Thoughts/questions about IR stabilization

[rblilja]

Some thoughts/questions I have about IR sensor in the application of attitude stabilization…

First some calculations…

I’m trying to get an understanding of the IR sensors used regarding their output signal's bandwidth, let us look at the Paparazzi project which uses the MLX90247 sensor. The datasheet tells us that its time constant (tao) is 30ms, this implies that the rise time (t_rise) and bandwidth (B) is (regarding it as a first order linear system) …

t_rise ≈ 2.2 * tao => t_rise ≈ 2.2 * 0.03 = 0.066 s

B ≈ 0.35 / t_rise = 0.35 / 0.066 = 5.833… Hz

Simulating the filter used in the Paparazzi IR sensor board tells us that the cut off frequency is placed at about 2 Hz, with a 20 dB/decade roll off to stop band.

http://img4.imageshack.us/img4/5305/pzuavirfilterresponse.th.png (http://img4.imageshack.us/my.php?image=pzuavirfilterresponse.png)

Ok, now the thing I can’t understand…

Realizing that the IR system is working with a pretty small bandwidth, a much smaller bandwidth that I ever could have guessed makes me wonder how it is even possible to stabilize an airframe. My intuition (obviously nothing I can’t rely on) tells me that a pretty dynamic aircraft, e.g. a FunJet (?)… Needs a regulator working in the region of 30Hz maybe? Why is that possible, having a regulator at a relatively high frequency getting a feedback from the process (airframe) by a sensor working accordingly the above calculated values? Is the sensor just over sampled at the regulator’s working frequency? Would even an IR sensor working at a 3Hz bandwidth work?

These questions are not so well formulated, but I hope that someone can understand and make me realize what I’m missing…

// Lilja

[zlite]

I don't know about the Paparazzi one, but the similar FMA sensor is very fast, much faster than you describe. Just tilt the wings on the ground and watch the ailerons--it's pretty much an instantaneous response, as far as my eye can see. At least 60hz, I'd guess.

[rblilja]

Still I think the thermopile sensors generally have a high time constant, the fastest sensor I have found is the 10TP581 (near 11 Hz bandwidth)...

Obviously the concept is working very well, I understand the principles... But not in the above mentioned perspective.

[dmgoedde]

Still I think the thermopile sensors generally have a high time constant, the fastest sensor I have found is the 10TP581 (near 11 Hz bandwidth)...

Obviously the concept is working very well, I understand the principles... But not in the above mentioned perspective.I think you are making wrong assumptions about the time constant. I dug into this once, and they use a temperature stabilized oven and a chopper, and the time constant of the thermopile has to do with output slewing from some min to some max % of the total output. I believe it is like an RC time constant. It is really a measure of how fast the hot junctions of the thermocouples can dump heat to the fill gas and come into some equilibrium with the new object the thermopile is now pointed towards.

I have flown 12 ounce MAVs at 136 km/h (85 mph) using 3-axis and 2-axis thermopile autopilots. This MAV had 200 Watts of power, zero dihedral and a thin symmetric airfloil. The autopilot was a much more primitive version of the AttoPilot, and although it did have 50Hz attitude control rate, there was no Kd to dampen angular rates, nor was there airspeed-based gain scheduling, and the thing still flew perfectly stable even in extremely gusty wind (where it had to constantly make corrections).

Keep in mind that in our use of thermopiles they are NOT having such a severe test as a chopper hiding then showing an oven rapidly. I am inclined to think that thermopiles can track small angular changes at a somewhat shorter timescale than the 30ms from the chopper test method. If the 30ms is time required to slew over some large fraction of the output, then I'd venture a guess that a flight stabilization usage that slews only over a small fraction of that can at least respond in 10ms, meaning bandwidth near 100 Hz.

[rblilja]

I think I have obtained some kind of a understanding in a form that I can interpret and accept, the bandwidth calculation is correct (almost, B = 0.53.. Hz :rolleyes: )… However, I somehow neglected the fact of a first order system’s roll off (20 dB/decade) after the cut off frequency (read bandwidth)…. Dooh’

This allows signals of higher frequencies to pass the sensor with some amount off energy loss (depending on the frequency). Maybe this “leakage” is enough for making the regulation possible? Or it is so plain simple that the bandwidth is enough (we are in fact speaking of aerodynamically stable airframes)?

I admit, really impressive performance you obtained there dmgoedde. As I said, it works but I want to really understand it in a “regulator-ish” point of view.

In continuous time space a first order linear system’s rise time of 10 ms won’t correspond to a bandwidth of 100 Hz. However, considering the regulator working at 50Hz and that no digital LP filters are applied (SMA is not valid regarding the Shannon-Nyquist theorem), it simply feels like an over sampling to obtain a “nice” representation of the signal after the ADC quantification.

Who did design this system from the beginning, deciding filter frequencies and so on..?

Please correct me.

Anyone having a different aspect?

// Lilja

[dmgoedde]

Or it is so plain simple that the bandwidth is enough (we are in fact speaking of aerodynamically stable airframes)?We are NOT in fact talking about aerodynamically stable planes. I've seen 14 ounce 26" span plane handle gusty 30 mph wind, while being grossly tail heavy. Another plane (flying wing) actually had NEGATIVE dihedral after multiple epoxy repairs.

