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New Phase-Lead Compensator

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dude_500

Sun Oct 02 2011, 09:34PM

Registered Member #2288 Joined: Wed Aug 12 2009, 10:42PM
Location: Cambridge, MA
Posts: 179

ScotchTapeLord wrote ...

The differentiator should have its R and C set for a gain of 1 for your coil's frequency. Also, its negative feedback resistor needs to be significantly larger than the input resistor before the 3nF capacitor for maximum phase shift capability (which won't necessarily be necessary). The potentiometer should probably be pretty high, maybe 100k. It isn't dramatically different from the original design at all, but I needed to redeem myself after that last trainwreck that I posted.

The gain of having the differentiator at unity for the coil frequency was giving me troubles with distortion on a TL072. This is why I have the last op-amp following the differentiator, which is set to about 1/100 gain at coil frequency, then raised through the next inverting buffer. This likely wouldn't be necessary with an op-amp of probably >25mhz unity gain, which gets costly compared to other op-amps of a lower bandwidth.

Of course this all comes down to personal design styles and opinions, since at this point we're not even discussing chip counts (with dual op-amps, all the modifications in this thread are still two-chip).

axelro

Sun Oct 02 2011, 10:03PM

Registered Member #3640 Joined: Sat Jan 22 2011, 12:16PM
Location: Germany close to Heidelberg
Posts: 39

dude_500, Scotchtapelord, thank you both for your proposals and answers.

I did not have time to look closer yet, but I realised there is a high frequency swinging in your LTSpice model, Dude_500. It is at the second OpAmp. One can see it, if one only selects this voltage (low amplitude). The funy thing is it cancels out or disappears somehow and still works.

Scotchtapelord, my "mid" label is actually what usually would be called ground, so I think the grounding of the CT makes sense (doesn't work anymore, when I place it down to the -5V net label as you suggested). But anyway, I'll try to set it up again with your newest circuit and a clean dual voltage.

In parallel, I have been working on my uC based phase lead - one could say it's a software PLL. I am coming close to try it for real, hopefully tomorrow. While this is significantly more complex then your elegant circuitry, it has the additional advantage to be 100% controllable, dead time, phase lead, all just coming down to numbers. Should it work out, I will soon report in a seperate track.

ScotchTapeLord

Mon Oct 03 2011, 12:58AM

Registered Member #1875 Joined: Sun Dec 21 2008, 06:36PM
Location:
Posts: 635

dude_500, what kind of distortion were you getting? Phase? I can see in the datasheet that it could most definitely be an issue...

EDIT: Food for thought!

Just skip the op amps! It limits you to a bit less shift but the simplicity rivals an inductive burden, and you don't have to worry about active components and their bandwidth! The values were pulled from thin air, so feel free to change them, as I'm sure there's a sweet spot for any given frequency.

dude_500

Mon Oct 03 2011, 04:22PM

Registered Member #2288 Joined: Wed Aug 12 2009, 10:42PM
Location: Cambridge, MA
Posts: 179

ScotchTapeLord wrote ...

dude_500, what kind of distortion were you getting? Phase? I can see in the datasheet that it could most definitely be an issue...

EDIT: Food for thought!

It was having quite a bit of the input function coming out in the derivative (aka a significantly phase shifted derivative, which may actually be fine but I prefer to have it all working as expected).

Your new link is an interesting design. My simulations show it takes a cycle to settle in on a delay, but I may just have not found the sweet spot on component values. I'd be curious to see how it holds up in real life. I'm thinking it may suffer the same issue as the inductor, that is being stuck in the past.

ScotchTapeLord

Tue Oct 04 2011, 12:21AM

Registered Member #1875 Joined: Sun Dec 21 2008, 06:36PM
Location:
Posts: 635

Yeah, the TL072 specifies 90 deg phase shift for useful coil frequencies. I thought I was misreading that; it seems odd.

