Current Controlling a Large Inductor

If I wanted to control the current of an unknown and potentially very large inductance how do I approach that? Or more generally, how can you control any system with unknown and potentially large inertia (like a voltage source and large C).

So to state some possibly obvious control theory facts:
1) I've got 360 degrees to work with
2) My error amplifier consumes 180 of those degrees
3) The pole created by the inductor will create a 90 degree phase shift at a frequency that's realistically lower than where I want to cross over my compensator
4) So in theory I've got 90 degrees left to work with for my controller (and 45 would ideally be left as margin)

At first I thought I'd investigate various lead compensation schemes (like Type III compensation) however:
a) These have fixed zeros which can't be well tailored to my unknown pole frequency and inevitably crossover at roughly 90 degrees minimum anyway (correct?)
b) Or in general I'd like to push the phase as high as possible at compensator crossover however for the compensator to cross over a pole must be pushing it there, and that means ~90 degree phase shift (correct?)
c) So it appears that I can't do much better than a single pole compensator which shifts from ~0->~90 (leaving razor thin phase margins)

So where does that leave me?
A) Am I misunderstanding my options?
B) Can I live with razor thin phase margins in this application?
C) Is there no generalized solution to potentially infinite inertia?

Hi,

What about using local feedback?
Or phase shift circuits?

Klaus

If its just a huge low resistance inductor, for instance the iron cored field winding of an alternator, it can have a very long L/R time constant which can sometimes be measured as several seconds. (tens of henries and hundreds of milliohms)

As you say, that will produce a 90 degree phase shift, and the control amplifier an additional 180 degrees, giving an initial phase margin of 90 degrees.
Provided there is no significant additional phase shift within the loop, the system will be completely stable with any amount of open loop gain.

If the inductor is truly large, the time constant will always be very long with respect to any additional electronic delay within the control loop. So you will not loose any of that 90 degree phase margin, or perhaps only a negligible amount.

The system will naturally have a very low bandwidth, and closed loop gain will fall well below unity before there is any significant change in any additional phase.

All it should need is a current shunt in series with the load, an internally compensated op amp error amplifier, and a voltage follower to drive the inductive load.

Ok thanks, this is helpful but lets break this down. I have to have the compensation gain cross through unity at some point, lets call that 300hz (not ridiculously low but outside the range of any other system poles/delays). And per a and b above there is no way to cross through unity gain without approaching 90 degrees phase shift (definitely correct me if that's not a good assumption).

So now my load pole can be in 3 places. Well below 300hz, well above 300hz or near 300hz.

For the 'below' scenario your post is helpful and I don't think I'd analyzed it properly. If my compensation phase is zero at the point where the load crosses the system below unity I'll have a 90 degree phase margin. And this is easy if I make the right choice in control (a pure integrator would always contribute 90, so I avoid this). The 'above' scenario is obviously fine too, and is the normal operating point of most feedback systems.

But for the 'near' scenario it still seems like I'm at risk for low phase margin as it can be the case that both my load and my compensation contribute phase delay at the same time. Here the system seems sensitive to my open loop gain. If it's high, the phase contribution of the compensation + load L needs to be higher to have pushed the system gain down through unity.

In principle, the inductor current can be controlled by a current source with large output impedance (= current controlled voltage feedback with P characteristic and large gain). ω0 = R/L

In a real world, at least inductor parallel capacitance and respective self resonance will limit the bandwidth, also amplifier and controller limitations.

In principle controlling the current in a large high Q inductor isn't inherently more difficult than controlling the voltage across a large high Q capacitor, which is what power supplies typically do. Consider that if your controller has a voltage output, then a high Q inductor basically acts an an integrator, so your compensator may not need an integral term at all. Just look at the whole open system (including the amplifier and the inductor itself) and its transfer function and that should tell you what your controller will need to look like.

