# | In the time domain, the transient response of the opened... control

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In the time domain, the transient response of the opened and closed
control
loop can be simulated and optimized during disturbance or while
commanding.
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1. Command action, step response
2. Command action, position curve response
3. Disturbance action, disturbance function response
4. Command action + disturbance + chaos at t=Tst
5. Open control loop`s step response
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In the third menu-option, a disturbance function z=Ast*cos(Wst*t) or a
disturbance impulse of variable length and amplitude can randomly attack the
controller or control plant. With Ast=1 and Wst=0 for example, a
disturbance
With the fourth menu-option, a step, ramp, or postion curve response,
including an actuatabledisturbance function z=+Ast*cos(Wst*t) at the time
Tst
or a disturbance impulse of variable width can be viewed and optimized.
The disturbance function or impulse can be positively or negatively
here or shut off with Ast=0. Intervention is possible before or after the
control plant.
With the fifth menu-option, the step response of a many-membered control
loop
can be viewed through an opened control loop. With this, the differences
between real and ideal controllers can shown as well.
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P A R A B O L A
A N D
R U N - U P T I M E:
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The position curve is a set point function beginning with a parabola with
a
positive gradient. After the so-called parabola time Tve, the parabola
becomes a straight line with a gradient dependent upon Tve and the run-up
time The. After reading the time T=The-Tve, the straight line becomes a
parabola with a negative gradient so that the set point of 100% is
attained
at t=The.
Since the postion curve does not show any discontinuities, it is
especially
suited for an &quot;easily commanded&quot; start and deceleration.
If the parabola and run-up time are set at Tve=The=0, the postion curve
response and the step response are identical. This is one advantage
avilable
for the comparison of reference variable functions. Thus, with Tve=0 and
The&gt;0 one receives a ramp function limited to w=100%.
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O P T I M I Z A T I O N:
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Controller optimization with adjustment values, according to
Ziegler/Nichols,
is the starting point for the controller optimization developed by the
author. See:
Orlowski, P.F.: Praktische Regeltechnik.
4. Aufl. Springer-Verlag. Heidelberg 1994.
With Ziegler/Nichols, the same control-adjustment values always result in
plant parameters that have not been changed. The &quot;...opt-adjustment
values&quot;
from SIMLER-PC leads to results &quot;similar to Ziegler/Nichols&quot; or better.
This applies to numerous control plants (i.e. drive technique, process
engineering, etc.).
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The boundary Xs is also taken into consideration here.
What is of particular benefit is the &quot;asymptotic&quot; improvement, if you
will,
of the control-adjustment values after only a few simulations. The
'variance
band' can then be seen from the graph, in which the control parameter
to an optimal transient response of the control loop.
The optimal set point plays a significan roll for problems concerning the
starting and deceleration of panels or measurements (key words: position,
location-, or sequence-controls). The position curve optimization
developed
by the author shows very good results here.
With the optimal values or parabola time Tve_opt and the run-up time
The_opt,
those control loops having a small phase margin can be started and
decelerated
without any oscillation whatsoever since the position curve shows no
discontinuities.
If the postion curve corresponds to the position set point in an actual
scenario, one receives, as a side-product of the optimization so to say,
with
ds/dt and d&yacute;s/dt&yacute; the set points of the backing speed and power
controller
for starting and deceleration. This provides an optimal cascaded position
control as far as time is concerned.
Further assistance can be found in:
Orlowski, P.F.: Position Curve Computers for Drive Technology.
Electronics, H.2, 1985, pp. 53-57.
Studer, N.,
Orlowski, P.F.: Micro-computer Supported Position Curve Computers
Electro-technology. Publ. B. H.6, 1988, pp. 62.67.
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An optimization is provided as well for the correct settingof the
disturbance
function. Here Ast_opt is a fraction of the amplification Ko or Xs;
Wst_opt is
a multiple of the average frequency Wd. The disturbance function
actuation
desired, for example, is found with electro-hydraulic postion-controls
and
similar applications as a so-called dynamic lubrication. Static friction
should be avoided in all operating conditions - by continuous movement
around
the controlled postion value.
If a controller time constant in the pull-down menu PARAMETER PROCESSING
is
reset, the optimal values stand subsequently in relation to the
controllertype resulting from that (i.e. Tn=99999999, Tv=0 for a PID-controller is
based
on the P-controller). Reference variables and regulating variables are
relative numbers and are completely based on their respective physical
value.
When calculating rise and transient time (see DIN 19226), a tolerance
band
of +/- 2% is assumed. Ton and Toff are only given with a stable control
when
both values from the graph are legible. Toff is searched then as well by
the
last value x(t_2Toff) (right-hand screen margin) until the tolerance band
has
been left at t=Toff.
If the computer reaches the boundary of the number- or presentationdomain
when calculating stability or optimization, the result can only be
contingently received. Although the phase margin is still above 0&oslash; (i.e.
time domain_Tmax/Tmin chosen), the graph x(t) can indicate instability.
