Applicability of control theory to audio amplifier design and assessment

[Mr. Haelscheir]

I've seen https://www.audiosciencereview.com/...ad-for-power-amplifier-torture-testing.10298/, for example, and want to clarify whether it is necessarily the case that different amplifier designs that produce the same transfer function through a basic resistive load can when measurably exhibiting high linearity, flat response, low noise or distortion, and low output impedance (high damping factor) be expected to have nigh identical (within audible thresholds) control over the same real audio transducer provided that all these amps are driven within their nominal operating conditions.

From what control theory basics I learned in university, one could have the example of a motor whose position or velocity you want to control with an electronic signal, say, voltage, whereby the control circuit would exhibit a transfer function between the electronic signal and the desired position or velocity parameter. You could also take the transfer function between different nodes of the control system. Such control systems could be open or closed loop with certain benefits and drawbacks. They could also suffer issues with tracking, underdamping, overdamping, or instability due to the controller's parameters' interaction with the properties of the load (e.g. rotor mass). Most audio systems appear to be open loop with the amplifier driving the transducer with no feedback taken from the produced sound or the transducer's displacement.

1. By what principle or model is it that these audio transducers would not (or could) benefit from closed loop control or things such as PID control among other topologies particularly involving feedback from the transducer? Or do existing measurements of very low distortion out of transducers driven by reference amplifiers already demonstrate that transducer feedback is completely unnecessary in audio applications? Perhaps this has to do with audio transducers being LTI? E.g. Could incorporating transducer feedback help control a nonideal transducer's resonant modes, force a specific transfer function, or improve its transient response?
2. Does having an identical transfer function for the electric/driving signal (with respect to the original audio signal) running between the amplifier and the transducer guarantee identical tracking of the transducer with that driving signal (identical transfer function of the transducer's motion), or can there be other factors beyond the transfer function for the driving signal that may allow different amplifiers exhibiting the same driving signal transfer function to yield a different transfer function out of the transducer? Or if the only way to produce a different transducer transfer function is for the driving signal's transfer function to also differ, by what principle do amplifiers keep their driving signal transfer function invariant (or fail to do so) between different loads?
3. In audio, are we designing amps primarily to control transducers "with the firmest grip" and without being disturbed by those loads, or are we striving to design transducers that are best at obeying the amplifier's every command without disturbing the amplifier's operation? Or you could say that it goes both ways.

 

[MaxwellsEq]

In audio, are we designing amps primarily to control transducers "with the firmest grip" and without being disturbed by those loads, or are we striving to design transducers that are best at obeying the amplifier's every command without disturbing the amplifier's operation? Or you could say that it goes both ways

It goes both ways. There are few, if any, amplifiers designed with a specific transducer in mind. There are few, if any, transducers designed with a specific amplifier in mind. So both domains are designed as if the other is a pure black box with perfect behaviour.

In practice, relative to speakers, amplifiers are almost perfect; whilst relative to amplifiers, speakers are quite flawed. So amplifiers need control capabilities able to cope with any perturbation from the speakers. Speakers are designed to assume the amplifier acts as a perfect voltage source, regardless of impedance.

 

[somebodyelse]

There are certainly theoretical reasons why closed loop transducer control would be beneficial from a performance standpoint. From a commercial standpoint it will be about balancing costs - does feedback allow equivalent performance and reliability at a lower cost than open loop? There has also been an element of market expectation that amps and speakers are separate things, with acceptance of full active speakers changing at different rates in different sections of the market.

There have been a few systems manufactured over the years containing some form of motional feedback from the transducer. I believe Rythmik use a sense coil while Grimm use an accelerometer. I understand Apple may have used feedback from a microphone in some of their devices, but they're a lot more secretive about the internal workings of their equipment.
https://www.erinsaudiocorner.com/loudspeakers/rythmik-f12g-direct-servo-subwoofer/
https://www.audiosciencereview.com/forum/index.php?threads/rythmik-l12-subwoofer-review.12140/
There's a fair bit more detail in an earlier thread: https://www.audiosciencereview.com/forum/index.php?threads/motional-feedback-mfb.27956/

On the open loop side there are some efforts to more fully characterise the driver and to preprocess the signal to compensate. TI's SmartAmp is one example where large excursion and thermal characteristics are included, not just the usual frequency response correction.
https://www.ti.com/lit/an/slaa757/slaa757.pdf

There have also been amplifiers with negative output impedance, similar to some open loop dc motor drivers.

 

[AnalogSteph]

As illustrated by the now-legendary Philips MFB speakers that came out in the 1970s, the idea in itself isn't anything new. It is pretty much something that requires an active speaker design, as a passive crossover rather gets in the way.

I think adoption may have been limited by the need for custom transducers, which is generally expensive. (Transducer prices are a mucho economy of scale driven affair.) You might just as well be throwing copper shorting rings and kevlar voice coil formers at the problem and do extensive FEM analysis of the magnetic field and improve performance this way. Or transition the amplifier to current driving well above fs, as Bruno Putzeys has done in the Kii Three if memory serves.

 

[MaxwellsEq]

I have a Deltec DPA50S Power Amplifier. This has a second set of sense cables that go to the speaker terminals, and extend the NFB loop. See section on DPA50S on this page

There are risks with this approach, since it's possible to accidentally interfere with the amplifier's internal NFB with the lid still on! So the owners need to be a bit more savvy than normal when plugging things in!

 

[restorer-john]

As illustrated by the now-legendary Philips MFB speakers that came out in the 1970s, the idea in itself isn't anything new.

Philips MFB was just one.

Aiwa (under Heitaro Nakajima at the time) did motional/mic based feedback (amp to speaker) very well too. Subwoofers under Velodyne did piezo? accelerometer based feedback and IIRC sense coil FB.

Plenty of amplifiers (Matsushita etc) did basic load sensing testing and I believe now there are a bunch of devices which can even measure the attached loads function. Negative impedance drive was another (Yamaha) and of course Kenwood with their famous "sigma drive" placing the speaker wire in the FB loop. (with explosive results).

 

[MaxwellsEq]

Kenwood with their famous "sigma drive" placing the speaker wire in the FB loop. (with explosive results).

Which is the risk with the Deltect DPA50S which does the same thing

 

[Philbo King]

This is probably more easily & reliably applicable to active speakers.

It is conceptually similar to lab grade DC power supplies that have a sense input for voltage at the load, thus compensating for voltage drop in the load wiring under heavy currents. That sounds dandy, until a sense connection fails, causing the power supply (sensing zero volts at the load) to instantly crank out maximum voltage. It is inherently dangerous in systems where boxes are wired together by the user. (Ask me how I found out...)