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Monday, August 16, 2021

Why You Should Avoid Using "Positive/Negative Feedback"

I ran into a discussion on Twitter about the use of the terms positive feedback and negative feedback. These phrases really should not be applied to discussions of things like economic dynamics. I have discussed this before, but I decided to give the full explanation.

The stand alone term feedback as it is commonly used is perfectly fine. (Whether it was turned into corporate manager-babble is one concern, but I will leave that aside.) The problem is adding the qualifier “positive” or “negative.” Someone could try to argue that “positive” is a synonym for “good,” and so “positive feedback” is equivalent to saying “good feedback.” The problem is that good feedback is a silly sounding phrase in most of the contexts where “positive feedback” shows up (but not in contexts where you compliment someone).

In the context of economic theory discussion my argument is that the “positive” and “negative” should be interpreted mathematically. Many economists do enjoy dropping technical jargon into their writing. Furthermore, adding the word "loop” to create the phrase like negative feedback loop definitely gives the connotation of being related to the source concept that appeared in engineering.

I will give a rough background of the phrase within engineering later, but I will offer a more sensible replacement — which is unfortunately not perfect if you run into an extreme pedant. The replacement equivalents would be “stabilising feedback” (“stabilizing feedback” if you speak American), and “destabilising (destabilizing) feedback.”

The longer version of the term would be “a feedback that tends to stabilise the system.” This admittedly is somewhat vague (and has issues when applied to control theory proper), but vagueness is one way to deal with uncertainty.

I will now give a history of the term feedback within engineering, with the first part being admittedly guesswork. However, the modern usage of the terms comes from control theory, where I have the credentials to claim to be an authority.

Amplifiers

The first area where the term feedback is commonly used now is in the design of amplifier circuits.

As the name suggests, amplifiers increase the magnitude of an input signal. They have been a part of electrical circuitry since the invention of the triode vacuum tube before World War II (with the silicon junction field effect transistor (JFET) largely taking over from triodes after the war).

The issue with amplifiers from a engineering standpoint is that the gains vary even for the same model of amplifier. It would not be too surprising to pick up two amplifiers with the same model number, and one would have a gain of 1000, the other 1200. A high level of uncertainty about the exact characteristics of an electrical component is extremely unwelcome if you are mass producing a product — you cannot fiddle around with each item to tune it. The solution is to develop amplifiers with extremely high levels of amplification, then embed them in a circuit to achieve a target amplification that is much lower than the maximum of the amplifier. The other circuit elements determines the gain, and those elements have more uniform electrical characteristics. (For those who are suckers for punishment, this is explained in the report “Understanding Operational Amplifier Specifications” by our friends at Texas Instruments.)

Those amplifier circuits are configured such that the output of the amplifier is fed back into the circuit that is leading to the input. Compared to power circuits, this is an unusual configuration — power circuits are normally akin to a piping system where the contents flow in a circle with various channels splitting off and rejoining further “downstream,” not coming back “upstream.”

I would find it unsurprising that the circuit designers used the term “feedback” in describing those circuits pre-World War II, but I have no references.

Audio Feedback

The term “feedback” is well known from experiences involving microphones and speakers. If you put a speaker that outputs sounds coming a microphone near that microphone, the “sounds” can go around in a loop.

All we need is for high frequency sounds to go around that loop with a magnification greater than one (or even close to one), and the speaker will end up spewing out high frequency noise at its power limit. (This high frequency noise is described as “screeching noise.”)

Given the overlap between people developing amplifier circuits and sound engineers, the technical use of “feedback” could have come from either side pre-World War II.

Feedback Control Engineering

My argument is that the modern usage of “positive feedback loops” and “negative feedback loops” is based on usage from control systems engineering. Old texts might refer to “feedback control engineering” as synonym for control engineering. As for the control systems academic literature, it magically appeared out of nowhere in a few years just after World War II.

Well, not exactly magically. The development of things like RADAR and military radios as well as flight control circuitry were extremely pressing technical concerns. Amplifier design went from being a thing that a few inventors working on radios cared about to being a state secret. What would refer to now as “classical control theory” was developed by a core group of researchers working for the United States Air Force (USAF). (The Soviets had their own version of the theory, but their public domain tradition was incorporated into the American over the span of the Cold War.)

As a post-doc, I worked with George Zames at McGill University, a well-known control theorist who started in the 1960s (and passed away in the mid-1990s). He was at MIT, and his professors were among the first civilians to be introduced to the Air Force’s new theory.

(The way it was taught was entertaining. The students presumably had background checks, and were let into the class without notebooks. The professor could write one equation on the blackboard, and discuss it. An Air Force officer would then erase that equation, then the professor could go into the next.)

The USAF decided it was in the national interest to disseminate the knowledge more widely, and thus the papers that formed the core of classical control theory appeared in academic journals. The papers were clean and instant classics, since they had been polished over an unknown span of time.

Since the researchers behind control theory were spending a lot of time working with amplifier circuits, they would have picked up the term “feedback loop” if its usage preexisted the formal appearance of control theory. Regardless of the original source, classical control theory cemented the position of the phrases “positive/negative feedback loops” within engineering.

Why Positive and Negative Feedback?

Where did positive and negative feedback come from? Tradition!

Control and communication systems engineering (the two traditional branches of systems engineering) were unusual within the engineering faculties: they did not refer to physical laws or technologies, only the mathematical specifications of engineered objects. Control was the science of using feedback to get a plant to operate as desired, while communications aimed at shipping information from point A to point B without being garbled. (Although the final application areas are wildly different, they share mathematical formalisms, which explains why I was able to teach the senior undergraduate communication systems course as a postdoc at McGill without the accreditation people barfing all over the floor.)

