Simulate adaptive and timevarying model predictive controllers
Model Predictive Control Toolbox
The Adaptive MPC Controller block uses the following input signals:
Measured plant outputs (mo
)
Reference or setpoint (ref
)
Measured plant disturbance (md
), if any
In addition, the required model
input signal specifies the prediction
model to use when computing the optimal plant manipulated variables mv
. The
linear prediction model can change at each control interval in response to changes in the real
plant at run time. The prediction model can represent a single LTI plant used for all
prediction steps (adaptive MPC mode) or an array of LTI plants for different prediction steps
(timevarying MPC mode). Two common ways to modify this model are as follows:
Given a nonlinear plant model, linearize it at the current operating point.
Use plant data to estimate parameters in an empirical lineartimevarying (LTV) model.
By default, the block estimates its prediction model states. Since the prediction model parameters change at run time, the static Kalman filter used in the MPC Controller block is inappropriate. Instead, the Adaptive MPC Controller block uses a lineartimevarying Kalman filter (LTVKF). For more information, see Adaptive MPC.
In all other ways, the Adaptive MPC Controller block mimics the MPC Controller block. Since the adaptive version involves additional overhead, use the MPC Controller block unless you need to control a nonlinear plant across a wide range of operating conditions where plant dynamics vary significantly.
Both the Adaptive MPC Controller block and the Multiple MPC Controllers block enable your control system to adapt to changing operating conditions at run time. The following table lists the advantages of using each block.
Block  Adaptive MPC Controller  Multiple MPC Controllers 

Adaptation approach  Update prediction model for a single controller as operating conditions change  Switch between multiple controllers designed for different operating regions 
Advantages 


model
— Updated plant model and nominal operating pointUpdated plant model and nominal operating point, specified as a bus signal. a bus
signal to the model
inport. At the beginning of each control
interval, this signal modifies the controller object Model.Plant
and Model.Nominal
properties.
The Adaptive MPC Controller requires the plant model to be an LTI discretetime statespace object with no delays. The following command extracts the statespace matrices comprising such a model.
[A,B,C,D] = ssdata(MPCobj.Model.Plant)
The purpose of the model
input is to replace these matrices
with new ones having the same dimensions and representing the same control interval.
You must also retain the sequence in which the input, output, and state variables
appear in the Model.Plant
property of the controller.
When operating in:
Adaptive MPC mode, the bus you connect to the model
inport
must contain the following signals, each identified by the specified name:
A
—
n_{x}byn_{x}
matrix signal, where n_{x} is the
number of plant model states.
B
—
n_{x}byn_{u}
matrix signal, where n_{u} is the total
number of plant model inputs (i.e., manipulated variables, measured
disturbances, and unmeasured disturbances).
C
—
n_{y}byn_{x}
matrix signal, where n_{y} is the
number of plant model outputs.
D
—
n_{y}byn_{u}
matrix signal.
X
— Vector signal of length
n_{x}, replacing the controller
Model.Nominal.X
property.
Y
— Vector signal of length
n_{y}, replacing the controller
Model.Nominal.Y
property.
U
— Vector signal of length
n_{u}, replacing the controller
Model.Nominal.U
property.
DX
— Vector signal of length
n_{x}, replacing the controller
Model.Nominal.DX
property. It must be appropriate for use
with a discretetime model of the assumed control interval. For more
information, see Adaptive MPC.
To compute DX
values, use the discretetime state
update function (f) for your model. Here,
u_{k} and
x_{k} are the respective input and
state values for the current time step.
$$DX=f({u}_{k},{x}_{k}){x}_{k}$$
Timevarying MPC mode, the bus you connect to the model
inport must contain the following 3–dimensional bus signals:
A
—
n_{x}byn_{x}by(p+1)
matrix signal
B
—
n_{x}byn_{u}by(p+1)
matrix signal
C
—
n_{y}byn_{x}by(p+1)
D
—
n_{y}byn_{u}by(p+1)
matrix signal
X
—
n_{x}by(p+1)
matrix signal
Y
—
n_{y}by(p+1)
matrix signal
U
—
n_{u}by(p+1)
matrix signal
DX
—
n_{x}by(p+1)
matrix signal
Here, p is the controller prediction horizon. For each signal, specify p+1 values representing the model and nominal conditions at each step of the prediction horizon. For more information, see TimeVarying MPC.
