Webcast presentation on feedback from Feb. 2006
Use of feedback
The use of feedback is an
important theme in many parts of our research. Most chemical
engineeers are (indirectly) trained to be ``feedforward thinkers''
and they immediately think of ``model inversion'' when it comes doing
control. Thus, they prefer to rely on models instead of data, although
simple feedback solutions in many cases are much simpler:
- Feedback solutions are less sensitive to uncertainty and disturbances.
- Feedback is the only way of changing the dynamics of a system.
- Feedback can be used without any model if applied locally such that
high-gain feedback can be used.
- Feedback applied locally may remove nonlinearity.
An interesting aspect is the use
of feedback hierarchies based on local feedback loops which operate
independently (in parallel). As everyone knows there are used
extensively in practice - in a chemical plant there may be 3 or 4 layers
- but there seems to be little theory (see again Chapter 10 in my book
for some initial attempts).
By closing a feedback loop, the number of independent variables remains
the same (the setpoint becomes the new one), but the price we have
to pay for using the local feedback loop is that it
uses up some part (the fastest)
of the dynamic range. A rule of thumb is that
the time scales for the layers must be separated by at least a factor 10; e.g.
we may have that layer 1 (the lowest) operates within a time
scale of 10 s, layer 2 within 100 s, layer 2 within 1000 s, etc.
The idea is that the time scale separation should be such that
we need not worry about the dynamics of the level
below works - we should be able to assume that when we change the
independent variable (a setpoint to the layer below) then it changes
``immediately'' (within the time scale of present interest).
In conclusion, an important reason for use feedback hierachies,
is to avoid the need for having a large model with all the dynamics
included; at each level one only needs to have a model which covers
the local variables and their dynamics at the time scale of the local
loop (if the dynamics are dominantly first order; then simple P-control
with needs essentially no model may be used).
We are also looking into how feedback can
be best utilized for online optimization. A key is to find the
appropriate feedback variable
-- see also Chapter 10 in my
book
for more details.
For example,
we have applied temperature control feedback to get a an indirect level
control which then provides a simple and workable scheme for
multivessel batch distillation.
Another somewhat indirect way of utilizing feedback, is to use the
measurements to update parameters and states in a model. We want to
compare this approach with the more ``direct'' approach of local
feedback loops. The goal is to find the right balance between
this ``indirect'' (using models) use of feedback and the
``direct'' approach (using data, i.e. measurements) with local feedback.
The idea of self-optimizing control is also very much related to the
above feedback ideas.
-Sigurd Skogestad (Aug./Sept. 1997)