Specifications

MPC Modeling

2-5

You can provide the input disturbance model as an LTI state-space (ss), transfer

function (tf), or zero-pole-gain (zpk) object. See “Controller State Estimation” for more

details about the input disturbance model.

The MPC controller converts the input disturbance model to a discrete-time, delay-free,

LTI state-space system using the same steps used to convert the plant model (see “Plant

Model” on page 2-2). The result is:

x k A x k B w k

d k C x k D w k

id id id id id

id id id id

( )

Here, A

, B

, C

, and D

are constant state space matrices and:

• x

(k) — n

xid

≥ 0 input disturbance model states.

• d

(k) — n

dimensionless unmeasured input disturbances.

• w

(k) — n

≥ 1 dimensionless white noise inputs, assumed to have zero mean and

unity variance.

Output Disturbance Model

The output disturbance model is a special case of the more general input disturbance

model. Its output is directly added to the plant output rather than affecting the plant

states. The diagram shows its location in the MPC model hierarchy. The output

disturbance model indicates how the disturbance will evolve with time (in other words,

what type of disturbance signal you would expect) and it is often used in practice. See

“Controller State Estimation” for more details about the output disturbance model.

If you don’t provide an output disturbance model, the MPC controller will create one by

default when there is no input disturbance model and augmenting the plant model does

not violate state observability.

The getoutdist command provides access to the model being used.

Using the same steps as for the plant model (see “Plant Model” on page 2-2), the

MPC controller converts the output disturbance 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

od od od od od

( )