would you solve this kind of issue?
To elaborate more, I've solved it, but my solution worked only when I knew the power of the thrusters, the air drag, the gravity, the mass, etc. While I could also measure these units, I like the "let me adapt to the current conditions" of the PID more appealing.
If required exact P force cause overshoot , D damp is applied to restrict overshoot in return to achieve target PD INSTEAD intially apply (P-D) calculated force P-D
Id like to see deadbeat controller/regulator in unity it is much faster than PID, but have to know object denamics to calculate regulator. BTW really nice video.
It is possible to have a PID controller that controls 2 axes at once. However it is more common to have two separate controllers that can be tuned individually.
Sometimes this is true, but not in the majority of cases. Games mostly just need to 'fake' it. Auto aim is typically applied to turrets which are not affected by 'outside' influences like gravity, momentum, drag or other physics forces. Typically turrets just have their aim changed by directly setting rotation values rather than using forces to add torque and rotate with physics. So the target rotation is known, the error is 100% predictable, so it's more of a case of just applying a proportional change every frame (let's say 10%) which is kind of like a smooth lerp.
As a Mechanical Engineer that works with these things, very well explained to the point where I saved the video
just finished mechanical vibrations class and still didn't get the integral part
@@bakersbread104 Integral part is for eliminate the error of proportional part and make the transition faster in time. The more time the error signal exists, the bigger the effect of the integral part to compensate this. Let's consider we have a PI: proportional tag by itself cannot eliminate the error value, the bigger the proportional coefficient the less error you have, but the more unstable can the system be. Let say we have an error value which cannot be compensated by the proportional tag: f(x)=-1. Try to integral this in time and summ the two function together: f(f)+F(x) = -x-1. You can see if you check the integral value on the for example t=[0,2] domain, at t0=0 the error value is -1, meanwhile t1=2 the error value is -3.
I think i did not make any mistake here but correct me if i have done :)
@@gazsope oh woops. Meant to say I still didn’t get it until I watched the video. Thanks though
This is fantastic. This is the first video I've found that explains PID in detail enough, without being too complicated.
And a GitHub code sample to refer to the implementation instead of manually rewinding the video to refer to each section as well
This is literally the best explainer I've *ever* seen on PIDs in over 3 years of re-implementing and using PIDs. THANK YOU!
You explain these complex systems very well and your videos are well made, keep it up!
This is the best explanation of a PID controller I've ever seen, and even shows an excellent breakdown of its implementation. I've been using PIDs for many years but never really thought much about how the math works. Your implementation is actually much more robust than the one I use and addresses some issues I've noticed using mine over the years.
The missile knows where it is at all times. It knows this because it knows where it isn't.
Dude, the video is so well made. Great explanation of PID, now I understand it fully, wow
Just when I had given up hope of ever understanding pid controllers, along comes you and explains it with a minimum of algebra and a maximum of understandability.
to calculate a phyisical turret you could predict the targets position instead = cause a bullet got traveltime as well.
step 1: grab the target position and store it as a vector3 and give it a fancy name like "oldTargetPosition"
step 2: grab the distance towards the target starting from the firepoint(barrelEnd) and use it to calculate the time the bullet would travel
step 3: wait for as long as the bullet would take to travel towards the target
step 4: grab the "current target position" again and "substract" it from the "old position" to get the difference between both position and call it Vector3"DistanceMoved"
step 5: create a new Vector3 and call it somting like "predictedTargetLocation = currentTargetPosition + DistanceMoved"
step 6: if the bullet is a victim of gravity (like in RL) -> calculate the bullet falloff from its "traveltime(step2)" towards the target and store it in a Vector3 called "bulletFalloff"
step 7: add "bulletFalloff" to "PredictedTargetLocation"
step 8: now if the target keeps moving at a more or less constant pattern the turret would precalculate the point where the bullet would connect with the target.
if this would be connected to an AI that has stored targetspecific information about manouverability weakspots etc. , then it could use those informations and add them into the equation.
This video simplified and taught the main part of a PID system in a magnificent way. Thank you for this valuable video!
I have tried a little bit to understand PID controllers in the past but failed. This video explains it so well, and it's very easy to follow along.