If your inductance is unknown, then that's a challenge, much like it would be a challenge to design a power supply controller without knowing the output capacitance. Unless you resort to something elaborate like nonlinear or adaptive control schemes, you will either have to design with very large stability margins, or make the controller tunable. At work we have a lab high power amplifier meant for driving arbitrary impedance, but it requires that you change jumpers around depending on the approximate impedance being driven and the required bandwidth.

I find it difficult to believe that any large inductor can have a self resonant frequency anywhere nearly as low as 300 Hz all by itself.

Where is all this extra phase shift coming from to reduce the existing 90 degree phase margin at 300Hz ?

Warpspeed said:

I find it difficult to believe that any large inductor can have a self resonant frequency anywhere nearly as low as 300 Hz all by itself.

Where is all this extra phase shift coming from to reduce the existing 90 degree phase margin at 300Hz ?

Click to expand...

Well I have to have a pole in the control somewhere right? The reality is that I have a voltage loop with bandwidth ~4khz or so and I'm therefore planning to put a pole in the current loop (which is wrapping the voltage loop) at roughly 1/10th of that.

While inductance may be high it may also be low or zero. That leaves the possibility of the load pole and phase shift encroaching on the 300hz territory that my control pole will be set at. What I see in worst case simulation configurations is that with high open loop gain both poles have caused significant phase shift (>90 total) prior to bringing system gain below unity.

Or to put it more simply, I think, it's a two pole system (where I don't have control over one pole) and two pole systems can shift up to 180 degrees.

Does that make sense or am I still missing something?

mtwieg said:

In principle controlling the current in a large high Q inductor isn't inherently more difficult than controlling the voltage across a large high Q capacitor, which is what power supplies typically do. Consider that if your controller has a voltage output, then a high Q inductor basically acts an an integrator, so your compensator may not need an integral term at all. Just look at the whole open system (including the amplifier and the inductor itself) and its transfer function and that should tell you what your controller will need to look like.

If your inductance is unknown, then that's a challenge, much like it would be a challenge to design a power supply controller without knowing the output capacitance. Unless you resort to something elaborate like nonlinear or adaptive control schemes, you will either have to design with very large stability margins, or make the controller tunable. At work we have a lab high power amplifier meant for driving arbitrary impedance, but it requires that you change jumpers around depending on the approximate impedance being driven and the required bandwidth.

Click to expand...

Right or the speed of a large mass etc. My hypothetical is how I might approach things if I know nothing about my load inductance.

That's interesting. I have a lab amplifier advertising unconditional stability with any load.

asdf44 said:

If I wanted to control the current of an unknown and potentially very large inductance how do I approach that? Or more generally, how can you control any system with unknown and potentially large inertia (like a voltage source and large C).

So where does that leave me?
A) Am I misunderstanding my options?
B) Can I live with razor thin phase margins in this application?
C) Is there no generalized solution to potentially infinite inertia?

Click to expand...

Higher order systems are often reduced to a 1st order open loop system so the phase comparator makes a stable 2nd order systems. This can be compensated with a 1st order or lag-lead filter. High order amplifiers with negative external feedback have internal integration with a small cap to dominate the other poles. THis is how Op Amps work to be unconditionally stable at unity loop gain.

But reactive components with inertia have back EMF` so when a change in direction is forced a negative voltage or current is required. this is not the same as a phase shift in a reactive component. The method used to analyze or design a closed loop system is done with transfer functions in the frequency domain with variables like mass, velocity acceleration, position, voltage and current, phase, time and frequency. A VCO for example is Hz/volt while a tach is volt/Hz.

The loop compensation does not need to be restricted to 90 or 180 degrees of compensation. But the loop will be most stable when the forcing function is conditioned to be in the same units of measurement as the feedback. So a complex servo with mass may have a mass with a target position change, a target velocity & acceleration profile with feedback for each with variable and compensation for each. Feedback can also be non-linear and have noise so correction must be constrained when there is loss of signal so that drift or massive error from hunting does not occur.

Phase margin of a 2nd order system is directly related to overshoot, ringing and other factors so thin margin means on the verge of instability and wild oscillations from a disturbance.

