Control System Toolbox™ software supports transfer functions that are continuous-time or discrete-time, and SISO or MIMO. You can also have time delays in your transfer function representation.
You can represent linear systems as transfer functions in polynomial or factorized (zero-pole-gain) form. For example, the polynomial-form transfer function:
can be rewritten in factorized form as:
tf model object represents transfer functions in
polynomial form. The
zpk model object represents transfer
functions in factorized form.
MIMO transfer functions are arrays of SISO transfer functions. For example:
is a one-input, two output transfer function.
Use the commands described in the following table to create transfer functions.
This example shows how to create continuous-time single-input, single-output
(SISO) transfer functions from their numerator and denominator coefficients using
Create the transfer function :
num = [1 0]; den = [1 3 2]; G = tf(num,den);
den are the numerator and
denominator polynomial coefficients in descending powers of s.
den = [1 3 2] represents the denominator polynomial s2 + 3s + 2.
G is a
tf model object, which is a data
container for representing transfer functions in polynomial form.
Alternatively, you can specify the transfer function G(s) as an expression in s:
Create a transfer function model for the variable s.
s = tf('s');
Specify G(s) as a ratio of polynomials in s.
G = s/(s^2 + 3*s + 2);
This example shows how to create single-input, single-output (SISO) transfer
functions in factored form using
Create the factored transfer function :
Z = ; P = [-1-1i -1+1i -2]; K = 5; G = zpk(Z,P,K);
P are the zeros and poles (the roots
of the numerator and denominator, respectively).
K is the gain of
the factored form. For example, G(s) has a
real pole at s = –2 and a pair of complex poles at
s = –1 ± i. The
P = [-1-1i -1+1i -2] specifies these pole
G is a
zpk model object, which is a data
container for representing transfer functions in zero-pole-gain (factorized) form.