The explanations and pacing are good and it follows through everything without too much or too little detail. Very well done!
The explanation of each term, why they're needed, and how they affect the result is such a good way to understand it.
This is the best PID video! I hope there will be a new video for the more advanced anti-wind-up measures.
This video is actually really good. I had classes on PID controllers, but this is really well explained, and the demo and code makes it super usefull. Thanks a lot, great job !
This is one of the best explanations of PID that I've seen. As a simulations engineer, seeing this work in Unity was also incredibly helpful. Thank you sir!
Absolutely invaluable for those who implement advanced control systems in flight simulators of any kind. Thank you for introducing PID controllers to game developers since this topic is mostly covered only in the engineering context.
Big kudos for pointing out that PID systems are a simple starting point, rather than a perfect solution. And great explanation overall! Only criticism is that the suggestion of starting with 1 as a starting point for the integration saturation is a bit weird, as the units of storedIntegration (and, therefore integrationSaturation) are unit-seconds. Hence the max possible response time of the system (as measured in Hertz/seconds) has to be a factor -- even if the inputs and outputs are -1 to 1, a servo motor vs a oven require very different values. I think better advice would have been to inspect what the largest storedIntegration value encountered in the strongest wind/gravity scenarios are, and then setting integrationSaturation just a little bit bigger than that.
What other control systems track like this better than a PID system?
Thanks
@@Joe-zw9ep Depends entirely on what you're optimizing for: shortest time to tracking, lowest fuel consumption, smoothest ride, or some tradeoff between those. I don't want to be that guy, but there's a reason that there are entire university courses on control systems engineering! But one example of a compromise between lowest fuel consumption and short time would be a suicide-burn-style controller (look up KSP suicide burn or SpaceX suicide burn if you're not familiar with the term). I.e., full thrust toward the target for a bit, and then coast for a while, and then full thrust away from the target initiated at just the right time so that velocity and error reach zero and the same instant, at which point the engine turns off. Another perspective on the same basic idea is to do regularly a cheap simulation going in to the future to figure out when the perfect time to start the braking burn is; the same principle can be used for any control system (and the simulation model can incorporate inconsistencies in the landscape, nonlinearities, and all sorts of stuff like that that is way beyond the understanding of a PID controller). Anyway, that's just one specific example.
@@TheHuesSciTech I am familiar with KSP and the suicide burn! Sorry my question was not really up to par but I don't know much about control theory.
Don't worry you're not "that guy" it is all interesting, I know there are things beyond PID :)
This is EXACTLY what I needed for my game! I managed to make the P part, but I was struggling with oscillations. I knew I'd have to incorporate a derivative in there somewhere, but I didn't know how. Thank you!!!
I take offense to the fact that someone could dislike such a well made and paced video that delivers complex topics in byte sized chunks. Keep it up :fire:
Byte sized, huh.
I can totally see the tweaking of PID parameters as difficulty mode for AI ennemies in a game.
2:00 made me think of Felix Baumgartner jumping from the top of the atmosphere and recover from a hard spinning.
Thanks for sharing this interesting topic!
Man woke up and make THE BEST PID explanation video I've ever seen, even if it is for unity context
The use cases seem very specific but if ever needed this video is perfect. Hope to see more
Maybe not as specific as you think, whenever you're animating or moving an object in a game, and you want it to look more natural and less jerky, you'd put in something like this. For instance, a you might have a hitscan turret in your game. Maybe it sometimes shows up in places without cover. If it tracks player position perfectly, there's no way the player can avoid its damage. But if it aims using a PID controller, you can twiddle the values so it's a bit slow or it overshoots, so a skilled player doing rapid strafing motions can avoid most of the shots.
As an electrical engineer who programs these things and use them to balance electrical circuits it's amazingly defined and this 100% is the reason I bookmarked this and will be subbing to you. Without a doubt better than a lot of University teachers are capable of explaining it.
THE best explanation I have seen regarding PID controllers. Thanks!
I wish this system had a more intuitive name.
As a 3D artist with no engineering knowledge whatsoever, I've been struggling for a couple of years with this problem looking for smooth rotation tutorials that just work off of LERPs and the likes, never touching on physics or the 15° to 345° problem. This entire time I've been thinking "there must be a better solution to this..." but without knowing the name of it, or even the names of the problems I was trying to solve, I had no way to look it up.
