Specifications

2 Building Models
2-6
Here, A
od
, B
od
, C
od
, and D
od
are constant state space matrices and:
• x
od
(k) — n
xod
≥ 1 output disturbance model states.
• y
od
(k) — n
y
dimensionless output disturbances to be added to the dimensionless plant
outputs.
• w
od
(k) — n
od
dimensionless white noise inputs, assumed to have zero mean, unity
variance.
Measurement Noise Model
One of the controller design objectives is to distinguish disturbances, which require a
response, from measurement noise, which should be ignored. The measurement noise
model has this purpose. The diagram shows its location in the MPC model hierarchy. The
measurement noise model indicates how the noise will evolve with time (in other words,
what type of noise signal you would expect).
See “Controller State Estimation” for more details about this model.
Using the same steps as for the plant model (see “Plant Model” on page 2-2), the
MPC controller converts the measurement noise model to a discrete-time, delay-free, LTI
state-space system. The result is:
x k A x k B w k
y k C x k D w k
n n n n n
n n n n n
+
( )
=
( )
+
( )
( )
=
( )
+
( )
1
.
Here, A
n
, B
n
, C
n
, and D
n
are constant state space matrices and:
• x
n
(k) — n
xn
≥ 0 noise model states.
• y
n
(k) — n
ym
dimensionless noise signals to be added to the dimensionless measured
plant outputs.
• w
n
(k) — n
n
≥ 1 dimensionless white noise inputs, assumed to have zero mean, unity
variance.
If you do not supply a noise model, the default is a unity static gain: n
xn
= 0, D
n
is an n
ym
-
by-n
ym
identity matrix, and A
n
, B
n
, and C
n
are empty.
For an mpc controller object MPCobj, the property MPCobj.Model.Noise provides
access to the measurement noise model.