Process Control for 3 variables: Target and 2 Disturbances

: On the basis of the topic already discussed I made a compensation and add
: disturbances to see whether this concept will work properly.
:
: Basically I fed back a PI controller for handling the disturbances. I'd
like
: to call it optimal feedforward control with PI feedback.
:
: See
: http://home.arcor.de/janch/janch/_control/20070519-controldoc/
:
: This is thought to be a benchmark scheme for
:
: t = 0.2, 0.4, 0.6, and 0.8
:
: --
: Regards/Grüße    http://home.arcor.de/janch/janch/menue.htm
: Jan C. Hoffmann  eMail aktuell: janch@nospam.arcornews.de
:                 Microsoft-kompatibel/optimiert für IE7+OE7
This doesn't make sense.  The top left looks OK but the bottom left is not
right.   If the PI controller is following the target the controller output
v2 will not be a step jump as you have indicated. I don't understand why the
v1 Disturbance and the v1 Process looks like the same line.  So far all you
have done with your posts and graphs is mislead rookies that don't know any
better.  In any case you don't show the calculations, again, so this is all
meaningless.  At least you are not using the infinite gain controller, PD3
or whatever.

Peter Nachtwey

<I have written for using F2(s)>
Basically I fed back a PI controller for handling the disturbances. I'd like
to call it optimal feedforward control with PI feedback.

The integral feedback I was discussing before I called 'correcting'. Test
showed that PI works better.

See appropriate diagrams:
http://home.arcor.de/janch/janch/_control/20070520-controldoc/



F2(s) Feedforward controller with PI
------------------------------------

Error e = u - v1

v2 = u + B1 * u' + B2 * u'' + B3 * u''' +
     ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
     Recognize PD3!

     + K * (e + 30 * Integrator(e)) + z1
            ^^^^^^^^^^^^^^^^^^^^^^    ^^
            PI!
K = 1
Integration[0...t] e dt + C
C=0
Forced disturbance z1
z1=0.1 at t=0.3



F1(s) Process transfer function
-------------------------------

A3*v1''' + A2*v1'' + A1*v1' + v1 + z2  = v2
                                   ^^
Forced disturbance z2
z2=-0.1 at t=0.5



F3(s) Target filter
-------------------

C3*u''' + C2*u'' + C1*u' + u  = w (w = scheme)



If you combine all DEs mentioned you will get the result I showed in
http://home.arcor.de/janch/janch/_control/20070519-controldoc/

The set point is changed and the simulated disturbances are controlled to
zero. It works as you can see. That's all about. It is MATHEMATICS. No
doubt!

Here you also find the start values.

Looking at the graphics shows that the 'benchmark data are met' despite the
disturbances I forced for testing.

Data used:

A1 = 0.0371717
A2 = 0.0004699841
A3 = 0.000002771629

B1 = A1
B2 = A2
B3 = A3

C1 = A1
C2 = A2
C3 = A3

These simplified example data make tests easier understandable.

General note:

F2(s) became an integro differential equation. It sounds complicated but it
is just an integrator to add.


--
Regards/Grüße    http://home.arcor.de/janch/janch/menue.htm
Jan C. Hoffmann  eMail aktuell: janch@nospam.arcornews.de
                 Microsoft-kompatibel/optimiert für IE7+OE7

:: Basically I fed back a PI controller for handling the disturbances. I'd
like
: to call it optimal feedforward control with PI feedback.
: </cited>
:
: The integral feedback I was discussing before I called 'correcting'. Test
: showed that PI works better.

This is more realistic.
:
: See appropriate diagrams:
: http://home.arcor.de/janch/janch/_control/20070520-controldoc/
:
:
: F2(s) Feedforward controller with PI
: ------------------------------------
:
: Error e = u - v1
:
: v2 = u + B1 * u' + B2 * u'' + B3 * u''' +
:     ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
You need a B0.  What you have may be OK for a type 0 system.   B0 would be 0
for a type 1 system like a position control system.  In a position control
system you don't have a feed forward gain for the position.

:     Recognize PD3!
Yes, but these coefficients are used as feed forards, not as closed loop
gains.   There is a difference.  There are problems trying to compute the
second and third derivatives from the feedback.  It is easy to calculate the
second and third derivative from the target generator.
:
: F3(s) Target filter
: -------------------
:
: C3*u''' + C2*u'' + C1*u' + u  = w (w = scheme)
:
Now you need a better target generator so one can enter that maximum
velocity and accelation etc.
:
: If you combine all DEs mentioned you will get the result I showed in
: http://home.arcor.de/janch/janch/_control/20070519-controldoc/
:
:
: F2(s) became an integro differential equation. It sounds complicated but
it
: is just an integrator to add.
:
This makes sense. I am a big believer in feed forwards. You have shown the
ideal case where the system is known so the feed foward gains can generate
exactly correct control outpuit..  In reality there are disturbances, as you
show, and the system model is not exact.  In this case the PI controller
must make of the difference in the control output.  If the feed forwards are
accurate within 5% then the PI controller only needs to make of the last 5%
which means the errors are reduced by roughly 95%.  I have never understood
those that said gains must be tuned and dismissed the use of models.  Any
decent estimate will be better than none.

Notice the overshoot of the PI's response to the disturbances.   What are
you going to do about that?  You didn't show what you used for the PI gains.

Stick with the feed forwards with closed loop control and give up on the
infinite gain controller.

Peter Nachtwey