This video would have saved me dozens of hours of trial and error trying to solve something myself I wasn't qualified for, and which was already solved in the first place.
It will still probably save me dozens of hours in the future, so thank you.
Very true, I asked in unity discord and someone immediately mentioned it and I quickly realised they saved me a ton of hassle! Thanks PraetorBlue 😁
As someone whos done 3 years of programming for a FIRST robotics team in high school (making me by no means an expert) you explained it really well!
After 2 years in university where I had to go through all the Laplace explanations, found this video incredibly useful to explain what a controler is and how it works. Good work
Thanks for short and clear explanation of specific problem with actual showcase. Definitely this video will be in my list for reference.
Holy cow, now that 4 second intro has made me subscribed. THAT is an opening.
thank u so much, my control systems and advanced controls systems classes for electrical engineering have been completely theoretical and this video has explained so much for me
Great video, thank you! I work with PID controllers every day, but I've never really understood the theory behind tuning the derivative term, and this really helped.
Man, I love when the algorithm matches me with an incredibly good video from a growing channel like this. KEEP GOING MY MAN!
I personally have never driven a car but I have flown a rocket, so thanks for that example in the beginning of the video
Also glad I found this! XD
A long time ago I remember trying to make a hoverboard demo game, but I had such bad oscilation and the thing would always resonate out of control and flip over. This might be what I needed.
wow from oscilloscope magic mushrooms to PID controllers XD this channel is gold
Thanks for sharing! Your blog, GitHub, and videos have been beneficial!
Why hit the dislike button? This video is great! So well explained and super useful for many cases. Great. Thank you so much for your work ❤
Incredible video! you helped me make an autopilot system for my unity game, and I will be using this system to make an autopilot for an RC plane in the future also.
Thank you for such a well made video. Idk how you are not famous yet. Truly amazing quality and easy to understand expainations!
This is the best non AI. 3D AI navigation tutorial. You just solved all my problems with one video.
This is an extremely well done and intuitive explanation, as well as invaluable knowledge. Thank you so much for making the video!
I liked your "call to action" at the end of the video.
Another great place to learn about pids is a game called storm works, a sandbox game made in unity that works on node based math and logic, they also lets you built vehicles and objects using pids
As someone looking to make physics games, I'm gonna get a lot of use from this
I was searching for this exactly. Perfect!
Love your visualisations and the different dimensions involved, they really help explain the concepts.
Blew my mind when I realised how many game AIs probably use it to target me.
Text from another video (qKy98Cbcltw),"
P: if you’re not where you want to be, get there.
I: if you haven’t been where you want to be for a long time, get there faster
D: if you’re getting close to where you want to be, slow down.
"
Wow excellent tutorial man. Subbed!
I learned more here than a semester in class
like most things, the first time i met PIDs the explanations were poorly understood and expressed. thank you! for imparting your thoroughness of erudition! if society had had an egalitarian attitude (and chatgpt) decades ago, we'd be decades ahead!
wow, ive tried to do something with a PID controller a few months back, but failed due to lack of understanding how to implement one. but now ive found your video and understood it instantly. you earned a sub!
As a sidenote, you can implement very simple motion smoothing to stuff like the camera by putting a proportional controller to handle the error between desired and actual position.
Best explanation I have seen on PIDs!
This is perfect visualization as it can be 👌 I'm building PID control self-balancing robot for my final year project soon, hopefully it goes well.
Best PID video I have seen so far !
ok this is really helpful, as i was trying to learn how to make AI in Newtonian space, and now that i have knowledge i now know where to start with it.
Last time I piloted a rocket didnt go so well. thank god for this video cuz i gotta renew my license next week.
I was struggling with an issue due to fast changing target position and thanks to you, it's now fixed. Thanks a lot, very good video !!
It would be great to see how you adapt your code to work with Vector3 in current and target value. I just did overcharged and change every float in Vector3 but I am sure there is a way of doing it better.
thanks for the good video! it would be cool to see the more advance methods and controllers too!