Infinite mass or inertia is possible but requires equally infinite force and would be the situation with a singularity. Even less than infinite mass with less than infinite gravity can cause a disturbance when two forces collide. Such as the recent report with the pico-resonance of space-time fabric on our gravity from such a disturbance from the collision and merging of two black holes. .. but I digress.

A megawatt power transformer might have an induction of hundreds of Henries and the oil insulation might result in uF's of capacitance but the parallel or series resonant frequency would never be 300 Hz or 60 or 50 Hz unless it was a ferroresonant transformer which suffer from higher ESR and poor load regulation but good voltage regulation for input fluctuations. They also have poor transient rejection from coupling capacitance... but I digress again..

The original question was:

If I wanted to control the current of an unknown and potentially very large inductance how do I approach that?

Click to expand...

Now it has changed to :

While inductance may be high it may also be low or zero.

Click to expand...

And that is a very different thing.

asdf44 said:

Right or the speed of a large mass etc. My hypothetical is how I might approach things if I know nothing about my load inductance.

Click to expand...

One way to make things easier is to add built-in inductance to your amplifier output. That way at least you know there is a minimum on the total inductance. Again this is comparable to the output capacitance built into voltage regulator circuits. If there's 1000uF built into a power supply, then you can be pretty sure that it will be fine driving an extra 0-100uF.

If your load inductance gets very large, then the voltage range of your driver will probably be the limiting factor rather than small signal response.

mtwieg said:

If your load inductance gets very large, then the voltage range of your driver will probably be the limiting factor rather than small signal response.

Click to expand...

Good point.
Its no good designing for a 300 Hz bandwidth if there is insufficient voltage swing available, and that may require many hundreds of volts to achieve with a large inductor.

Warpspeed said:

The original question was:

Now it has changed to :

And that is a very different thing.

Click to expand...

Sorry for not being clearer. Does this mean you agree with my assessment of the phase margin situation given a hypothetical unknown inductance? It appears that I can get some phase margin, but only by reducing open loop gain.

mtwieg said:

One way to make things easier is to add built-in inductance to your amplifier output. That way at least you know there is a minimum on the total inductance. Again this is comparable to the output capacitance built into voltage regulator circuits. If there's 1000uF built into a power supply, then you can be pretty sure that it will be fine driving an extra 0-100uF.

If your load inductance gets very large, then the voltage range of your driver will probably be the limiting factor rather than small signal response.

Click to expand...

And now that's making more sense. For example a TL431 has a band of output capacitance where it's unstable but above or below that it's stable. That seems to mirror the scenario I'm describing here where a problem area arises when both the loop compensation and the load are contributing phase shift simultaneously (but prior to system gain crossing unity) but if the load pole moves significantly in either direction that problem is mitigated.

Warpspeed said:

Good point.
Its no good designing for a 300 Hz bandwidth if there is insufficient voltage swing available, and that may require many hundreds of volts to achieve with a large inductor.

Click to expand...

But that bandwidth may be advantageous in the lower inductance scenarios.

Though of all things bandwidth is something I'd give up. But given the above discussion, I don't see what going significantly lower buys me.

We have absolutely no idea what this is, what it is supposed to do, or what constraints there may be placed on any of it.

Without some kind of full specification its not really possible to suggest a solution.

If you need a large inductor but low current, use a gyrator Op Amp circuit.

If you want to define your requirements in clearer terms from the starting point and end result.
You will learn faster. Otherwise your incorrect assumptions confuse the issues.

Ok lets try again: the hypothetical application is a source regulating DC current in a winding (think motor/generator/transformer) which has significant inductance. The upper inductance bound is both large and unknown to me and the lower bound is zero inductance (just R). Naturally I'd like to be able to ensure stability. The system I'm working with is a relatively high power amplifier capable of ~100V and 10's of amps.

On top of the fact that the starting inductance is unknown the DC target current may or may not saturate the core, which would cause a potentially rapid inductance change during operation.