One way to form the bus is to use a Bus Creator (Simulink) block.
The dimensions of the bus elements in model depend on the operating mode of the controller. To place the controller in:
Adaptive MPC mode, clear the Linear TimeVarying (LTV) plants parameter
Timevarying MPC mode, select the Linear TimeVarying (LTV) plants parameter
ref
— Model output reference valuesPlant output reference values, specified as a row vector signal or matrix signal.
To use the same reference values across the prediction horizon, connect ref to a row vector signal with N_{Y} elements, where N_{y} is the number of output variables. Each element specifies the reference for an output variable.
To vary the references over the prediction horizon (previewing) from time k+1 to time k+p, connect ref to a matrix signal with N_{y} columns and up to p rows. Here, k is the current time and p is the prediction horizon. Each row contains the references for one prediction horizon step. If you specify fewer than p rows, the final references are used for the remaining steps of the prediction horizon.
mo
— Measured outputsMeasured outputs, specified as a vector signal. The block uses the measured plant outputs to improve its state estimates. If your controller uses default state estimation, you must connect the measured plant outputs to the mo input port. If your controller uses custom state estimation, you must connect the estimated plant states to the x[kk] input port.
To enable this port, clear the Use custom state estimation instead of using the builtin Kalman filter parameter.
x[kk]
— Custom state estimateCustom state estimate, specified as a vector signal. The block uses the connected state estimates instead of estimating the states using the builtin estimator. If your controller uses custom state estimation, you must connect the current state estimates to the x[kk] input port. If your controller uses default state estimation, you must connect the measured output to the mo input port.
Even though noise model states (if any) are not used
in MPC optimization, the custom state vector must contain all the
states defined in the mpcstate
object of the
controller, including the plant, disturbance, and noise model
states.
Use custom state estimates when an alternative estimation technique is considered superior to the builtin estimator or when the states are fully measurable.
To enable this port, select the Use custom state estimation instead of using the builtin Kalman filter parameter.
md
— inputIf your controller prediction model has measured disturbances you must enable this port and connect to it a row vector or matrix signal.
To use the same measured disturbance values across the prediction horizon, connect md to a row vector signal with N_{md} elements, where N_{md} is the number of manipulated variables. Each element specifies the value for a measured disturbance.
To vary the disturbances over the prediction horizon (previewing) from time k to time k+p, connect md to a matrix signal with N_{md} columns and up to p+1 rows. Here, k is the current time and p is the prediction horizon. Each row contains the disturbances for one prediction horizon step. If you specify fewer than p+1 rows, the final disturbances are used for the remaining steps of the prediction horizon.
To enable this port, select the Measured disturbances parameter.
ext.mv
— Control signals used in plant at previous control intervalControl signals used in the plant at the previous control interval, specified as a vector signal of length N_{mv}, where N_{mv} is the number of manipulated variables. Use this input port to improve state estimation accuracy when:
You know your controller is not always in control of the plant.
The actual MV signals applied to the plant can potentially differ from the values generated by the controller, such as in control signal saturation.
Controller state estimation assumes that the MVs are piecewise constant. Therefore, at time t_{k}, the ext.mv value must contain the effective MVs between times t_{k–1} and t_{k}. For example, if the MVs are actually varying over this interval, you might supply the timeaveraged value evaluated at time t_{k}.
Note
Connect ext.mv to the MV signals actually applied to the plant in the previous control interval. Typically, these MV signals are the values generated by the controller, though this is not always the case. For example, if your controller is offline and running in tracking mode (that is, the controller output is not driving the plant), then feeding the actual control signal to ext.mv can help achieve bumpless transfer when the controller is switched back online.
When the controller is driving the plant, insert a Memory block or Unit Delay block to feed back the MV signal applied to the plant at the previous control interval. This also avoids a direct feedthrough from the ext.mv inport to the mv outport, therefore preventing algebraic loops in the Simulink^{®} model.
For an example that uses the external manipulated variable input port for bumpless transfer, see Switch Controller Online and Offline with Bumpless Transfer.