Such an amazing video and explanation
Fantastic video! I've always wanted to build my own quadcopter flight controller, and I will definitely be using this as a reference when doing controller logic. :)
This is “the missile knows where it is going” logic with extra steps.
Better explained than in my controls class in university...
I've used this pattern without knowing it was one, to resolve verlet elastics ropes !
Fantastic stuff, just what I needed. Thank you!
Properly good stuff. Thank you.
this is a fantastic overview thanks
thanks for this. I wonder, at 14:08, where did 'velocity' variable came from?
Bit tangential, but you could implement the PID conveniently as a method returning an IEnumerator because the produced "enumerables" are stateful. So you can just keep the previous by iterating through it.
Love to see if you apply Fuzzy logic into PID also. Thanks
This is amazing. Big thanks!
This is soooo useful! Thank you very much.
Now I need to find a situation where I can use this knowledge
You can run different optimizations to find optimal parameters. Like a gradient descent or a genetic algorithm
Great explanation. Thanks!
Man, I wish I would’ve found this a couple weeks ago when I was trying to tune my 3D printer’s PID. Autotune just wasn’t cutting it
Super cool explanation! :D
Awesome video man!
Thanks a lot man, u saved me
I like it!
TY for you explanation
good one! some background information (from theory) would be nice. Some times the WHY is missing.
I used something similar to write a 3d flocking program in Blitz3D ( anyone remember that? ) Specifically I was experimenting with Subsumption architecture to produce more complex behaviours
Very clear, thanks!
I like this video very much!
The calculation of the derivative-measure doesn't need the errorRateOfChange. Always take the negative valueRateOfChange and there is no derivative-kick. If the setpoint stays constant, the negative valueRateOfChange is the same as the errorRateOfChange.
Or am I wrong?
amazing video !
Are you sure you're not Kyle from Door Monster? You two sound very similar.
Interesting video btw, keep em coming
This explanation is awesome. I would love it when I was looking into it. Great stuff.
BTW I was trying to create a perfect stop thruster (as in thruster that will stop the fall at the exact target height... also known as suicide burn). I was only able to implement it with gravity/drag calculations, not with PID, because with PID it was either falling slower than possible, or overshooting (therefore crashing). Since you seem to know your engineering, how would you solve this kind of issue?
To elaborate more, I've solved it, but my solution worked only when I knew the power of the thrusters, the air drag, the gravity, the mass, etc. While I could also measure these units, I like the "let me adapt to the current conditions" of the PID more appealing.
The missle now knows where it is. (ah because of the rotating into the wrong direction issue)
If required exact P force cause overshoot , D damp is applied to restrict overshoot in return to achieve target
PD
INSTEAD intially apply (P-D) calculated force
P-D
That's the first time someone asks for a dislike instead of a like. Good video nonetheless
for rotation system, dont use eulerAngles, use Quaternion.x,y and z
Great video!
"..., worked as a robot in a factory ..." :DD
Beautiful!!!!!!
Id like to see deadbeat controller/regulator in unity it is much faster than PID, but have to know object denamics to calculate regulator.
BTW really nice video.
Does it cost us anything to use the Unity 3D Library in commercial desktop application? Thanks
My question is if you introduce a y axis, do you have to compute it separately, same as the x axis? Seems like it. Amazing tutorial btw!
It is possible to have a PID controller that controls 2 axes at once. However it is more common to have two separate controllers that can be tuned individually.
can this work for aiming with a controller? ive really been looking for a good system to make aiming with controller viable
ouch, my eyes, light mode hurts
Imagine living your whole life in darkness. Like that guy Plato locked in a cave.
Is it hard to code automatic tuning for a PID controller?
2:38
Welcome, to Jurassic Park
I didnt realise that games used PID's for the automatic aiming lol
Sometimes this is true, but not in the majority of cases. Games mostly just need to 'fake' it. Auto aim is typically applied to turrets which are not affected by 'outside' influences like gravity, momentum, drag or other physics forces. Typically turrets just have their aim changed by directly setting rotation values rather than using forces to add torque and rotate with physics. So the target rotation is known, the error is 100% predictable, so it's more of a case of just applying a proportional change every frame (let's say 10%) which is kind of like a smooth lerp.