Simulation of Dynamic Responses of First Order and Second Order Systems (in LabView)

1069 words 5 pages
Objectives:
As part of the experiment requirements, we were required to simulate the dynamic response of a first order and a second order linear system with the help of LabVIEW. One of our first objectives of this experiment was to observe the response of the first order system to the input step signal and then relate it to the time constant of that specific first order system. The second objective of this experiment included observing the second order system to the input step signal and then relating it to the damping ratio of the specific second order system. The third and most important objective of this experiment was to use different functions of LabVIEW including loop execution control, LabVIEW formula node, LabVIEW graph, LabVIEW
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So when the time constant is 0.01, the graph swiftly reaches to peak amplitude of 1 within 0.152 seconds, and when the time constant is 0.03, the graph reaches peak amplitude in 0.442 seconds. For time constants 0.05, 0.07 and 0.1, the graph reaches the peak amplitude at a much later time. Thus the graphs and VI show that the higher the time constant, the longer it takes for the graph to reach the maximum amplitude. This in turn shows that the graphs support the relationship between time constants and input signals. So in systems with lower time constants, the inputs work faster and thus the outputs reach the peak amplitude faster than those in systems with higher time constants.
In case of the second order differential systems, the VI was created in LabVIEW and then run with undamped natural frequency at 100 Hz and six different damping ratios (0.2, 0.5, 0.7, 1, 1.5 and 2):

Figure : LabVIEW generated graph of amplitude against time for damping ratio ζ = 0.2

Figure : LabVIEW generated graph of amplitude

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