To enable this port, select the External manipulated variable parameter.
switch
— Enable or disable optimizationTo turn off the controller optimization calculations, connect switch to a nonzero signal.
Disabling optimization calculations reduces computational effort when the controller output is not needed, such as when the system is operating manually or another controller has taken over. However, the controller continues to update its internal state estimates in the usual way. Therefore, it is ready to resume optimization calculations whenever the switch signal returns to zero. While controller optimization is off, the block passes the current ext.mv signal to the controller output. If the ext.mv inport is not enabled, the controller output is held at the value it had when optimization was disabled.
For an example that uses the external manipulated variable input port for bumpless transfer, see Switch Controller Online and Offline with Bumpless Transfer.
To enable this port, select the Use external signal to enable or disable optimization parameter.
mv.target
— Manipulated variable targetsTo specify manipulated variable targets, enable this input port, and connect a row vector or matrix signal. To make a given manipulated variable track its specified target value, you must also specify a nonzero tuning weight for that manipulated variable.
To use the same manipulated variable targets across the prediction horizon, connect mv.target to a row vector signal with N_{mv} elements, where N_{mv} is the number of manipulated variables. Each element specifies the target for a manipulated variable.
To vary the targets over the prediction horizon (previewing) from time k to time k+p1, connect mv.target to a matrix signal with N_{mv} columns and up to p rows. Here, k is the current time and p is the prediction horizon. Each row contains the targets for one prediction horizon step. If you specify fewer than p rows, the final targets are used for the remaining steps of the prediction horizon.
To enable this port, select the Targets for manipulated variables parameter.
ymin
— Minimum output variable constraintsTo specify runtime minimum output variable constraints, enable this input port. If
this port is disabled, the block uses the lower bounds specified in the
OutputVariables.Min
property of its mpc
controller object. If an output variable has no lower bound specified
in the controller object, then at run time the block ignores the corresponding connected
signal.
To change the bounds over the prediction horizon from time k+1 to time k+p, connect ymin to a matrix signal with N_{y} columns and up to p rows. Here, N_{y} is the number of plant outputs, k is the current time, and p is the prediction horizon. Each row contains the bounds for one prediction horizon step. If you specify fewer than p rows, the bounds in the final row apply for the remainder of the prediction horizon. If there is only one output variable, and a vector signal with no more than p entries is connected, then these entries are used across the prediction horizon.
The i
th column of the ymin signal corresponds
to the i
th plant output, and replaces the
OutputVariables(i).Max
property of the mpc
object at run time. The replacement behavior depends on the dimensions
of both variables.
Scalar OutputVariables(i).Min
in the mpc
object (a constant bound for the i
th plant output to be applied
to all prediction steps)
ymin Dimension  Replacement Behavior 

Scalar ymin (single output, constant bound)  ymin replaces the constant bound defined in
OutputVariables(i).Min 
Column vector ymin (single output, timevarying bound)  ymin replaces the constant bound defined in
OutputVariables(i).Min with a timevarying
bound. 
Row vector ymin (multiple outputs, constant bounds)  The i th element of ymin
replaces the constant bound defined in
OutputVariables(i).Min 
Matrix ymin (multiple outputs, timevarying bounds)  The i th column of ymin
replaces the constant bound defined in
OutputVariables(i).Min with a timevarying
bound. 
Vector OutputVariables(i).Min
in the mpc
object (a timevarying bound for the i
th plant output with
different values at different prediction steps)
ymin Dimension  Replacement Behavior 

Scalar ymin (single output, constant bound)  ymin replaces the first finite entry
in OutputVariables.Min and the remaining entries
in OutputVariables.Min shift up or down with the same
amount of displacement to retain the profile defined by the original
OutputVariables.Min vector. 
Column vector ymin (single output, timevarying bound)  ymin replaces the timevarying bound defined in
OutputVariables(i).Min , and the original bound
profile is discarded. 
Row vector ymin (multiple outputs, constant bounds)  The i th element of ymin
replaces the first finite entry
in OutputVariables(i).Min and the remaining
entries in OutputVariables(i).Min shift up or down
with the same amount of displacement to retain the profile defined by
the original OutputVariables(i).Min vector. 
