It’s on-line so I suppose this is acceptable behavior. Lord Monkton and Roy Spencer are having a discussion. I’m not a particular expert in control theory but I did do almost seven years of engineering college at some point.
The argument stems from a claim that in control theory, you have to use the entire perturbation signal in an equation in order to get a proper feedback model. This means that if you don’t know the zero state, you cannot calculate the feedback and future requirement. This claim ‘almost’ ignores the fact that the derivative of the equations also have a solution. If you are looking for a change in temperature, instead of actual temperature, the entire control set can be created with a derivative of error. Add the offset back in, and you have the actual temperature. This is vastly less difficult from a mathematical standpoint than trying to encompass the entirety of the error as it allows errors to be linearized or at least expressed as low order equations.
This link has an explanation of the process in terms of industrial control.
PID Controller
A PID Controller or a Proportional-Integral-Derivative controller is a control loop feedback mechanism (controller) widely used in industrial control systems.
PID control is the most common control algorithm used in industry and has been universally accepted in industrial control. The popularity of PID controllers can be attributed partly to their robust performance in a wide range of operating conditions and partly to their functional simplicity, which allows engineers to operate them in a simple, straightforward manner.
A PID controller calculates an error value as the difference between a measured process variable and a desired setpoint (desired outcome). The controller attempts to minimize the error by adjusting the process through the use of a manipulated variable.
The PID controller algorithm involves three separate constant parameters, and is accordingly sometimes called three-term control:
- Proportional ( P)
- Integral (I)
- Derivative (D)
Simply put, these values can be interpreted in terms of time: ‘P’ depends on the present error, ‘I’ on the accumulation of past errors, and ‘D’ is a prediction of future errors, based on the current rate of change. The weighted sum of these three actions is used to adjust the process via a control element such as the position of a control valve, a damper, or the power supplied to a heating element.
Terminology:
The basic terminology that one would require to understand PID are:
- Error: The error is the amount at which a device isn’t doing something right. For example, suppose the robot is located at x=5 but it should be at x=7, then the error is 2.
- Proportional (P): The proportional term is directly proportional to the error at present.
- Integral (I): The integral term depends on the cumulative error made over a period of time (t).
- Derivative (D): The derivative term depends on rate of change of error.
- P-Factor (Kp): A constant value used to increase or decrease the impact of Proportional
- I-Factor (Ki): A constant value used to increase or decrease the impact of Integral
- D-Factor (Kd): A constant value used to increase or decrease the impact of Derivative
Note- Each term (P, I, D) will need to be tweaked in the code. Hence, they are included in the code by multiplying with respective constant factors.
I like this link because it shows the basic idea behind what I’m trying to say (in terms of climate models). The integral term is cumulative error (temperature gain from all greenhouse gasses). Essentially, how far feedback has pushed the system off of its root gain. They literally treat it as constant in climate models considering a stable non-human influenced climate. The derivative term is continuously updating rate of change in error, I don’t believe climate models even use this factor but I don’t know without research. The proportional constant is simply how far of center the error is after the offset. This is the argument it seems these folks are having. Monkton seems to say you need to use integral and proportional factors to predict the future, the confusion exists in that Climate science DOES use both integral and proportional error. Climate science uses the simple way. What is temperature 50 years ago, that is the integral. Add the proportional, ignore the derivative because climate changes slowly and you’re done.
It’s possible I don’t understand something else about this disagreement but it seems pretty much semantic, rather than mathematical.
There is a second bit of the discussion which should be handled separately. The electrical circuit.
So he built a feedback amplifier circuit and tested the matter for himself. That was not easy, because so small is the true unit feedback response that he had to run wires into the next room so that his body temperature did not affect the readings. To his surprise, he found that the underlined words are correct.
I left several comments in Roy’s thread, having never been to the Monkton paper. I explained that this implies high gain in the circuit or that it wasn’t built with operational amplifiers. Op amp’s have been the choice of the electrical feedback mathematician since pre-calculator days. I did click the link briefly just now, and found that numerous folks also had the same critique of the electrical circuit. In a climate model, NOBODY thinks gain is very high in an electrical sense. It’s more like an off-center teeter totter where your kid sister flies a little higher than you. It isn’t you going flying because a butterfly stomping on the end. Every scrap of science implies low gain, so this means someone used transistors to look fancy or overgained a circuit or did some other uselessly complex thing which in the end, only confused people.
I had dinner with Lord Monkton and a bunch of other folks once. He’s a good guy for sure. I’m not even remotely convinced that this work is accurate. We’ve used proportional feedback since well before I was in college. Drones use it, car control systems, even linkages are built with these basic concepts.