Despite these problems, the free choice of parameter is also given in
this
version of the program for didactic reasons and due to a sensible
limitation
of processing time. There is no automatic control optimization for these
reasons as well.
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If the phase margin is between 0&oslash; and 1&oslash;, the text &quot;stab.lim.&quot; (stability
boundary) is shown; for &gt; 1&oslash;, &quot;stable&quot; is shown.
If a disturbance function is actuated in menu-option 4, the stability
indicator is then dependent upon disturbance function z.
For an undisturbed, stable control, this dependency is made clear in the
text &quot;comm.stab.&quot;.
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I D E N T I F I C A T I O N
of a T R A N S I E N T R E S P O N S E:
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Files IDEN_01.PJD - IDEN_05.PJD furnished are examples of measured plants
on
which one can immediately try out on-line identification. Pertinent plant
parameters in the ASCII-code are provided as well for comparison. To do
this,
go into FILE MANAGING for the DOS-version, mark a file with the [SPACE
BAR],
and enter the command abbreviation [E]. In the WINDOWS version, SIMLER-PC
INI-file editor can be used.
To identify the step response of an unknown control plant or transient
function y=f(t) measured in ASCII-code, files IDEN_01.PJD - IDEN_03.PJD
can be
used as well. These files are assigned to certain plant types. This way
the
menu-layout used in SIMLER-PC remains unchanged. It is required however
that
the recorded step response can be described by the model used in SIMLERPC.
This applies to:
IDENKOP1.DAT
IDENKOP2.DAT
IDENKOP3.DAT
Identification file
IDEN_01.PJD
IDEN_02.PJD
IDEN_03.PJD
Plant type
4*PT1-PT2-PTT
3*PT1-PT2-PTt-I
2*PT1-PT2-PTa-PTt
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Identification of a measured step response is done in the following
manner:
1. There are basically 2 possible ways to reconstruct ASCII-files in an
identification file from type *.PJD.
a) Highlight one of the example files with the [SPACE BAR] in FILE
MANAGING
and load it with [E], or use the file-editor in WINDOWS.
Then, susbtitute the 1200 plot points on the curve with the
recorded
measurment values in REAL or INTEGRAL format.
A few command for processing in the editor (like TURBO-PASCALeditor):
Command abbreviations
Action
F7
highlights the beginning of the text
(blocks)
F8
highlights end of text (blocks)
CTRL K C
copies highlighted text to position of
CURSOR
CTRL K Y
erases highlighted text (blocks)
CTRL K H
remove text or block highlighting
CTRL Y
erase line
b) With files IDENKOP1.DAT - IDENKOP3.DAT, the matching data-head for
SIMLER-PC can be copied as well from the DOS-level of the userfile.
The command for preparing a *.PJD-file reads as follows:
COPY IDENKOP1.DAT+USER.DAT IDEN_X.PJD
2. If only 1024 plot points of the curve were measured for example, the
corresponding graph in SIMLER-PC would run to zero from point 1025-1200. If
the
time or coordinate standard must be corrected in such a case, it must
then
be multiplied, in this case, by 1200/1024=1.172. The correct
coordinatestandard is then subsequently inserted in the highlighted part of the
identification file.
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3. The ordinate-standard of the identification file is now replaced.
4. If necessary, restart SIMLER-PC and load the processed file.
5. It is often appropriate to work on the graph with the help of
measurementsmoothing (especially for curves with a &quot;rushing&quot; or &quot;buzzing&quot;).
With SIMLER-PC smoothing-algorithm, this can be done in several runthroughs with a variable scanning-screen-width. After accepting the
smoothing results with [J], the file is saved as IDEN_TEM.PJD.
6. Load file IDEN_TEM.PJD and approximate the graph by hand with the help
of
PARAMETER PROCESSING along with the identification instructions.
As a result one receives plant-parameters with which the optimal
controller
can be found with SIMLER-PC.
as
well. This is done as follows:
1. The innermost control loop is optimized and resaved as file IDENT.
2. Next, exit file managing and call up menu-option 5 &quot;Identification
of
a transient function&quot; and load the resaved file IDENT.
3. Identify the parameter of the substitute control plant with the
help
of the parameter input and the identification instructions.
4. Take the parameters found in the optimization of the nearest overlapping control loop as plant parameters.
good
result. Plants of a higher order are reduced accordingly to a model 3. or
4.
with or without all pass / dead time.
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P O S I T I O N
V E C T O R:
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The position vector can be used in every graph for the measuring of time
periods or cycles. dt/s=t2-t1 is given if t1 has been highlighted with
[INS]
and t2 with [DEL].
Time constants T2 and damping factor d&lt;1 from the identification files
graph
can be identified at oscillating transient functions with the assistance
of
the position vector.
The files IDEN_04.PJD and IDEN_05.PJD are examples of the manipulation of
functions that overlay through additional time constants and whose
SIMLER-PC
identification instructions fail. The main time constant for file IDEN05.PJD,
for example, can be determined with measurement-smoothing, whereas T2 and
d
of the overlapping oscillation can be found with the position vector.
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