Matrix ymin (multiple outputs, timevarying bounds).  The i th column of ymin
replaces the timevarying bound defined in
OutputVariables(i).Min , and the original bound
profile is discarded. 
To enable this port, select the Lower OV limits parameter.
ymax
— Maximum output variable constraintsTo specify runtime maximum output variable constraints, enable this input port. If
this port is disabled, the block uses the upper bounds specified in the
OutputVariables.Max
property of its mpc
controller object. If an output variable has no upper bound specified
in the controller object, then at run time the block ignores the corresponding connected
signal.
To change the bounds over the prediction horizon from time k+1 to time k+p, connect ymax to a matrix signal with N_{y} columns and up to p rows. Here, N_{y} is the number of plant outputs, k is the current time, and p is the prediction horizon. Each row contains the bounds for one prediction horizon step. If you specify fewer than p rows, the bounds in the final row apply for the remainder of the prediction horizon. If there is only one output variable, and a vector signal with no more than p entries is connected, then these entries are used across the prediction horizon.
The i
th column of the ymax signal corresponds
to the i
th plant output, and replaces the
OutputVariables(i).Max
property of the mpc
object at run time. The replacement behavior depends on the dimensions
of both variables.
Scalar OutputVariables(i).Max
in the mpc
object (a constant bound for the i
th plant output to be applied
to all prediction steps)
ymax Dimension  Replacement Behavior 

Scalar ymax (single output, constant bound)  ymax replaces the constant bound defined in
OutputVariables(i).Max 
Column vector ymax (single output, timevarying bound)  ymax replaces the constant bound defined in
OutputVariables(i).Max with a timevarying
bound. 
Row vector ymax (multiple outputs, constant bounds)  The i th element of ymax
replaces the constant bound defined in
OutputVariables(i).Max 
Matrix ymax (multiple outputs, timevarying bounds)  The i th column of ymax
replaces the constant bound defined in
OutputVariables(i).Max with a timevarying
bound. 
Vector OutputVariables(i).Max
in the mpc
object (a timevarying bound for the i
th plant output with
different values at different prediction steps)
ymax Dimension  Replacement Behavior 

Scalar ymax (single output, constant bound)  ymax replaces the first finite entry
in OutputVariables.Max and the remaining entries
in OutputVariables.Max shift up or down with the same
amount of displacement to retain the profile defined by the original
OutputVariables.Max vector. 
Column vector ymax (single output, timevarying bound)  ymax replaces the timevarying bound defined in
OutputVariables(i).Max , and the original bound
profile is discarded. 
Row vector ymax (multiple outputs, constant bounds)  The i th element of ymax
replaces the first finite entry
in OutputVariables(i).Max and the remaining
entries in OutputVariables(i).Max shift up or down
with the same amount of displacement to retain the profile defined by
the original OutputVariables(i).Max vector. 
Matrix ymax (multiple outputs, timevarying bounds).  The i th column of ymax
replaces the timevarying bound defined in
OutputVariables(i).Max , and the original bound
profile is discarded. 
To enable this port, select the Upper OV limits parameter.
umin
— Minimum manipulated variable constraintsTo specify runtime minimum manipulated variable constraints, enable this input port.
If this port is disabled, the block uses the lower bounds specified in the
ManipulatedVariables.Min
property of its mpc
controller object. If a manipulated variable has no lower bound
specified in the controller object, then at run time the block ignores the corresponding
connected signal.
To change the bounds over the prediction horizon from time k to time k+p1, connect umin to a matrix signal with N_{mv} columns and up to p rows. Here, N_{mv} is the number of manipulated variables, k is the current time, and p is the prediction horizon. Each row contains the bounds for one prediction horizon step. If you specify fewer than p rows, the bounds in the final row apply for the remainder of the prediction horizon. If there is only one manipulated variable, and a vector signal with no more than p entries is connected, then these entries are used across the prediction horizon.
The i
th column of the umin signal corresponds
to the i
th manipulated variable, and replaces the
ManipulatedVariables(i).Max
property of the mpc
object at run time. The replacement behavior depends on the dimensions
of both variables.
