Contents
What is a frequency transfer function?
Frequency-domain transfer functions describe the relationship between two signals as a function of s. For example, consider an integrator as a function of time. From Table 3-1, the integrator has an s-domain transfer function of 1/s.
Why transfer function is used in control system?
A transfer function represents the relationship between the output signal of a control system and the input signal, for all possible input values. Thus the cause and effect relationship between the output and input is related to each other through a transfer function.
How to calculate frequency response of transfer function?
You may remember from linear systems course that, for a continuous-time transfer function described in terms of Laplace variable s, frequency response can be achieved by letting s = jω. By this relationship, a frequency response of a transfer function can be plotted “the hard way.”
When is the transfer function evaluated at S = j ω?
When the transfer function is evaluated at s = j ω, it is also known as the systems’s frequency response. Note that the transfer function is more general than the frequency response, and can provide more insight into a system’s behavior, for example about transient response or stability.
How is the frequency response of a system evaluated?
In fact the frequency response of a system is simply its transfer function as evaluated by substituting s = jw. The frequency response H(jw) is in general is complex, with real and imaginary parts. This is often more useful and intuitive when expressed in polar coordinate.
What happens when the frequency of an input changes?
In words, for a Linear Time-Invariant (LTI) system driven by a sinusoid input, the output is a sinusoid with same frequency, only its magnitude A and phase φ might change. When the input frequency varies, this results in new values for A and φ.