Global warming is real, it is very small, it is not dangerous, and it is a positive influence on God’s green Earth.
the Air Vent 
In college, I was garbage picking with a friend and found a tiny printing press in the university dumpster that had two full-bridge strain gauges mounted professionally on the top and bottom of spring hardened stainless steel strips about 6 inches long. I took one of them and built s scale from it that had ridiculously high gain daisy chained operational amplifiers. They ran completely cool but even at the milliamps of current an air current on the circuit itself would deflect the needle.
You could weigh scraps of paper that looked like bits of fluff.
Some of us have weird hobbies but I did learn that if you want to gain something in a crazy high manner, thermal correction, air currents and all kinds of things become factors. That the ‘expert’ needed to leave the room is a huge alarm bell that something is wrong.
Thanks for pointing out that the expert’s needing to leave the room should have been an alarm bell. It sounded wrong to me, too, but as far as I’m aware no one brought it up before you did.
On the other hand, I think discussion of PID controllers may be somewhat orthogonal to what Lord Monckton’s doing. Note that the operation of PID controllers is described by differential equations, whereas all of Lord Monckton’s work employs only algebraic equations. To me his restricting the discussion to algebraic equations seems appropriate, because he’s dealing only with equilibrium quantities, i.e., with what remains after the time derivatives have decayed to zero; he doesn’t concern himself with transients. So the “perturbations” are slight changes in quantities, such as the input, that affect what the equilibrium state will end up being. They may cause transient behavior, but he’s discussing only what remains after the transients have died out.
Specifically, his work deals with the equilibrium temperature E and the value R that the equilibrium temperature would have assumed if there had been no feedback. (See Fig. 1 at https://wattsupwiththat.com/2022/09/12/refutation-of-the-forgotten-sunshine-theory/.) To my way of thinking that’s acceptable in theory–if we avert our eyes as I did in that refutation from the fact that R is a completely counterfactual quantity and therefore does not exist in the real-world feedback system.
My point was that the equilibrium quantities which include all of solar forcing and climate model quantities which include all of solar forcing and PID controllers also include all of total forcing. Algebra is what is left after differential feedback is time-integrated.
They are the same thing. I’m having a lot of difficulty telling the difference between each method. The differences exist in the values and equations used but each method should work just fine – with the correct values and equations.
From your article “Similar forbearance is requested of those who unlike Lord Monkton look upon feedback as only a small-signal quantity, i.e., as operating only on departures from some baseline condition”
This is how weather models operate as the complexities of all of history would serve little purpose without today’s observation of weather events. We can’t predict a hurricane seven decades in advance. We can predict a hurricane’s probability as long as we maintain what the weather guys call a persistence model, which is a fancy way of saying ‘same as yesterday’.
My point is that in feedback modeling, nothing strikes me as unreasonable or even significantly different, about using a small change in forcing vs the whole amount. In the case of PID controllers, which happen to work well, all forcing factors are taken into account. I’m trying to think of a physical analogy which makes it more obvious that they are all the same thing.
If you have a heater on a block of metal, the heater will drive energy into the metal. If that metal was cooled by air, you would have radiative cooling as well as conductive air cooling drawing heat from the block of metal. In a pid controller above, you would have the integrated (summed) amount of cooling I, which acts as the offset value RCS from Monkton’s equations. In a climate model, fired up similarly to a weather model, it would be the starting temperature. Same thing to me.
All three versions contain the same offset.
In the case of the PID controller, not only does it do offset, it looks to the change in offset, P. In a climate model, through different looking math, this is the forcing value resulting in ECS. In your post on Monkton’s work, this is the value C.
Now the PID controller includes the rate of change of error D. This is not something useful in climate models of the resolution we use. The value is ignored as a zero as is the second and higher derivation value. Assuming these derivatives as zero in climate feedback is completely rational. This same assumption is also (apparently) the case in Monkton’s work.
In climate models Monkton’s R is the temperature. In a PID controller of my example where things are STABLE, the R essentially becomes the temperature set by the controller and only differential values become critical. In monkton’s model, R is set explicitly – and well after the complex integrations have occurred.
As always, I reserve the right to be wrong, but I’m not seeing anything this time.
I think we basically agree. I certainly agree in principle with your statement, “My point is that in feedback modeling, nothing strikes me as unreasonable or even significantly different, about using a small change in forcing vs the whole amount,” as you can see in my post at https://wattsupwiththat.com/2019/07/16/remystifying-feedback/, which is a mathematical treatment of the relationship between small- and large-signal quantities.
So I think it contributed needlessly to the confusion for people like Dr. Spencer and Nick Stokes to insist that feedback can only be viewed as a small-signal quantity. In practice, though, basing calculations just on perturbations is indeed the only way to do it, because if you think about it you run into a lot of pointless difficulty in deciding what the entire equilibrium temperature would be without feedback.
I replied to you yesterday but it went into the aether (old spelling is better. sounds like a fantasy novel)
100% agree with your statement. Didn’t even realize Nick got into this, but your last sentence is perfect.