Scalar ManipulatedVariables(i).Min
in the mpc
object (a constant bound for the i
th manipulated variable to be
applied to all prediction steps)
umin Dimension  Replacement Behavior 

Scalar umin (single output, constant bound)  umin replaces the constant bound defined in
ManipulatedVariables(i).Min 
Column vector umin (single output, timevarying bound)  umin replaces the constant bound defined in
ManipulatedVariables(i).Min with a timevarying
bound. 
Row vector umin (multiple outputs, constant bounds)  The i th element of umin
replaces the constant bound defined in
ManipulatedVariables(i).Min 
Matrix umin (multiple outputs, timevarying bounds)  The i th column of umin
replaces the constant bound defined in
ManipulatedVariables(i).Min with a timevarying
bound. 
Vector ManipulatedVariables(i).Min
in the mpc
object (a timevarying bound for the i
th manipulated variable
with different values at different prediction steps)
umin Dimension  Replacement Behavior 

Scalar umin (single output, constant bound)  umin replaces the first finite entry
in ManipulatedVariables.Min and the remaining
entries in ManipulatedVariables.Min shift up or down
with the same amount of displacement to retain the profile defined by
the original ManipulatedVariables.Min vector. 
Column vector umin (single output, timevarying bound)  umin replaces the timevarying bound defined in
ManipulatedVariables(i).Min , and the original
bound profile is discarded. 
Row vector umin (multiple outputs, constant bounds)  The i th component of umin
replaces the first finite entry
in ManipulatedVariables(i).Min and the remaining
entries in ManipulatedVariables(i).Min shift up or
down with the same amount of displacement to retain the profile defined
by the original ManipulatedVariables(i).Min
vector. 
Matrix umin (multiple outputs, timevarying bounds).  The i th column of umin
replaces the timevarying bound defined in
ManipulatedVariables(i).Min , and the original
bound profile is discarded. 
To enable this port, select the Lower MV limits parameter.
umax
— Maximum manipulated variable constraintsTo specify runtime maximum manipulated variable constraints, enable this input port.
If this port is disabled, the block uses the upper bounds specified in the
ManipulatedVariables.Max
property of its mpc
controller object. If a manipulated variable has no upper bound
specified in the controller object, then at run time the block ignores the corresponding
connected signal.
To change the bounds over the prediction horizon from time k to time k+p1, connect umax to a matrix signal with N_{mv} columns and up to p rows. Here, N_{mv} is the number of manipulated variables, k is the current time, and p is the prediction horizon. Each row contains the bounds for one prediction horizon step. If you specify fewer than p rows, the bounds in the final row apply for the remainder of the prediction horizon. If there is only one manipulated variable, and a vector signal with no more than p entries is connected, then these entries are used across the prediction horizon.
The i
th column of the umax signal corresponds
to the i
th manipulated variable, and replaces the
ManipulatedVariables(i).Max
property of the mpc
object at run time. The replacement behavior depends on the dimensions
of both variables.
Scalar ManipulatedVariables(i).Max
in the mpc
object (a constant bound for the i
th manipulated variable to be
applied to all prediction steps)
umax Dimension  Replacement Behavior 

Scalar umax (single output, constant bound)  umax replaces the constant bound defined in
ManipulatedVariables(i).Max 
Column vector umax (single output, timevarying bound)  umax replaces the constant bound defined in
ManipulatedVariables(i).Max with a timevarying
bound. 
Row vector umax (multiple outputs, constant bounds)  The i th element of umax
replaces the constant bound defined in
ManipulatedVariables(i).Max 
Matrix umax (multiple outputs, timevarying bounds)  The i th column of umax
replaces the constant bound defined in
ManipulatedVariables(i).Max with a timevarying
bound. 
Vector ManipulatedVariables(i).Max
in the mpc
object (a timevarying bound for the i
th manipulated variable
with different values at different prediction steps)
umax Dimension  Replacement Behavior 

Scalar umax (single output, constant bound)  umax replaces the first finite entry
in ManipulatedVariables.Max and the remaining
entries in ManipulatedVariables.Max shift up or down
with the same amount of displacement to retain the profile defined by
the original ManipulatedVariables.Max vector. 