The implementation plan was to build a current loop wrapping an existing voltage loop (again with a range of say +/-100V).

The fact that the inductance is truly large and truly variable is why I initially tried to frame things in terms of theory. And I wanted to be standing on a solid base of theory, as opposed to potentially application specific answers. I apologize if that confused things.

If its a motor/generator, the field excitation current is not directly in itself of any great interest, so long as the current cannot rise to destructive levels. There may actually be enough residual resistance in the winding to cover that situation.
The rating plate of the machine should tell you.
It may very well cope with the full 100 volts dc applied all day long at full rated output.

The control loop will take the final output of the machine (whatever that is) and use it to control the field excitation via a feedback loop.

Now a machine of that size (several kilowatts of field excitation) is not going to be small. And it certainly is not going to have a natural time constant of 300 Hz.
Probably more like three seconds or multiples of that.

You will probably find that the combination of inductance and mechanical inertia will have a surprisingly long time constant, and response to a step input of field excitation will take a relatively long time to take any effect.

A hysteric regulator, sometimes called a "bang - bang regulator" often works amazingly well in this type of application. It will self oscillate generating a slow PWM effect and hold the output constant, yet respond as rapidly as the machine possibly can to sudden step load changes with complete stability.

And nothing you can do in the feedback loop is going to hurry it up.

Voltage regulators and similar applications have been using vibrating contacts since the 1920,s for control of large motors and alternators, and they worked perfectly adequately in their day without any instability. A modern electronic version with a voltage reference, voltage comparator (with hysteresis), and monster IGBT would very likely do everything you expect.

It will probably PWM away at a few tens or hundreds of Hz and give excellent control.

Everything is interesting to someone.

No I'm referencing the 300hz because I'd prefer not to have a ridiculously slow system in the case where I don't actually have much inductance (or to track load changes during saturation if encountered, though 300 isn't some magic number for that). I fully understand that when faced with a time constant in the seconds that the system would sit pinned at its voltage limit waiting for current to increase.

Thanks for bringing up hysteric control because that hadn't entered my mind for this application and is a great answer for stability.

But going back to where we were before I had nearly convinced myself that I could guarantee at least some phase margin if I had sufficiently low gain and just a single pole in my control. Given a choice between a system with low worst case phase margin that might ring (but is ultimately stable) and a hysteretic system which oscillated by design I'd still be pretty tempted by the former.

Though there would be ways to implement hysteric control without the 'bang' I suppose, such as implementing more controlled voltage up/down ramps. Such an implementation would trade effective bandwidth and transient response for a smoother voltage on the output.

The ramps come for free from the inherent inductance.

And if the field winding is rated for 100v dc operation, it should smoothly rise up to that, even if it does get finally up near saturation.
But I cannot imagine an experienced electrical engineer designing a very large machine where the normal performance envelope included complete hard magnetic saturation.

Hysteric control is fairly common in this type of application, It certainly eliminates the not inconsiderable problem of a linear dissipative power amplifier stage.
A hundred volts at tens of amps is a lot of useless watts to burn up.
A switching power amplifier, or mains phase control would be far more preferable, even if you do decide the liner amplifier feedback route.

Hysteric control with a hard switched output is the simplest way to drive a simple inductor, and it will offer the best possible transient response to load change possible and complete stability.

Right I get that current ramps are free in this scenario but I was suggesting ramping the voltage. Instead of the comparator triggering a hard switch to the opposite rail it could trigger a controlled ramp towards the opposite rail. This avoids the 'bang'. It also handles primarily restive loads somewhat gracefully (as opposed to the theoretically infinite self oscillating frequency and wild current that would result from hard switching an R). Again, the tradeoff would be effective bandwidth and transient response. But it some cases (perhaps not all) it might settle in at a fairly well controlled voltage. Worst case with a very large time constant inductor the voltage would hit the opposite rail before the current hit the other side of the comparator window, but that would be no worse than hard switching.