Specifications
MPC Modeling
2-3
• Identified models (requires System Identification Toolbox™): idss, idtf, idproc,
and idpoly.
The MPC controller performs all the estimation and optimization calculations using
a discrete-time, delay-free, state-space system, with dimensionless input and output
variables. Therefore, when you specify a plant model in the MPC controller, the following
model-conversion steps are automatically carried out, if needed:
1
Conversion to state-space. The ss command appropriate for the supplied model
format generates an LTI state-space model.
2
Discretization or resampling. If the model’s sample time differs from the MPC
controller’s sample time (defined in the Ts property), one of the following occurs:
• If the model is continuous-time, the c2d command converts it to a discrete-time
LTI object using the controller’s sample time.
• If the model is discrete-time, the d2d command resamples it to generate a
discrete-time LTI object using the controller’s sample time.
3
Delay removal. If the discrete time model includes any input, output, or internal
delays, the absorbDelay command replaces them with the appropriate number
of poles at z = 0, increasing the total number of discrete states. The InputDelay,
OutputDelay, and InternalDelay properties of the resulting state space model
are all zero.
4
Conversion to dimensionless input and output variables. The MPC controller allows
you to specify a scale factor for each plant input and output variable. If you do not
specify scale factors, they default to unity. The software converts the plant input and
output variables to dimensionless form as follows:
x k A x k BS u
y k S Cx k S DS u k
k
p p p i p
p o p o i p
+
( )
=
( )
+
( )
=
( )
+
( )
( )
- -
1
1 1
.
Here, where A
p
, B, C, and D are constant state space matrices determined in step 3,
and:
• S
i
— Diagonal matrix of input scale factors in engineering units.
• S
o
— Diagonal matrix of output scale factors in engineering units.
• x
p
— State vector from step 3 in engineering units. No scaling is performed on
state variables.