Re: [PATCH 2/5] writeback: dirty position control

[Peter Zijlstra]

On Fri, 2011-09-02 at 14:16 +0200, Peter Zijlstra wrote:
> On Mon, 2011-08-29 at 21:37 +0800, Wu Fengguang wrote:
> > > 
> > > Ok so this argument makes sense, is there some formalism to describe
> > > such systems where such things are more evident?
> > 
> > I find the most easy and clean way to describe it is,
> > 
> > (1) the below formula
> >                                                           write_bw  
> >     bdi->dirty_ratelimit_(i+1) = bdi->dirty_ratelimit_i * --------- * pos_ratio
> >                                                           dirty_bw
> > is able to yield
> > 
> >     dirty_ratelimit_(i) ~= (write_bw / N)
> > 
> > as long as
> > 
> > - write_bw, dirty_bw and pos_ratio are not changing rapidly
> > - dirty pages are not around @freerun or @limit
> > 
> > Otherwise there will be larger estimation errors.
> > 
> > (2) based on (1), we get
> > 
> >     task_ratelimit ~= (write_bw / N) * pos_ratio
> > 
> > So the pos_ratio feedback is able to drive dirty count to the
> > setpoint, where pos_ratio = 1.
> > 
> > That interpretation based on _real values_ can neatly decouple the two
> > feedback loops :) It makes full utilization of the fact "the
> > dirty_ratelimit _value_ is independent on pos_ratio except for
> > possible impacts on estimation errors". 
> 
> OK, so the 'problem' I have with this is that the whole control thing
> really doesn't care about N. All it does is measure:
> 
>  - dirty rate
>  - writeback rate
> 
> observe:
> 
>  - dirty count; with the independent input of its setpoint
> 
> control:
> 
>  - ratelimit
> 
> so I was looking for a way to describe the interaction between the two
> feedback loops without involving the exact details of what they're
> controlling, but that might just end up being an oxymoron.


Hmm, so per Vivek's argument the system without pos_ratio in the
feedback term isn't convergent. Therefore we should be able to argue
from convergent/stability grounds that this term is indeed needed.

Does the stability proof of a control system need the model of what its
controlling? I guess I ought to go get a book on this or so.



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