Column vector umax (single output, timevarying bound)  umax replaces the timevarying bound defined in
ManipulatedVariables(i).Max , and the original
bound profile is discarded. 
Row vector umax (multiple outputs, constant bounds)  The i th element of umax
replaces the first finite entry
in ManipulatedVariables(i).Max and the remaining
entries in ManipulatedVariables(i).Max shift up or
down with the same amount of displacement to retain the profile defined
by the original ManipulatedVariables(i).Max
vector. 
Matrix umax (multiple outputs, timevarying bounds).  The i th column of umax
replaces the timevarying bound defined in
ManipulatedVariables(i).Max , and the original
bound profile is discarded. 
To enable this port, select the Upper MV limits parameter.
E
— Manipulated variable constraint matrixManipulated variable constraint matrix, specified as an N_{c}byN_{mv} matrix signal, where N_{c} is the number of mixed input/output constraints and N_{mv} is the number of manipulated variables.
If you define E
in the mpc
object, you must
connect a signal to the E input port. Otherwise, connect a zero
matrix with the correct size.
To specify runtime mixed input/output constraints, use the E input port
along with the F, G, and
S ports. These constraints replace the mixed input/output
constraints previously set using setconstraint
. For more information on mixed input/output constraints,
see Constraints on Linear Combinations of Inputs and Outputs.
The number of mixed input/output constraints cannot change at run time. Therefore,
N_{c} must match the number of rows in
the E
matrix you specified using
setconstraint
.
To enable this port, select the Custom constraints parameter.
F
— Controlled output constraint matrixControlled output constraint matrix, specified as an
N_{c}byN_{y}
matrix signal, where N_{c} is the number of mixed
input/output constraints and N_{y} is the number
of plant outputs. If you define F
in the mpc
object, you must connect a signal to the F input port with same
number of rows. Otherwise, connect a zero matrix with the correct size.
To specify runtime mixed input/output constraints, use the F input port
along with the E, G, and
S ports. These constraints replace the mixed input/output
constraints previously set using setconstraint
. For more information on mixed input/output constraints,
see Constraints on Linear Combinations of Inputs and Outputs.
The number of mixed input/output constraints cannot change at run time. Therefore,
N_{c} must match the number of rows in
the F
matrix you specified using
setconstraint
.
To enable this port, select the Custom constraints parameter.
G
— Custom constraint vectorCustom constraint vector, specified as a row vector signal of length
N_{c}, where
N_{c} is the number of mixed input/output
constraints. If you define G
in the mpc
object,
you must connect a signal to the G input port with same number of
rows. Otherwise, connect a zero matrix with the correct size.
To specify runtime mixed input/output constraints, use the G input port
along with the E, F, and
S ports. These constraints replace the mixed input/output
constraints previously set using setconstraint
. For more information on mixed input/output constraints,
see Constraints on Linear Combinations of Inputs and Outputs.
The number of mixed input/output constraints cannot change at run time. Therefore,
N_{c} must match the number of rows in
the G
matrix you specified using
setconstraint
.
To enable this port, select the Custom constraints parameter.
S
— Measured disturbance constraint matrixMeasured disturbance constraint matrix, specified as an
N_{c}byn_{N}
matrix signal, where N_{c} is the number of mixed
input/output constraints, and N_{v} is the number
of measured disturbances. If you define S
in the
mpc
object, you must connect a signal to the
S input port with same number of rows. Otherwise, connect a
zero matrix with the correct size.
To specify runtime mixed input/output constraints, use the S input port
along with the E, F, and
G ports. These constraints replace the mixed input/output
constraints previously set using setconstraint
. For more information on mixed input/output constraints,
see Constraints on Linear Combinations of Inputs and Outputs.
The number of mixed input/output constraints cannot change at run time. Therefore,
N_{c} must match the number of rows in
the G
matrix you specified using
setconstraint
.
To enable this port, select the Custom constraints parameter. This port is added only if the mpc
object has measured disturbances.
y.wt
— Output variable tuning weightsTo specify runtime output variable tuning weights, enable this input port. If this port is disabled, the block uses the tuning weights specified in the Weights.OutputVariables
property of its controller object. These tuning weights penalize deviations from output references.
