Transfer Functions - Basics
What is a transfer function?A transfer function mathematically defines or represents a system.
Transfer Function = Output of the System/Input of the System
In engineering, a system often handles signals. An example of a signal is a second order sinusoidal signal. Thus, an output signal divided by the input signal results in a signal. A signal can be defined in the time domain or in the frequency domain. Consider the following example of a transfer function defined frequency domain
How do we define a transfer function in Matlab?
% Transfer Functions: % polynomial form: G(s) = (2s + 3)/ (s/\2 + 3s + 2) % the tf command creates the MATLAB'S LINEAR TIME INVARIANT (LTI) % SYSTEMS OBJECT which stores and assumes a number of characterisitics Num = [2, 3]; Den = [1, 3, 2]; G1 = tf(Num, Den) % factored polonomial form: G(s) = (2(s + 1.5))/((s+2)(s + 1)); % zero-pole-gain form: % this is another way to express the transfer function z = -1.5; p = [-2, -1]; k = 2; G2=zpk(z, p, k) % tfdata is a MATLAB function which gives you back the G1(s) % no clue about what that 'v' is about k=dcgain(G2); [t, b] = tfdata (G2, 'v'); G3=tf(t, b)
The result of the above Matlab code:
