Harry said:
I like your "even....S.Cuk"
Hey, if Dr Cuk writes papers on it, it probably works. Unlike much of
the crap published in some professional comics
, which look something
like this:
1. design a topology have way too many magnetic components, switches,
diodes and capacitors than necessary. If possible, ensure > 3
semiconductors in power path at all times.
2. write the NLTV equations for the system.
3. run thru maths package and draw pretty pictures
4. spice circuit - ie enter graphically, then let spice numerically
extract & solve much the same equations as (2), and draw some more
pretty pictures
5. Compare and contrast the pretty pictures. If they are very similar,
pat self on back and proudly announce "it works" (or in other words the
analytic solution mathced the numeric one)
6. Add to list of published papers, lean back at desk and sigh
contentedly. Outside, the real world rushes madly by.
So Terry, will this controller cure sub harmonic oscillation in CCM >50%
duty??
I think in general it will do so, but you can perhaps design one that
doesnt.
OCC is by definition a non-linear controller, so there is no need to
"linearize" (read as: pretend it is something it is not) the system
before designing the controller. Quite the opposite in fact.
You design a One-Cycle Controller by developing a non-linear
time-varying mathematical description of the converter to be controlled.
We do this anyway when designing a conventional linear controller.
After adopting a suitable pose and expression, stare long and hard at
the mathematical description, and voila - the desired OCC control law
comes leaping out at you.
This is basically a kind of feedback linearization controller (eg
Applied Nonlinear Control, Slotine, pp207-271). The idea is to cancel
the nonlinearities in a nonlinear system so that the closed-loop
dynamics are in a linear form. Traditional LTI system theory can then be
used to design the controller, and assuming there are no model
uncertainties the controller behaves as predicted, for large as well as
small signals.
[linearisation is actually "do a taylor/maclaurin series expansion and
throw almost all of it away". Often the bits you discard are important,
which is why linearised controllers dont necessarily work so well for
say large signals]
A simple example of this concept is a boost PFC. When designing the
voltage control loop, if you use square of the DC bus voltage and
compare it with the square of the setpoint voltage (trivial in s/w) - in
other words implement a DC bus energy controller - then analysis shows
the closed loop behaviour is in fact linear (assuming the current
controller is fast enough to reach setpoint faster than the voltage loop
sample time).
Its interesting that one method of nonlinear stability analysis,
Lyapunovs 1st (or is it 2nd? someone will correct me im sure) method
uses suitable "lyapunov functions" to check asymptotic stability. Common
functions are the so-called "energy functions" that mathematically are
similar to physics equations for energy like 0.5CV^2 etc. Oops,
rambling...its because of the 2nd law of thermodynamics, real systems
are always asymptotically stable (if not they would be perpetual motion
or free energy machines) blurble.
that control systems label isnt necessarily right either - I suspect
some OCC designs may look more like a straight nonlinear controller
rather than the aforementioned feedback linearisation. who cares, its
only a label, but the techniques are interesting.
A significant drawback with non-linear control is the lack of a
handle-cranking mechanism for, say, proving stability, or even choosing
a controller. Its a big nasty world out there....time to go shelter
behing whats left of Maclaurin....
What about using it's voltage feedforward ability in DC/DC loops?
Regards,
Harry
as usual, *it depends*. Each OCC strategy is (or can be) unique - define
your system, design the controller. A literature search will save you a
fair chunk of work here, but in practice if you're gonna design a loop
you might as well analyse the entire thing. Or at least load up the last
mathcad file, save as and twiddle the numbers....
One potential problem with feedback linearisation is its robustness to
parameter variations. Some implementations may be very sensitive, others
may not. The published results I've read for many OCC converters look
pretty good, probably because the integration smooths over any errors.
But I betcha you could come up with really lousy OCC's if you tried
I (hopefully) have a project coming up where I will implement a whole
raft of feedback linearisation controllers. Maybe they will even
work.....the idea is to implement non-linear controllers to enable the
system to maintain control (not saturate) for large setpoint & load
changes, along with a high closed-loop bandwidth for relatively low
sampling rates. This stuff (in some respects) is quite easy in a DSP,
whereas a lot of it is a pig in hardware (until IR, ST etc. make nice
cheap chips)
Cheers
Terry