[From Bill Powers (2009.12.28.1530 MST)]
Martin Taylor 2009.12.28.10.50 --
MT to Rick: Let's suppose that what you had proposed was what you say here. Some planning system knew that the disturbance would be a sine wave, and moreover knew that it would have a particular frequency, phase, and amplitude. Wouldn't all the arguments made in the Powers and Bourbon paper "Models and their Worlds" apply? To avoid the Powers-Bourbon problem of blind planning, this hypothetical higher-level system would actually have to be three scalar control systems, one controlling for the sine-wave's frequency, one for its phase, and one for its amplitude. The outputs of these control systems would have to be numbers corresponding to a sine wave that should be generated by the output of the lower control system -- the one tracking the target. Somewhere there would have to be a function generator that took these three outputs and generated the sine wave reference signal for the tracking controller.
BP: This is way too complicated. What's needed, as you suggest, is an oscillator in the output function that can produce a repetitive on-off pattern at a variable frequency (what others have called a "central pattern generator", but simpler than that). The oscillator has to be adjustable in two dimensions: frequency and amplitude. Phase will take care of itself.
This suggests something like a voltage-controlled oscillator and a variable gain in the output function. The frequency comparison is done with a multiplier circuit that outputs the output signal waveform times the perceptual signal waveform. The product is smoothed, and is used to drive the voltage-controlled oscillator, with a positive voltage increasing the output frequency and a negative voltage decreasing it. Anti-aliasing may be needed, but isn't complicated. A second system can compare peak voltages and adjust the output magnitude accordingly, for the other dimension of control. Phase errors are automatically corrected by slight increases and decreases in the oscillator frequency.
MT: Yes, that would be feedback all the way. But it's very complicated, and it's not at all clear why a system that would be useful only for tracking sine waves would have evolved in a biological system.
It wouldn't be limited to comparing sine waves, and it isn't complicated. Tjhe frequency and phase of any repetitive pattern can be controlled if the output function is organized to produce it. Sine-wave frequencies can be controlled even if the multiplication is with a square-wave with a variable frequency. I have toyed for a long time with the idea of putting this sort of circuit into the "event" level to create repetitive events. Never tried any actual models, although I have built a number of control systems using the principle of phase-locked loops.
MT: As Bill points out [From Bill Powers (2009.12.26.0300 MDT)] in his mission to define "feedforward" out of existence, all we are ever doing is controlling current perceptions. If those perceptions involve using the derivative of a value to predict its future course, that future course is a current perception, too.
That's too complex an interpretation of rate feedback. If you control the variable x + k*(dx/dt), k becomes the damping factor in the control system, slowing the changes in output as k increases (NOT SPEEDING THEM UP). See Demo 5-1 in LCS3 to see the effect of increasing the gain of the rate-sensitive level Rick describes. You can vary that gain with a slider and see the effects, which are non-intuitive.
I'm not trying to redefine feedforward out of existence -- only to show that it is a lot less effective than is commonly assumed, and in most cases (all cases I have modeled) adds very little to the quality of control. The reason people so often assume it is useful is that they don't realized how large the effects of common disturbances on controlled variables really would be without negative feedback. The reason they don't realize that is that they don't see the negative feedback that is taking place to stabilize those variables against disturbances, making them think that the effects are generally small and that the universe is a lot more repeatable and reliable than it actually is. You have to know some physics or mechanical engineering to understand what would happen without the feedback component, and few psychologists have that sort of knowlege. I know you understand physics, so don't take that personally. But it definitely applies to a lot of people who think feedforward can acomplish everything. They haven't "done the numbers."
Best,
Bill P.
(at the bothom of the page)