Simulation of Dynamic Responses of First Order and Second Order Systems (in LabView)
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 Waveform functions and LabVIEW express Vis.
Theory:
The dynamics of a linear system can be represented through linear derivative equations. The representative equation of a first order system is as follows:
Here τ is the time constant, x(t) is the input and y(t) is the output. The discrete form of the equation is as follows, with t=n:
This is the iteration used in the simulation of the dynamic response of the first order system.
The typical representation of the second order system is as follows:
The ωn is the undamped natural frequency and the ζ is the damping ratio. The discrete form of the above equation is as follows (with t=n):
This is the iteration used in the simulation of the dynamic response of the second order system.
Description of how the LabVIEW simulated the system responses:
In order to simulate the dynamic response of a first order system, we first created a blank VI on LabVIEW, and added a numeric control for the time constant input and a graph indicator for the result display. Then a “Simulated Signal” express VI was used in the block diagram with a square wave as signal type, 1 Hz frequency, 1000 Hz sample frequency, 500 data points, and was set to convert the
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 Waveform functions and LabVIEW express Vis.
Theory:
The dynamics of a linear system can be represented through linear derivative equations. The representative equation of a first order system is as follows:
Here τ is the time constant, x(t) is the input and y(t) is the output. The discrete form of the equation is as follows, with t=n:
This is the iteration used in the simulation of the dynamic response of the first order system.
The typical representation of the second order system is as follows:
The ωn is the undamped natural frequency and the ζ is the damping ratio. The discrete form of the above equation is as follows (with t=n):
This is the iteration used in the simulation of the dynamic response of the second order system.
Description of how the LabVIEW simulated the system responses:
In order to simulate the dynamic response of a first order system, we first created a blank VI on LabVIEW, and added a numeric control for the time constant input and a graph indicator for the result display. Then a “Simulated Signal” express VI was used in the block diagram with a square wave as signal type, 1 Hz frequency, 1000 Hz sample frequency, 500 data points, and was set to convert the