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

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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 …show more content…

A shift register was then used to store the y value for the next iteration (y(n-1)) in case of the first order system while a 2 stacked shift register, in case of a second order system, was used to store the y values from previous iterations (y(n-1) and y(n-2)). A formula node was used in order to input the formula required to program the algorithm for each of the first and second order systems respectively. After providing the required number inputs and outputs (as per the requirement of each of the formula respectively), a waveform function was used to create the waveform data from the output data and determine the time interval of the input waveform. After using an array to contain all the input and output waveforms, a graph indicator was finally added to the VI to display the final graphical representation of the output data.
After saving, each of the VI were run separately set at different time constants (for the first order system) and different damping ratios and 100 Hz undamped natural frequency (for the second order ratio).

Results:
After creating the VI for first order differential systems in LabVIEW, we ran the VI using five different time constant values (0.01, 0.03, 0.05, 0.07, 0.1) and received the following graphs:

Figure : LabVIEW generated graph of amplitude against time for