Re: The Cascade Control Architecture - controlguru post

On Jul 7, 8:01 am, Doug Cooper <publicp...@xxxxxxxxxxxxxxx> wrote:
Tim Wescott <t...@xxxxxxxxxxxxxxxx> wrote innews:7smdnYJMPo_FoBLbnZ2dnUVZ_s6onZ2d@xxxxxxxxxxxx:



On Fri, 06 Jul 2007 20:38:20 +0000, Doug Cooper wrote:

Two popular control strategies for improved disturbance rejection
performance are cascade control and feed forward with feedback trim.
Improved performance comes at a price. Both strategies require that
additional instrumentation be purchased, installed and maintained.
Both also require additional engineering time for strategy design,
tuning and implementation. It is important to understand that neither
strategy benefits nor detracts from set point tracking performance.

Cascade and feed forward are control architectures designed with the
sole purpose of minimizing the impact of disturbances on our measured
process variable (PV). To construct a cascade architecture, we
literally nest a secondary control loop inside a primary loop as
shown in the block diagram...

To read the rest of this article, please visit:
http://www.controlguru.com/2007/070607.html

The complete table of contents for the "Practical Process Control"
e-book are available online at:
http://www.controlguru.com/pages/table.html

Au contraire, mon ami! "It is important to understand that neither
strategy benefits nor detracts from set point tracking performance."

In your cascade control* example the improvement in disturbance
rejection is a direct consequence of being able to increase the
reaction speed of the loop. You can do this because measuring the
flow allows you to wrap that part of the system with a fast, robust
loop. This fast loop, in turn, gives you the ability to tune the
whole loop for faster response while maintaining robustness in the
face of plant variations, nonlinearities, and all those other nasty
things that we must work around.

If you put on your rose-colored glasses and pretend that the system is
linear, time-invariant, and has all discrete states, then the
additional sensor lets you shove the poles farther into the left-half
plane. Doing so decreases the system's sensitivity to low- and
medium-frequency disturbances at the same time that it increases it's
ability to track low- and medium-frequency setpoint changes (the plant
will act like a low-pass filter, giving the system an intrinsic
ability to reject really fast disturbances, as well as an intrinsic
tendency to resist all attempts to speed it up beyond a certain
point).

In fact, both the disturbance rejection and the tracking ability are
tightly bound to the system sensitivity: if we keep those rose-colored
glasses on the disturbance rejection is the plant transfer function
(the tank level process transfer function, in your example) numerator
over the system sensitivity, and the error between the setpoint and
the final process variable is simply one over the system sensitivity.
With your loop as shown, you _cannot_ improve the disturbance
rejection without also improving the set point tracking.

In the case of disturbance feed-forward this is not the case -- there
(I assume this is what you're thinking, at least) you measure the
disturbance outside the loop, and feed in a signal to null out the
effect of the disturbance. Of course, if your system is predictable
enough to use disturbance feed forward on it, you can also feed the
setpoint forward if you really need to track it well.

I have to admit that I only skimmed the article to make sure that I
knew where you were coming from, so you may well have clarified this
point there -- but in your post here you certainly mis-state it.

Otherwise it looks like a good article, at least to the extent that I
can tell from just skimming it.

* "Nested loops" would be a much better term, IMHO.

Tom

Indeed, a proper cascade (nested loops) can:
- improve the rejection of disturbances that hit the inner secondary
measured process variable,
- speed up the outer primary loop to permit an improved set point
response,
- even temper nonlinearities associated with the inner secondary loop to
the benefit of the outer primary loop.

I am working on a series of articles that compare/contrast cascade with
feed forward and that focus got me off track.

Thanks for the catch. I will have the article updated in the next few
days.

Doughttp://www.controlguru.com/

Doug,

That was a really good article. The example was also excellent. If and
when I become a Prof one day, I will have to use a similar example to
show the benefits of nested loop control.

As a side note, in many mechanical systems it is possible to utilize
feedforward to improve tracking control. For example, many mechanical
system can be modeled as mass-spring-damper systems:

M*q_dot_dot + C*q_dot + K*q = u(t)

All feedforward is, is a control that mimics the plant dynamics in
order to "cancel" them out. For example, if I had a feedfoward +
feedback (PD feedback) controller of the form:

u(t) = M*q_dot_dot_desired - Kp(q - q_desired) - Kd(q_dot -
q_dot_desired)

then the resultant dynamics would be

M*q_dot_dot + C*q_dot + K*q = M*q_dot_dot_desired - Kp(q - q_desired)
- Kd(q_dot - q_dot_desired)

and provided q approx = q_desired (and q_dot_dot ~= q_dot_dot_desired,
q_dot ~= q_dot_desired) the above equation simplifies too

(C + Kd)*q_dot + (K + Kp)*q = Kp*q_desired + Kd*q_dot_desired

The only reason I mention this is because in some fields such as
robotics, feedforward control is used with great success because of
the very deterministic properties of the plant, that being the robot.
I have successfully implemented many nonlinear feedforward + feedback
(in the form of PD, PID, PI, Lead-Lag, H2 etc feedback) controllers on
both rigid and flexible mechanical systems (mostly robotic
manipulators).

I also feel inclined to mention something Peter Nachtwey posted a link
too : http://www.convolve.com/ These guys seem to have a "fancy"
feedfoward controller that is basically a convolution of the control
and the output. I have not had much time to read up on it... perhaps
Tim or Peter could give me a brief tutorial on what it is. From what I
have read, it does sound interesting though. Although I have some
doubts as to their claim of "input shaping does not effect the
stability of the closed loop system in any way"... anytime you add
dynamics in the form of feedforward or feedback you are effecting the
stability of the closed loop. You may be making the CL MORE stable,
but your changing it none the less. The plant has its own eigenvlaues,
the control has its own eigenvalues and the closed loop is the
combination. If you has some more control in the form of feedforward,
you are again adding some eigenvalues (poles) which will effect the CL
system in some way.

James Forbes

.

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