If the MPC controller object uses constant output tuning weights over the prediction horizon, you can specify only constant output tuning weights at runtime. Similarly, if the MPC controller object uses output tuning weights that vary over the prediction horizon, you can specify only timevarying output tuning weights at runtime
To use constant tuning weights over the prediction horizon, connect y.wt to a row vector signal with N_{y} elements, where N_{y} is the number of outputs. Each element specifies a nonnegative tuning weight for an output variable. For more information on specifying tuning weights, see Tune Weights.
To vary the tuning weights over the prediction horizon from time k+1 to time k+p, connect y.wt to a matrix signal with N_{y} columns and up to p rows. Here, k is the current time and p is the prediction horizon. Each row contains the tuning weights for one prediction horizon step. If you specify fewer than p rows, the tuning weights in the final row apply for the remainder of the prediction horizon. For more information on varying weights over the prediction horizon, see TimeVarying Weights and Constraints.
To enable this port, select the OV weights parameter.
u.wt
— Manipulated variable tuning weightsTo specify runtime manipulated variable tuning weights, enable this input port. If
this port is disabled, the block uses the tuning weights specified in the
Weights.ManipulatedVariables
property of its controller object.
These tuning weights penalize deviations from MV targets.
If the MPC controller object uses constant manipulated variable tuning weights over the prediction horizon, you can specify only constant manipulated variable tuning weights at runtime. Similarly, if the MPC controller object uses manipulated variable tuning weights that vary over the prediction horizon, you can specify only timevarying manipulated variable tuning weights at runtime
To use the same tuning weights over the prediction horizon, connect u.wt to a row vector signal with N_{mv} elements, where N_{mv} is the number of manipulated variables. Each element specifies a nonnegative tuning weight for a manipulated variable. For more information on specifying tuning weights, see Tune Weights.
To vary the tuning weights over the prediction horizon from time k to time k+p1, connect u.wt to a matrix signal with N_{mv} columns and up to p rows. Here, k is the current time and p is the prediction horizon. Each row contains the tuning weights for one prediction horizon step. If you specify fewer than p rows, the tuning weights in the final row apply for the remainder of the prediction horizon. For more information on varying weights over the prediction horizon, see TimeVarying Weights and Constraints.
To enable this port, select the MV weights parameter.
du.wt
— Manipulated variable rate tuning weightsTo specify runtime manipulated variable rate tuning weights, enable this input port. If this port is disabled, the block uses the tuning weights specified in the Weights.ManipulatedVariablesRate
property of its controller object. These tuning weights penalize large changes in control moves.
If the MPC controller object uses constant manipulated variable rate tuning weights over the prediction horizon, you can specify only constant manipulated variable tuning rate weights at runtime. Similarly, if the MPC controller object uses manipulated variable rate tuning weights that vary over the prediction horizon, you can specify only timevarying manipulated variable rate tuning weights at runtime
To use the same tuning weights over the prediction horizon, connect du.wt to a row vector signal with N_{mv} elements, where N_{mv} is the number of manipulated variables. Each element specifies a nonnegative tuning weight for a manipulated variable rate. For more information on specifying tuning weights, see Tune Weights.
To vary the tuning weights over the prediction horizon from time k to time k+p1, connect du.wt to a matrix signal with N_{mv} columns and up to p rows. Here, k is the current time and p is the prediction horizon. Each row contains the tuning weights for one prediction horizon step. If you specify fewer than p rows, the tuning weights in the final row apply for the remainder of the prediction horizon. For more information on varying weights over the prediction horizon, see TimeVarying Weights and Constraints.
To enable this port, select the MVRate weights parameter.
ecr.wt
— Slack variable tuning weightTo specify a runtime slack variable tuning weight, enable this input port and connect a scalar signal. If this port is disabled, the block uses the tuning weight specified in the Weights.ECR
property of its controller object.
The slack variable tuning weight has no effect unless your controller object defines soft constraints whose associated ECR values are nonzero. If there are soft constraints, increasing the ecr.wt value makes these constraints relatively harder. The controller then places a higher priority on minimizing the magnitude of the predicted worstcase constraint violation.
