The
second-order system model is a set of mathematical equations used to describe
the behavior of nonlinear systems. It consists of two nonlinear differential
equations and a set of constants that define how those variables change over
time. The system is defined by its state variables and the values for their
respective operators at each instant in time.
Standard
mathematical form of a second-order differential equation is as below:
Where
A and B are constants.
For
control system, the standard mathematical form of second order system with Unit
step input is as below:
Where
ξ is the damping factor and ωn is the natural frequency.
The
system will be underdamped when 0 < ξ < 1. The particular solution,
yp(t) = 1 determines the steady state solution of the system. The homogeneous
solution determines the transient solution which is
1. Methods
This
project report will be executed using LabVIEW. The first part of the report
will be presenting Numeric block based code for analyzing the response of the
system based on the following solution:
Where
ξ is the damping factor and ωn is the natural frequency. If T is the total time
for which response is analyzed, N is the number of points then time step is ∆t
= T/N. At ith iteration, t= i*∆t = i*T/N.
We
will be using this equation for different parameters of ζ , ωn, T and N to
analyze its response on graph.
In
next part of the lab we will be using another method which is call formula node.
In formula node we write the formula in script and then give input and output arguments
to it.
Below code is written using Numeric blocks in LabvIEW.
We can simulate the same model using Formula script node also.
No comments:
Post a Comment