User`s guide

2 LTI Models
2-20
Discrete-Time Models
Creating discrete-time models is very much like creating continuous-time
models, exce p t that you must als o spe cif y a samp ling pe riod o r sample time for
discrete-timemodels.Thesampletimevalueshouldbescalarandexpressedin
seconds. Y ou c a n also us e the value –1 to leave t h e sample t ime unspecified.
To specif y discrete-time LTI models us ing
tf, zpk, ss,orfrd, simply append
the desired s amp le time value
Ts to the list of i nputs.
sys1 = tf(num,den,Ts)
sys2 = zpk(z,p,k,Ts)
sys3 = ss(a,b,c,d,Ts)
sys4 = frd(response,frequency,Ts)
For example,
h = tf([1 –1],[1 –0.5],0.1)
creates t he discrete-time transfer function with
sample time 0.1 seconds, and
sys = ss(A,B,C,D,0.5)
specifies the discrete-time state-space model
with sampling period 0.5 second. The vectors denote the
values of the state, input, and output vectors at the nth sample.
By convention, the sample time of continuous-time models is
Ts = 0.Setting
Ts = –1 leaves the sample time of a discrete-time model unspecified. For
example,
h = tf([1 –0.2],[1 0.3],–1)
hz
()
z 1
–()
z0.5
–()⁄=
xn 1
+[]
Ax n
[]
Bu n
[]+=
yn[] Cx n[] Du n[]+=
xn
[]
un
[]
yn
[],,