Response of a system (Control theory)

AI Thread Summary
The discussion focuses on understanding the response of a control system, particularly regarding oscillations characterized by a transfer function. The user is studying for an exam and seeks clarification on calculating maximum elongation when the final value is zero. The formula provided for maximum elongation involves the damped coefficient, but it becomes problematic when the final value is zero. Participants are encouraged to provide insights or solutions to this specific scenario. The conversation highlights the complexities of control theory in relation to system responses.
Domenico94
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Hi everyone. I'm studying for the exam of control theory, and now I'm having an hard time with the response of a system, in particular when we have oscillations.
Suppose you have a system, with a transfer function, say, G(S), in the form:

G(S) = 1
-------------------
(s ^2 + 2a*w (s) + w^2)

Then, if we have oscillations, we can calculate the maximum elongation (in percentage), over final value, with the formula

S = (final value)* 100 * e ^ ((-pi * a)/sqrt(1 - a^2)),
in which a is the damped coefficient.
The problem is, if the final value is 0, what should I do there? Thank you for your help
 
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