In the traditions of systems engineering, for a system with a single input and a single output (SISO), the usual convention is to define the sign convention of the input and output so that the gain at low frequencies (0 Hertz or DC) is a positive number.

If one wants to dig into the technical version, for linear system model, we write the transfer function as a Laplace transform (continuous time) or z transform (discrete time) as a ratio of polynomials with the leading terms positive.

So if we have a mathematical model of the system that gives a negative gain at 0 Hz from the input to output, engineers would tend to flip the sign convention of the input to get it to conform to tradition. This made life simpler. Back in the good old days, a lot of analysis was done by the examination of what are called step responses. Textbooks included diagrams of how to analyse the step responses of systems. So long as you followed the sign convention, you could compare your system’s step response to the ones in the textbook. If you flip the sign, you need to turn your book upside down to do the comparison, and you look silly doing that.

Once we accept the sign convention, one can then take an undergraduate course on classical control theory, and they would find the following principle: if we feed back the control input (which is the output of the controller we are designing) into the plant that we are trying to control, we generally need to multiply the output of the controller by -1 in order for it to have a stabilising effect. In other words, we generally want the negative of the feedback output to stabilise the system.

As an example, imagine you are taking a shower. You can turn the faucet to adjust the temperature of the water, with a turn to the left increasing the flow of hot water. If we treat the angle of the dial as the input variable, the sign convention means turning left increases the input variable. If the shower is too warm (cold), we need to turn the dial to the right (left). This means that the adjustment to the dial has the opposite sign to the temperature deviation — negative feedback.

(If I still owned an undergraduate text on control engineering, I could probably find a semi-convincing explanation of the previous assertion, but from my memories of my academic research, I think “just because I said so” is probably the cleanest explanation for my purposes here. Perhaps if I had taught at the undergraduate level, I might have absorbed whatever explanation they use.)

Since most engineers in practice deal with systems as SISO systems and do not spend any time worrying about the traditions around sign conventions, they would not have problems with using “negative feedback” as being synonymous with “stabilising feedback.”

(Note: some raise the issue of linearity assumptions. This is somewhat of a red herring, since all real world engineering systems are nonlinear, yet systems engineers apply linear system theory to them. All we need is that the linearisation of the nonlinear system to conform the sign convention, and we should end up in the same place. If the nonlinearity messes things up so badly it has stability properties that are the opposite of its linearisation, you probably have a very badly designed engineering system.)

Problems With the Terms

There are a few issues with using positive/negative feedback outside that context.

  • Even within control engineering, it breaks down. The addition of multiple inputs means that sign conventions will break down. For example, if a system has two inputs and outputs, the simplest control laws (proportional feedback laws) will be a 2x2 matrix of gains. In general, the signs of the matrix entries will be mixed.

  • Just using negative feedback is not enough. Even if we have a system that meets the usual conventions, a negative feedback with too high a gain can destabilise a system that was previously stable. (Taking the shower example, if you overreact to the current water temperature, you will end up swinging the dial wildly since there is a time lag from your control action to the observed temperature output.) In other words, a “negative feedback loop” can still be bad for system stability.

  • Applying a “negative feedback rule” may not be stabilising if the system we are dealing with is more complex than an engineering system. Engineers design things so that they can be controlled, so simple control laws are supposed to work. A complex system like an economy is not designed (unless you want to start debating some branch of theology).

  • Why apply a niche engineering term to complicated systems that do not conform to the teaching conventions of undergraduate electrical engineering?

If we look at something like economic dynamics, we have oodles of variables doing whatever they are doing, and they all interact in wacky ways. We cannot isolate a single variable that is controlled by a single variable. (Even conventional beliefs about using the policy to control inflation do not completely fit the SISO framework, since things like “expectations” show up.) If you are going to grab a technical term from a field of study, you probably want to use it correctly.

“Stabilising Feedback” Not Perfect

If one wants to pedantic about control theory, one might object to some phrasings involving “stabilising feedback.”

Standard technical definitions of stability are binary: a system is either stable, or not. (There are multiple ways of defining stability, but they generally end up being equivalent for linear systems.) So, phrasings that imply that one configuration of a system is “more stable” than the other might be objected to. That said, this really only would matter if one is discussing control theory itself.


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(c) Brian Romanchuk 2021

3 comments:

  1. Amplifiers increase the energy level of the input signal, which is more significant than just raising the magnitude of the input signal. The power level of the output is greater than the input.

    This added energy comes from someplace.

    Now relate this to the monetary system. Money would be like the energy in the system, not the magnitude of the signal (which would be measured in volts or amps).

    Like energy, the presence of money persists over time. Volts and amps are momentary readings, more like prices.

    Feedback, whether positive or negative, has to do with how the output signal might influence the input signal. If energy feedback is positive, the fed back signal can be greater than the input signal, a situation wherein the output signal takes control and the amplifier goes into self oscillation.

    Negative feedback then is intentional feedback, fed out of phase with the incoming input, intended to buck/oppose the unavoidable/undesirable positive feedback.

    I mentioned that money is like energy in that it is persistent. Thus, adding money to the economy is like adding energy to an input signal. Adding money to the system is positive feedback for input prices; removing money from the system is negative feedback for input prices.

    (Written from the perspective of a longtime Amateur Radio operator.)

    ReplyDelete
    Replies
    1. The power of a signal is related to its amplitude. If the signal is defined as a voltage (usual), power = V^2/R.

      The power does not magically get multiplied. The amplifier draws power, and the magnified output comes out of that. If the input signal is too large, the amplifier hits its rated potential, and ceases to magnify at the desired gain.

      Delete
  2. It’s actually a great and helpful piece of info. I’m happy that you just shared this helpful info with us. Please keep us informed like this. Thanks for sharing! Best Commercial Electrician Noble Park service provider.

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