How can stabilize the simple system?
How to stabilize
the system response with feedback
In
the previous discussion has been discussed about how to simplify the system
response using a simple manner, namely by eliminating the roots of the
characteristic equation value that causes instability, now we discussing“how to
stabilize the response system using feedback”. The system that will be
discussed is the same as the existing system on the previous discussion:
if
given feedback will be obtained as follows:
From the results above, the value of C(s) are:
From the equation above, the value of H(s) can
be searched by outlining the value (s + 1) (s-2) in advance which becomes
s2-s-2. To get the value that caused the system will be stable, then the value
of H(s) must be filled with a value that can change the value equation has
roots that cause the system is stable, for example, to replace
s2-s-2 with s2 + 3s + 2 then the value of H(s) must be filled with a value 4s +
3. The value of H (s) can be changed according to taste.
So
the result is as follows:
The
roots of the characteristic equation is -2 and -1. By looking at the roots of
the characteristic equation are all negative, it can be concluded that the
system is stable.
To
prove necessary inverse of the equation, namely:
In
accordance with the Laplace transform table above equation if given the inverse
would be
The graph of the equation is:
From
the graph above getting the response time goes nearly zero and it is proving
that the system is stable. At the beginning of system response slightly upward,
to fix it can replace the value of H(s) so as to have a better response.
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