While I am schooled in kinetics and so forth, from my perspective you are thinking about this too hard.

Don't need to guess about what the 30ms thermopile bandwidth means: read page 9 of the following GE technical document that says "The time constant shall be decided by the time required 63% of the detector output voltage" http://www.thermometrics.com/assets/images/thermopile.pdf


Some more info: http://www.eoc-inc.com/dexter/8585%20Rev%20B.pdf

[rblilja]

I have not guessed. I’m well aware of the time constant’s definition regarding a first order linear system. The connection between the time constant and the sensor’s bandwidth is done in my first post.

rise_time = 2.2 * time_constant, bandwidth = 0.35 / rise_time

Originally Posted by dmgoedde
We are NOT in fact talking about aerodynamically stable planes. I've seen 14 ounce 26" span plane handle gusty 30 mph wind, while being grossly tail heavy. Another plane (flying wing) actually had NEGATIVE dihedral after multiple epoxy repairs.

Ok, so they have a negative static stability? That would be like flying a Eurofighter (or alike) without the flight computer?

Since you are schooled in kinetics and seems to have an in depth knowledge of aircraft stability (I'm not), would you please explain the connection between an airframe’s bandwidth and its design, or point me to any source of information. This would be the key factor; showing that the airframe’s bandwidth is less than the sensor’s would settle my mind.

Thank you for your correspondence.

[kodel]

what I have noticed in my tests on my own autopilot is that output amplitude swing from the sensor board is definitely lower when the frequency is high (e.g. oscillating wing rock) then when the frequency is low (e.g. airframe in a static 1 wingtip down attitude).

This is something I had to factor in when calibrating sensor output swing from a static situation. In the dynamic situation my algorithms would severly underestimate the airframe angle and control algorithm would undercompensate. So we are definately working in an area somewhere on the 20db slope.

Another factor is that due to the aerodynamical resistance the wing rocking frequency is inversely (and probably quadratically) proportional to the amplitude of the wing rock. This means that although our control algorithms would not be able to see and compensate for the fast oscillations of the airframe, they will be able to compensate for the slower larger oscillations.

The point is that any stabilisation of an airframe is always settling in an oscillation around the control point of the process (eg.wings level). I don't believe that anyone using IR-sensor stabilisation can achieve a "stabilised" oscillation of faster then about 3 Hz. But at 3hz wing rock oscillation the amplitudes that are reached in even a fast unstable delta wing are so small that the airframe appears to be rock-stable for your eyes.

So in my opinion your answer lies in the fact that even the unstable airframes we are talking about have an infinite bandwidth at 0 amplitude but only about a 2Hz bandwidth at the smallest noticeable amplitude by the eye. Bandwidth goes down fast when amplitude goes up (e.g.how many timesper second can you rock the wings of your delta from 45degrees left to 45 degrees right and back. I bet if you reach 1 Hz it's already considered a very fast rolling and unstable airframe. Don't mistake this with the roll rate, since you need to take into account the slowing down of the airframe to standstill and speeding up again in the other direction)

So I think the short answer is that for the amplitudes we're interested in the airframe's bandwith is indeed less then the sensor's cut off frequency (+ some small amplitude decaying fast beyond the filter frequency)

[rblilja]

Thank you very much for that explaining answer. My mind is settled.

[bmw330i]

what I have noticed in my tests on my own autopilot is that output amplitude swing from the sensor board is definitely lower when the frequency is high (e.g. oscillating wing rock) then when the frequency is low (e.g. airframe in a static 1 wingtip down attitude).

This is something I had to factor in when calibrating sensor output swing from a static situation. In the dynamic situation my algorithms would severly underestimate the airframe angle and control algorithm would undercompensate. So we are definately working in an area somewhere on the 20db slope.

Another factor is that due to the aerodynamical resistance the wing rocking frequency is inversely (and probably quadratically) proportional to the amplitude of the wing rock. This means that although our control algorithms would not be able to see and compensate for the fast oscillations of the airframe, they will be able to compensate for the slower larger oscillations.

The point is that any stabilisation of an airframe is always settling in an oscillation around the control point of the process (eg.wings level). I don't believe that anyone using IR-sensor stabilisation can achieve a "stabilised" oscillation of faster then about 3 Hz. But at 3hz wing rock oscillation the amplitudes that are reached in even a fast unstable delta wing are so small that the airframe appears to be rock-stable for your eyes.

So in my opinion your answer lies in the fact that even the unstable airframes we are talking about have an infinite bandwidth at 0 amplitude but only about a 2Hz bandwidth at the smallest noticeable amplitude by the eye. Bandwidth goes down fast when amplitude goes up (e.g.how many timesper second can you rock the wings of your delta from 45degrees left to 45 degrees right and back. I bet if you reach 1 Hz it's already considered a very fast rolling and unstable airframe. Don't mistake this with the roll rate, since you need to take into account the slowing down of the airframe to standstill and speeding up again in the other direction)

So I think the short answer is that for the amplitudes we're interested in the airframe's bandwith is indeed less then the sensor's cut off frequency (+ some small amplitude decaying fast beyond the filter frequency)
That is a really good illustrative reply to the question. Thank you, I just learned quite a bit from your reply.