Proper transfer function
Encyclopedia
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.
because
.
The following transfer function however, is not proper
because
.
Control theory
Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems. The desired output of a system is called the reference...
, a proper transfer function is a transfer function
Transfer function
A transfer function is a mathematical representation, in terms of spatial or temporal frequency, of the relation between the input and output of a linear time-invariant system. With optical imaging devices, for example, it is the Fourier transform of the point spread function i.e...
in which the degree
Degree (mathematics)
In mathematics, there are several meanings of degree depending on the subject.- Unit of angle :A degree , usually denoted by ° , is a measurement of a plane angle, representing 1⁄360 of a turn...
of the numerator does not exceed the degree of the denominator.
Example
The following transfer function is properbecause
.The following transfer function however, is not proper
because
.Implications
A proper transfer function will never grow unbounded as the frequency approaches infinity.