On 11.11.2015 20:30, Alexander E. Patrakov wrote: > 11.11.2015 23:36, Tanu Kaskinen wrote: >> Sorry for being obtuse, but I don't follow what this simple bit of code >> is doing. You mentioned "P-controller" and the "Ziegler-Nichols >> method". I followed the Wikipedia link, and found that a P-controller >> is a very simple thing: > > Actually it was me when splitting the patch :) > >> >> u(t) = Kp * e(t) >> >> where >> >> u(t): the new control variable value (the new sink input rate) > > No. The control variable is new_rate - base_rate. > >> >> Kp: a tunable parameter (a magic number) >> >> e(t): the error value, i.e. the difference between the current process >> variable value and the target value (current latency minus configured >> latency) > > Correct. > >> The Ziegler-Nichols method can be used to choose Kp. For a P-controller >> Kp is defined as >> >> Kp = 0.5 * Ku >> >> where >> >> Ku: a number that, when used in place of Kp, makes u(t) oscillate in a >> stable manner > > See below, I'll comment on that. > >> >> (A sidenote: I probably have understood something wrong, because Kp is >> a plain number, and u(t) and e(t) have different units, so there >> appears to be a unit mismatch. u(t) is a frequency and e(t) is a time >> amount.) > > Kp is not a plain number. It has the unit necessary to convert from > the unit of error value to the unit of the control variable. > >> >> Figuring out Ku seems to require having an initial calibration phase >> where various Ku values are tried and the oscillation of u(t) is >> measured. The code doesn't seem to do this. Could you explain how you >> have derived the formula in rate_controller()? >> > > The formula is indeed not the most obvious one. We have exchanged some > emails with Georg. If he permits, I can forward his email with the > derivation of the non-linear part written on paper and scanned. But, > to answer the question about the "optimal tuning" in the sense of > Ziegler-Nichols method, we only need to talk about the linear > approximation in latency_difference_usec, that is, put min_cycles to 1.0. > > So: > > new_rate = base_rate * (1.0 + latency_difference_usec / adjust_time) > > I.e. here Kp = 1 / adjust_time, that's all. > > Assuming that the correct rate is the nominal one (i.e. base_rate), > which is a crude approximation but good enough for evaluating > stability, the latency difference accumulates with the speed which is > exactly (base_rate - new_rate) / base_rate. Indeed, in one second > according to the input, base_rate samples will be pushed, but only > new_rate samples will be pulled from the queue. So, each second, the > queue grows by base_rate - new_rate samples. According to base_rate, > it's (base_rate - new_rate) / base_rate seconds per second. > > Now note that the new latency difference will be evaluated again in > adjust_time. So, if we put Kp = 2 / adjust_time instead of what we > did, then see what happens: by the time we look again, the latency > difference will be overcorrected by a factor of 2. I.e. changes the > sign. Then the rate controller will try to correct that again, and > will again overshoot by a factor of 2, i.e. it will return to the > original value. I.e. it will exhibit oscillations with constant > amplitude - exactly what Ziegler-Nichols method calls for, when > calibrating. We actually use Kp = 1 / adjust_time, i.e. half of the > critical value, which is exactly what Ziegler-Nichols method prescribes. > > Note: I did not say that following this method is good for our > purposes. The PID controller recommended in these papers (and used in > Jack) is not optimal in the sense of Ziegler-Nichols method: > > http://kokkinizita.linuxaudio.org/papers/usingdll.pdf > http://kokkinizita.linuxaudio.org/papers/adapt-resamp.pdf > Hi Alexander, regarding your note: I was under the impression that we agreed that we could both not come up with a better way of controlling the latency in this context. And - as another side note - my controller is only optimal in the sense of Ziegler-Nichols for small latency differences. Regards Georg
