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sistem kendali menggunakan labsoft
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The little that most of us think we know about the circumstances of Hitler's demise comes to us courtesy of British MI6 agent Hugh Trevor-Roper, and there are many reasons why we shouldn't believe ...
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Classification of the P ElementDeskripsi lengkap
The finite element method
Classification of the P ElementFull description
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homoeopathy book by dr sankaran
Full description
Variation of ParametersFull description
Parameters of the PT1 element Classification of the PT 1 element A time delay delay element of the 1st order is called a PT1 -element. In this context the relationship between the input variable y(t) and the output variable x(t) can be expressed by the differential euation
The parameter !P is referred to as the proportional the proportional coefficient " the parameter T is called the time constant of of the PT1 element. The followin# $i#ure shows the step response and the bloc% s ymbol of the PT 1 element.
&ere the final steady-state value of the output variable is assumed to be only asymptotic" i.e. time delayed. The time constant T specifies how fast the output variable tends towards the final value. In mathematical terms the followin# euation expresses the characteristic of the output variable for t '
A PT1 element is thus a system with compensation and time delay (see (see the followin# $i#ure).
Determining the time constants on the basis of the step response hereas the proportional coefficient !P of the PT1 element for an input variable step chan#e of the hei#ht 1 can be read directly off the step response (as it corresponds to the final steady-state value of the output variable)" findin# out the time constant T is somewhat more complicated. It can be achieved in two different ways.
Determining the value of T using the tangent method The so-called tan#ent method uses the application of tan#ents on the step response to determine the time constant T. The point where the tan#ent intersects with the final steady-state value of the output variable and then drop a perpendicular line down to the time axis. The resultin# se#ment of the time axis corresponds to the time constant.
$i#. on the left* +eterminin# the time constant T accordin# to the tan#ent method. The tan#ent is drawn as a red line to the step response from the time point t , .
Determining the value of T according to the 63% method The so-called 63% method is based on the fact that the time correspondin# to the time constant T has elapsed when / of the final value has been reached. This can
be derived directly from the euation #iven above by insertin# the value T for the time variable t. e thus obtain the followin# for the output variable
The followin# #raph illustrates how the time constant can be derived directly from the step response by this method.
$i#. left* +eterminin# the time constant T accordin# to the / method. This method #ives relatively #ood results even when the si#nals are distorted.
Example for a PT1 element PT1 behavior is evident wherever there is a system with precisely one ener#y stora#e element. The $i#ure below shows a mechanical system comprisin# a mass m (ener#y stora#e element) and a shoc% absorber r" whose frictional force is assumed to be proportional to the velocity. $urthermore an external force $ acts on the mass. If you ta%e the sum of the forces" you arrive at the followin# expression for the motion
As can be seen from a comparison to the differential euation of the #eneral PT1 element shown above" this mechanical system demonstrates PT1 characteristics.
$i#. ri#ht* 0hoc% absorber system for a mass as an example of a mechanical PT 1 element.
hat are the systems proportional coefficient and time constant2 3nter your answer into the followin# answer box.
Experiment In the followin# experiment you shall determine the step response of the two PT1 elements of the P element of the experiment card 4controlled system simulation4 (05671-89). 9se the step response to determine the respective proportional coefficient !P and the time constant T. $irst set up the followin# experiment circuit.
Activate the step response plotter and confi#ure it as shown in the followin# Table.
Settings nput :hannel A
;eas. ran#e* 1 <
:ouplin#* +:
:hannel =
;eas. ran#e* 1 <
:ouplin#* +:
>an#e* 1
5ffset*
5ther
Settings !utput 0tep response from ... to ...
8/
+elay time?ms
;easurements
Settings Diagram
+isplay
:hannel A
x-axis from ... to ...
.7 s
y-axis from ... to ...
1
@ow determine the step response of the left-hand PT1-element and copy the dia#ram into the upper space reserved for the #raph. +etermine the proportional coefficient and time constant in accordance with both the tan#ent and the / method. Then repeat the experiment with the ri#ht-hand PT 1 element" copy the step response into the lower space reserved for #raphs and determine from this the proportional coefficient and time constants. 3nter the numerical values obtained for the parameters in the answer box below. 1
/
x1* y 1*
C
.16 x7* .61
B
y 7* 8.1 dx*
.61 dy * 6C.C
dy?dx* 1.1eD
8
6
7
1
t? s
0tep response of the left-hand PT 1 element
1
/
x1* y 1*
C
x7* .1C6
B
y 7* 6B.C dx*
.1C6 dy * 6B.C
dy?dx* 787
8
6
7
1
t? s
0tep response of the ri#ht-hand PT 1 element
Proportional coefficients and time constants determined* Feft-hand (!p, 8/ t , .6 s) >i#ht-hand (!p , 6B.C/ t , .1C
@ow repeat the experiment usin# the ri#ht-hand PT 1 element" but for a different amplitude of the input variable step chan#e (alter the step chan#e from to 78/). +ra# and drop the step response into the space reserved for the #raphic below and use this to also determine proportional coefficient and time constant. +o the parameters chan#e because the hei#ht of the step response chan#es2 3nter the your answer with your reasons into the answer box belowE
1
/
x1* y 1*
C
x7* .1
B
y 7* 76.8 dx*
.1 dy * 76.8
dy?dx* 181
8
6
7
1
t? s
0tep response of the ri#ht-hand PT 1 element for a chan#e in the hei#ht of the input variable step