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Classification of the P ElementDeskripsi lengkap
Classification of the P ElementFull description
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A response to Mufti Wajid Iqbal’s article “The Parameters of Sunni Islam”
Parameters of the PT1 element Nim wika : 061430321134 Nim salsa : 061430321169 Nim nina : 061430320210 Nim harumi : 061430320198 Nim Erick : 061430320197 Nim roby : 061430320213 Classification of the PT1 element A time delay element of the 1st order is called a PT 1 -element. In this context the relationship between the input variable y(t) and the output variable x(t) can be expressed by the differential equation
The parameter KP is referred to as the proportional coefficient, the parameter T is called the time constant of the PT1 element. The following Figure shows the step response and the block symbol of the PT 1 element.
Here 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 following equation expresses the characteristic of the output variable for t > 0
A PT1 element is thus a system with compensation and time delay (see the following Figure).
Determining the time constants on the basis of the step response Whereas the proportional coefficient KP of the PT1 element for an input variable step change of the height 1 can be read directly off the step response (as it corresponds to the final steady-state value of the output variable), finding 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 tangent method uses the application of tangents on the step response to determine the time constant T. The point where the tangent intersects with the final steady-state value of the output variable and then drop a perpendicular line down to the time axis. The resulting segment of the time axis corresponds to the time constant.
Fig. on the left: Determining the time constant T according to the tangent method. The tangent is drawn as a red line to the step response from the time point t = 0.
Determining the value of T according to the 63% method The so-called 63% method is based on the fact that the time corresponding to the time constant T has elapsed when 63% of the final value has been reached. This can
be derived directly from the equation given above by inserting the value T for the time variable t. We thus obtain the following for the output variable
The following graph illustrates how the time constant can be derived directly from the step response by this method.
Fig. left: Determining the time constant T according to the 63% method. This method gives relatively good results even when the signals are distorted.
Example for a PT1 element PT1 behavior is evident wherever there is a system with precisely one energy storage element. The Figure below shows a mechanical system comprising a mass m (energy storage element) and a shock absorber r, whose frictional force is assumed to be proportional to the velocity. Furthermore an external force F acts on the mass. If you take the sum of the forces, you arrive at the following expression for the motion
As can be seen from a comparison to the differential equation of the general PT 1 element shown above, this mechanical system demonstrates PT 1 characteristics.
Fig. right: Shock absorber system for a mass as an example of a mechanical PT1 element.
What are the system's proportional coefficient and time constant? Enter your answer into the following answer box.
Experiment In the following experiment you shall determine the step response of the two PT 1 elements of the P element of the experiment card "controlled system simulation" (SO4201-5U). Use the step response to determine the respective proportional coefficient KP and the time constant T. First set up the following experiment circuit.
Activate the step response plotter and configure it as shown in the following Table. Settings Input Channel A
Meas. range: 10 V
Coupling: DC
Channel B
Meas. range: 10 V
Coupling: DC
Range: 100
Offset: 0
Other
Settings Output Step response from ... to ...
0
50%
Delay time/ms
0
Measurements
300 Settings Diagram
Display
Channel A
x-axis from ... to ...
0
0.2 s
y-axis from ... to ...
0
100
%
Now determine the step response of the left-hand PT 1-element and copy the diagram into the upper space reserved for the graph. Determine the proportional coefficient and time constant in accordance with both the tangent and the 63% method. Then repeat the experiment with the right-hand PT 1 element, copy the step response into the lower space reserved for graphs and determine from this the proportional coefficient and time constants. Enter the numerical values obtained for the parameters in the answer box below.
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Step response of the left-hand PT1 element
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Proportional coefficients and time constants determined:
1. Kp=63% t=0,2s 2. kp = % t= s Now repeat the experiment using the right-hand PT 1 element, but for a different amplitude of the input variable step change (alter the step change from 0 to 25%). Drag and drop the step response into the space reserved for the graphic below and use this to also determine proportional coefficient and time constant. Do the parameters change because the height of the step response changes? Enter the your answer with your reasons into the answer box below!
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Step response of the right-hand PT1 element for a change in the height of the input variable step
