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Proper transfer function : ウィキペディア英語版
Proper transfer function
In control theory, a proper transfer function is a transfer function in which the degree of the numerator does not exceed the degree of the denominator.
A strictly proper transfer function is a transfer function where the degree of the numerator is less than the degree of the denominator.
The difference between the degree of the denominator (number of poles) and degree of the numerator (number of zeros) is the ''relative degree'' of the transfer function.
==Example==
The following transfer function:
: \textbf(s) = \frac = \fracs^ + n_s^ + n_s + n_}s^ + d_s^ + d_s + d_}
is proper, because
: \deg(\textbf(s)) = 4 \leq \deg(\textbf(s)) = 4 .
is biproper, because
: \deg(\textbf(s)) = 4 = \deg(\textbf(s)) = 4 .
but is not strictly proper, because
: \deg(\textbf(s)) = 4 \nless \deg(\textbf(s)) = 4 .
The following transfer function is not proper (or strictly proper)
: \textbf(s) = \frac = \fracs^ + n_s^ + n_s + n_} + d_s^ + d_s + d_}
because
: \deg(\textbf(s)) = 4 \nleq \deg(\textbf(s)) = 3 .
The following transfer function is strictly proper
: \textbf(s) = \frac = \frac + n_s^ + n_s + n_}s^ + d_s^ + d_s + d_}
because
: \deg(\textbf(s)) = 3 < \deg(\textbf(s)) = 4 .

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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