Specifications

2 Building Models
2-10
Gtf1 = tf([1 2], [1 1 10], 'OutputDelay', 1.5)
Control System Toolbox software builds and displays it as follows:
Transfer function:
s + 2
exp(-1.5*s) * ------------
s^2 + s + 10
Zero/Pole/Gain Models
Like the TF, the zero/pole/gain (ZPK) format relates an input/output pair. The difference
is that the ZPK numerator and denominator polynomials are factored, as in
G s
s
s s i s i
( ) .
.
( . )( . . )( . . )
=
+
+ + + + -
2 5
0 45
0 3 0 1 0 7 0 1 0 7
(zeros and/or poles are complex numbers in general).
You define the ZPK model by specifying the zero(s), pole(s), and gain as in
Gzpk1 = zpk( -0.45, [-0.3, -0.1+0.7*i, -0.1-0.7*i], 2.5)
State-Space Models
The state-space format is convenient if your model is a set of LTI differential and
algebraic equations. For example, consider the following linearized model of a continuous
stirred-tank reactor (CSTR) involving an exothermic (heat-generating) reaction [9]
dC
dt
a C a T b T b C
A
A c Ai
¢
= ¢ + ¢ + ¢ + ¢
11 12 11 12
dT
dt
a C a T b T b C
A c Ai
¢
= ¢ + ¢ + ¢ + ¢
21 22 21 22
where C
A
is the concentration of a key reactant, T is the temperature in the reactor, T
c
is
the coolant temperature, C
Ai
is the reactant concentration in the reactor feed, and a
ij
and
b
ij
are constants. See the process schematic in CSTR Schematic. The primes (e.g., C′
A
)
denote a deviation from the nominal steady-state condition at which the model has been
linearized.