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Patrick

Wed Mar 04 2015, 08:04AM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

Ive got a new tri-copter, and its working so well, its amazing. My previous tri's and bi's were like Spanish bulls, bucking wildly.

So, given that, im trying the typical "guess-and-fly" method and next ill try the "Z-N" method, but id like to understand the theory of control loops better. (I understand the basics of the generic PID) Ive done the basic Googl'ing; but theres alot which is still a blur. I see this as a lesson for myself and others here on the forum. Mine maybe flight related, but others here on our forum could benefit from power or mechanical feedback too, in there own projects.

Id like to ask what these terms mean in control. We often see a graph of a step change, and then a f(x) non-ideal attempt to correct. But i fail to understand how poles, nodes, gain, phase and bandwidth apply or even what they mean. PID and Kalman filters are really valuable, so im studying them thoroughly, but i get random article online.

id like to be able to explain to others and especially college professors, why i chose these particular values, instead of random guessing.

this, for the uninitiated, i found valuable.

Im also looking into a method of measuring the frequency of oscillation from a excessive "P" value. (which is a requirement for "Z-N". ) but i dont know if a strobe or oscilloscope is a good method.

Kalman:

1425457340 2431 FT1630 Basic Concept Of Kalman Filtering

So, given the above math im fearful.

Im interested in figuring out the method used in the F-117, Su-47 and X-29, to maintain stability in otherwise dynamically unstable machines.

radiotech

Wed Mar 04 2015, 10:02AM

Registered Member #2463 Joined: Wed Nov 11 2009, 03:49AM
Location:
Posts: 1546

Graph's Law.

If the damn thing is unstable sometimes, don't mess with it.

Connect a chart recorder,and leave it running until someone can explain what the wiggly lines mean.

1425463358 2463 FT169481 Gould Recorder On Master Control

Shrad

Wed Mar 04 2015, 10:07AM

Registered Member #3215 Joined: Sun Sept 19 2010, 08:42PM
Location:
Posts: 780

don't forget that you can chain PIDs which is commonly done when a process needs to stabilize several parameters to control an output

Dr. Slack

Wed Mar 04 2015, 10:18AM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

Feedback stability is one of these instances where you get taught the simple theory on low order systems, but then find the practice is so much more complicated as the systems are necessarily much higher order. It's quite interesting to look at the history of how clever people 100+ years ago slowly moved from trial and error (hope'n'poke) to doing the maths, people like Bode, Nyquist, Routh and Horowicz.

Unless you are a maths freak (I'm not, but am in awe of folks who are) and can just look at an equation and use it, then you will have to get some feel for the underlying physics. There is no way you can simply dive into a high order system and do it right by seat of the pants. I suggest you get a simulator, find an online course on PID loops, and work through that. A pure P loop is easy, it's always stable. A pure PI, PD or PID loop will also tend to be always stable in practice. Use the language of the course and the behaviour of the simulator to understand what poles and zeroes are, and how they can be used to understand stability. Forget Kalman for the moment, it won't help you with the first steps.

Now the bad news, you will rarely meet anything as simple as a pure PID loop in the real world. Anything, any unintentional lag, any delay, any filtering, can destabilise it. In the world of flying, the order is already intentionally much higher. As control signal integrates to motor drive integrates to thrust integrates to velocity integrates to position, you start off with at least a PIIII loop, then add some sensor and calculation delays and you have some further destabilizing phase shift. The manufacturers will however have put in some phase advance to conditionally cancel some of the Is, and maybe feedback from accelerometers to give you a D term or two. The wonder is that commercial stuff is ever stable, given the range of hardware that a controller can stabilize.

The other bad news. With a high order loop, you have some quite complicated tools to predict stability. If you want to explain to your professors how your system satisfies the Routh-Horowicz criterion, then you have a lot of measurement and maths to do.

Start at the bottom. Simulate a P loop, then add an I to eliminate the DC error, then add a D to reduce overshoot. Do the maths at each stage and build up to it.

Sulaiman

Wed Mar 04 2015, 11:08AM

Registered Member #162 Joined: Mon Feb 13 2006, 10:25AM
Location: United Kingdom
Posts: 3140

What a can of worms you are about to open!

the only coursework text book that I kept from my uni. electronics course is
Principles of automatic control by Martin Healey
(there are probably newer clearer books but this is the one that we used)
It's somewhere around the house, I'll check isbn and the correct title when I find it.
I kept this book because feedback control is applicable to so many engineering control tasks,
and I was never able to fully understand and apply it.

