Specifications

2 Building Models
2-4
• u
p
— Dimensionless plant input variables.
• u
p
— Dimensionless plant output variables.
The resulting plant model has the following equivalent form:
x k A x k B u k B v k B d k
y k C x k D u k
p p p pu pv pd
p p p pu
+
( )
=
( )
+
( )
+
( )
+
( )
( )
=
( )
+
1
(( )
+
( )
+
( )
D v k D d k
pv pd
.
Here,
C S C
p o
=
-1
, B
pu
, B
pv
and B
pd
are the corresponding columns of BS
i
. Also, D
pu
,
B
pv
and B
pd
are the corresponding columns of
S DS
o i
-1
. Finally, u(k), v(k) and d(k) are
the dimensionless manipulated variables, measured disturbances, and unmeasured
input disturbances, respectively.
MPC controller enforces the restriction of D
pu
= 0, which means that MPC controller
does not allow direct feedthrough from any manipulated variable to any plant
output.
Input Disturbance Model
If your plant model includes unmeasured input disturbances, labeled as d(k) in the
diagram of the MPC system, the input disturbance model indicates how d(k) evolves with
time. That is, the input disturbance model specifies what type of signal you expect from
d(k). If you do not provide an input disturbance model, the controller uses a default input
disturbance model. The getindist command provides access to the model being used.
The input disturbance model is a key factor influencing the following controller
performance attributes:
• Dynamic response to apparent disturbances, i.e., the character of the controller’s
response when the measured plant output deviates from its predicted trajectory (due
to an unknown disturbance or modeling error).
• Asymptotic rejection of sustained disturbances. If the disturbance model predicts a
sustained disturbance, controller adjustments continue until the plant output returns
to its desired trajectory. This emulates an integral mode in a classical feedback
controller.