Proper transfer function

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.

Example

The following transfer function is proper: extbf{G}(s) = frac{ extbf{N}(s)}{ extbf{D}(s)} = frac{s^{4} + n_{1}s^{3} + n_{2}s^{2} + n_{3}s + n_{4{s^{4} + d_{1}s^{3} + d_{2}s^{2} + d_{3}s + d_{4because: deg( extbf{N}(s)) = 4 leq deg( extbf{D}(s)) = 4 .The following transfer function however, is not proper: extbf{G}(s) = frac{ extbf{N}(s)}{ extbf{D}(s)} = frac{s^{4} + n_{1}s^{3} + n_{2}s^{2} + n_{3}s + n_{4{d_{1}s^{3} + d_{2}s^{2} + d_{3}s + d_{4because: deg( extbf{N}(s)) = 4 leq deg( extbf{D}(s)) = 3 .

Implications

A proper transfer function will never grow unbounded as the frequency approaches infinity.: | extbf{G}(pm jinfty)| < infty

See also

* Strictly proper


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