Now that you mention it, there may be a tiny delay on the first pulse, but I think it depends on the capacitor impedance vs resistor impedance. I'm sure there's an optimal balance, and I think I will build and test this. It's one of those rare times my school lab has all the components I need (except the fast comparator, but that isn't the important part).

dude_500

Mon Oct 24 2011, 07:21PM

Registered Member #2288 Joined: Wed Aug 12 2009, 10:42PM
Location: Cambridge, MA
Posts: 179

So, I made the compensator last weekend and tested it on the coil. It works pretty well... better than an inductive burden, but there are still spikes at the starting couple of transitions. And I compared the current in the primary to the output of the phase leader, and indeed, it's not leading nearly as much on those first pulses.

But how can this be? It works perfectly on a sinusoidal input function from a function generator, it even responds nearly instantly to a gated 40khz signal as I had in the video of my first post! So why won't it respond to the current of the coil?

Resorting to a mathematical model to explain this (note that LTspice is not sufficient for this simulation, since as best I can tell, LTspice ignores the homogeneous solutions of all differential systems):

Let's model the system of a DRSSTC, which is just a driven RLC circuit (modeled in terms of q to get initial conditions to work well, which in this case are q(0)=0 and Dq(0)=0): Lq''+Rq'+q/c = drive, where in the case of a coil drive is a square wave. For this simulation, I used l=16e-6, c=0.35e-6, and R=2 (I know, that's like a bit high... but it makes the simulation illustrate the point better)

Now, let's push this through matlab with drive=sin(2*pi*fres*t), and plot the curve of 0.9*current+.000001*diff(current) on top of it, which should simulate any of the first order phase compensators we use, be it inductive burden or the op-amp circuits discussed in this thread.

This is the first picture attached, and the second picture is zoomed way in on the zero crossing. Looking pretty good, although there is a couple of percent error on the first lead.

But wait! This doesn't actually model the system, because as we all know the drive of a DRSSTC is a square wave. So, let's change the differential equation to being equal to the first two fourier terms, sin(2*pi*fres*t) + 1/3*sin(2*pi*3fres*t).

Again, plot 0.9*current+.000001*diff(current) on over the signal for this new current. Attached is the signal, and also zoomed in on the zero-crossings. Uh oh! It performs exactly as it does in real life. The first crossing is not as leading as later ones. The effect is much more significant in real life, presumably I could get a more dramatic illustration with many more terms of the fourier series. If you can't see it, the first crossing is about 25% less leading than later pulses. In reality, the first one barely leads at all compared to later ones.

I tried graphing the third fourier coefficient overnight (these take a very long time to run in higher orders), and I woke up to a frozen computer. But regardless, the point is clearly illustrated using only two terms.

Conclusion: A compensator following the signal model of A*I+B*dI/dt will never be a proper compensator for a DRSSTC. I haven't yet had time to try to design a new compensator, but I'm guessing it will have something to do with a second order term. If you have any suggestions, feel free to throw them out there. I don't have any formal training in designing these compensators so I'll be playing it by theory and trial and error for a while to come up with a new system.

Steve Conner

Sun Oct 30 2011, 09:27AM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

Hey guys, long time no see!

The problem (issue? opportunity?) with a DRSSTC is that the coil system resonates at two frequencies simultaneously. According to your driver design and tuning philosophy, you can excite one of them in preference, or try to drive both equally.

If you want to excite one of the frequencies and let the other die out, then you must start your burst with a phase error. This is because the impulse response of the coil system has its zero crossings at (f1+f2)/2, but you have to generate a drive waveform composed of only f1 or f2.

A phase error at the beginning of the burst doesn't really matter, as long as it has locked in before the primary current rings up to a level that would be dangerous to hard-switch.

Finally, in the old days of analog computing, there was a saying, "Never differentiate anything" as the large high frequency gain led to problems with noise and instability. This seems especially relevant around a Tesla coil spewing EMI from every port.

These last two are my excuses for not following the Predikter development and staying with my old PLL driver. I pay the price of not being able to drive both resonant frequencies at once, but I haven't yet figured out if that is significant.

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