The F-117 type scenario is a multi-variable high order system ... brain-pain !
If we are VERY lucky one of the members here can explain such things clearly and concisely
but I doubt it because there are so many things to consider
it would certainly not be a simple PID loop !
In effect the control system needs to have a mathematical model of the controlled system
and perform predictive feedback control.
(for an idea of the scope of learning required, have a look at the Common terms and phrases
from the book that I mentioned

)

i don't want to put you off this subject, just let you know what you would be getting into.
If you could master feedback control you would be very employable!

EDIT: oops! I posted without noticing the above, sorry for the overlap
ignore this and go with the above.

Ash Small

Wed Mar 04 2015, 11:27AM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

The simpler the software, the faster it runs.

Dr. Slack

Wed Mar 04 2015, 01:28PM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

Oh dear, I've just had a look at the first 3 minutes of the video you linked to. It's bad.

Let's look at a proportional controller? If the car's gas pedal controlled the speed of the car, and the speedo had no lag, it would be a P only system. But the gas pedal controls the torque, which integrates to speed, so it's already a PI system. Then he introduces an oscillation caused by an undefined lag, he appears to be sampling so perhaps he is hinting at the sampling latency (which is always an issue in a software-closed loop, and as Ash correctly says, minimise the lag by using fast software).

If you are going to understand the theory from the ground up, then you need to have the example match what the tutorial says it is, including the very first, simplest case.

Unfortunately, you will probably not appreciate which sources are good, and which bolox like that one, until you know as much as I do, which is still not enough to design high order flight systems systematically.

<edit> perhaps I've been guilty of confusing whether the PID is referring to the controller or the system. The problem is that the controller alone will not tell you how the whole system is going to behave. So, a P only controller, when closing the loop on the whole system that is a gas pedal, engine and speedo, will oscillate for certain gain settings because the complete system is higher order than simply P. Frequently a PID controller is not sufficiently flexible to stabilise a flight system </edit>

Patrick

Wed Mar 04 2015, 04:32PM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

Dr. Slack wrote ...

Unfortunately, you will probably not appreciate which sources are good, and which bolox like that one, until you know as much as I do, which is still not enough to design high order flight systems systematically.

YES! thats what i constantly worry about!

( ESC = electronic speed control )

As for the loop latency, the processor is putting out data pretty fast, but then to an "ESC," then the motor, which then changes inertia, then that causes a change in thrust. So theres a "series-circuit" like accumulation of the lag.

In terms of the ESC, many ESCs just try to increase the chopping speed - - usually to 8KHz upto 16kHz, regardless of whether this really changes the motors response time to a command. Now, several have either auto or manual set phase advance to help the motor. so given what Dr. Slack said, thats starting to make sense, though a poor solution which may not do anything.

Further, the new and best ESCs i just got are amazing. They run a program on board but between the microprocessor and 3-phase motor. this micro-ish program is a stunning difference, not sure how it works though, ill ask others in the RC forums.

Radiotech:
Absolutely agree with chart recorder, just dont know how to do it.

Dr. Slack:
yes, i see now how problems described, are just as important as a supposed explanation. that PIII comment was enlightening.

Sulaiman:
That F-117 comment scares me even more... i plan to build some of those types of systems eventually.

radiotech

Wed Mar 04 2015, 09:34PM

Registered Member #2463 Joined: Wed Nov 11 2009, 03:49AM
Location:
Posts: 1546

In the case of the chart recorder shown, the machine had about seven DC motors,
from a few hundred to over a thousand. Each motor had a tachometer and an
ammeter. Each motor had a control amplifier, with all the elements of a PID controller.

Water and wood pulp went in one end , paper came out the other end.

Everything, from the individual dye pumps, to the steam flow rate was on one giant
loop. The idea was to keep it running.

Since everything was interlinked, speed swings, sometimes happened.One section
sped up, another tried to compensate.

The multi channel recorder, watching several parameters showed where the first action
occurred. i.e tracked the event.

Just like a flight recorder.

Here's some stuff from the era. Anything like your quadcopter ?

BigBad

Thu Mar 05 2015, 12:51AM

Registered Member #2529 Joined: Thu Dec 10 2009, 02:43AM
Location:
Posts: 600

Basically, it's all to do with feedback loops.

You should hit wikipedia hard, go to feedback and follow the electronics, which is where the theory is the most complete.