wrote
My two cents worth: any autopilot that acts in that manner is probably
best not used for "coupled" approaches.

I concur. But then I'm not a fan of doing coupled approaches with
old-technology autopilots anyway.

I put "coupled" in quotes
because a truely coupled approach would be independent of the heading
bug once the localizer has been captured.

Do you fly an approach without reference to heading once the localizer
is captured? Of course not - you fly a heading, and use the CDI as a
correction on the heading. So do most Century autopilots. There is
nothing wrong with using heading information to stabilize the
approach. The problem is with the way the unit does it.

Century 2000 sounds all nice and modern, but really it's the same old
analog control loop design going all the way back to the Century II
with a digital false face hung on it. Here's how it really works:

At its core, the device is a wing leveler, and a crude one at that.
It runs a roll servo to attempt to keep the bank angle at some
setpoint. That set point can be zero bank, it can be some bank angle
dialed in by a roll knob, or it can come from the heading gyro. In
that case, the set point is a bank angle proportional to the deviation
between actual and bugged heading, with a limit (usually 25 degrees of
bank). When a nav coupler is used, the nav deviation is used to add
an offest to the bug. What I mean by this is, let's say in LOC mode,
one dot is worth five degrees. If the loc needle is a dot right, then
the nav converter will make the autopilot think that the bug is five
degrees to the right of where you set it. In reality, it's usually
not linear - past some point (say 3/4 scale) it will start making each
additional increment worth a lot more degrees, so that it can track a
course somewhat even if the user set the bug totally wrong. So really
we have another control loop, and a non-linear one at that.

Now, obviously with this kind of scheme, you never actually eliminate
offset unless you set the heading bug to the correct heading (not
course) to fly. That's why the approach was being flown two dots out.
This is normal behavior for the Century system.

The problem is that when the heading bug was reset, the system went
into oscillatory behavior.

Realize, though, that this is a system with three nested control loops
- a tight inner loop doing wing leveling, a more damped loop modifying
the bank angle setpoint on the inner loop based on heading deviation
to accomplish heading hold, and a third loop modifying the heading
setpoint on the middle loop based on course deviation to accomplish
course tracking.

Now realize that ultimately, that inner loop is deflecting ailerons -
and air loads on ailerons at any given bank angle depend quite a lot
on airspeed, not to mention control system friction (which can vary
with rigging and ambient temperature). The system is expected to work
over a range of airspeeds and temperatures for a given make and model,
and with only minor tweaks it is the same system for many makes and
models.

Note that turbulence will affect bank angle - adding noise into the
system.

The rate of heading change as a function of bank angle changes with
airspeed. Once again the system is expected to work over a range of
airspeeds.

The rate of angular course deviation as a function of heading change
depends on distance from the navaid and groundspeed. The system is
expected to function over a range of distances and groundspeeds.

It's pretty damn tough to do a triple nested control loop with
reasonably fast response across a variety of conditions and not have
oscillatory behavior somewhere. There are lots of adjustments to be
made. Then rigging changes over the years, things maybe don't get
lubed quite so well as they sould, electronic components drift out of
tolerance due to temperature extremes as the plane sits out in the sun
and heats up to 130 or chills in the winter to -20.

So the bottom line is what you saw is not so unusual, and the correct
solution (assuming there is one that does not involve hand flying)
will depend on what has drifted out of tolerance. Changing heading in
steps may be the way - usually the smaller the setpoint change the
lower the chance of oscillatory behavior. But the reality is that you
have an autopilot that, while still usable for lots of things, is
probably not quite exactly right, and probably should not be used for
actual coupled approaches. Which is pretty much the norm for older GA
autopilots.

Michael