To enable this port, select the ECR weight parameter.
p
— Prediction horizonPrediction horizon, specified as positive integer signal. The prediction horizon signal value must be less than or equal to the Maximum prediction horizon parameter.
At run time, the values of p
overrides the default prediction horizon specified in the controller object. For more information, see Adjust Horizons at Run Time.
To enable this port, select the Adjust prediction horizon and control horizon at run time parameter.
m
— Control horizonControl horizon, specified as one of the following:
Positive integer signal less than or equal to the prediction horizon.
Vector signal of positive integers specifying blocking interval lengths. For more information, see Manipulated Variable Blocking.
At run time, the values of m
overrides the default control horizon specified in the controller object. For more information, see Adjust Horizons at Run Time.
To enable this port, select the Adjust prediction horizon and control horizon at run time parameter.
mv
— Optimal manipulated variable control actionOptimal manipulated variable control action, output as a column vector signal of length N_{mv}, where N_{mv} is the number of manipulated variables.
If the solver converges to a local optimum solution (qp.status is positive), then mv contains the optimal solution.
If the solver fails (qp.status is negative), then mv remains at its most recent successful solution; that is, the controller output freezes.
If the solver reaches the maximum number of iterations without finding an optimal solution
(qp.status is zero) and the
Optimization.UseSuboptimalSolution
property of the controller
is:
true
, then mv contains the suboptimal solution
false
, then mv then mv remains at its most recent successful solution
cost
— Objective function costObjective function cost, output as a nonnegative scalar signal. The cost quantifies the degree to which the controller has achieved its objectives. The cost value is calculated using the scaled MPC cost function in which every term is offsetfree and dimensionless.
The cost value is only meaningful when the qp.status output is nonnegative.
To enable this port, select the Optimal cost parameter.
qp.status
— Optimization statusOptimization status, output as an integer signal.
If the controller solves the QP problem for a given control interval, the qp.status output returns the number of QP solver iterations used in computation. This value is a finite, positive integer and is proportional to the time required for the calculations. Therefore, a large value means a relatively slow block execution for this time interval.
The QP solver can fail to find an optimal solution for the following reasons:
qp.status = 0
— The QP solver cannot find a solution within the maximum number of iterations specified in the mpc
object. In this case, if the Optimizer.UseSuboptimalSolution
property of the controller is false
, the block holds its mv output at the most recent successful solution. Otherwise, it uses the suboptimal solution found during the last solver iteration.
qp.status = 1
— The QP solver detects an infeasible QP problem. See Monitoring Optimization Status to Detect Controller Failures for an example where a large, sustained disturbance drives the output variable outside its specified bounds. In this case, the block holds its mv output at the most recent successful solution.
qp.status = 2
— The QP solver has encountered numerical difficulties in solving a severely illconditioned QP problem. In this case, the block holds its mv output at the most recent successful solution.
In a realtime application, you can use qp.status to set an alarm or take other special action.
To enable this port, select the Optimization status parameter.
est.state
— Estimated controller statesEstimated controller states at each control instant, returned as a vector signal. The estimated states include the plant, disturbance, and noise model states. If custom state estimation is used, this output signal has the same value as the x[kk] input signal.
To enable this port, select the Estimated controller states parameter.
mv.seq
— Optimal manipulated variable sequenceOptimal manipulated variable sequence, returned as a matrix signal with p+1 rows and N_{mv} columns, where p is the prediction horizon and N_{mv} is the number of manipulated variables.
The first p rows of mv.seq contain the calculated optimal manipulated variable values from current time k to time k+p1. The first row of mv.seq contains the current manipulated variable values (output mv). Since the controller does not calculate optimal control moves at time k+p, the final two rows of mv.seq are identical.
To enable this port, select the Optimal control sequence parameter.
x.seq
— Optimal prediction model state sequenceOptimal prediction model state sequence, returned as a matrix signal with p+1 rows and N_{x} columns, where p is the prediction horizon and N_{x} is the number of states.
The first p rows of x.seq contain the calculated optimal state values from current time k to time k+p1. The first row of x.seq contains the current estimated state values. Since the controller does not calculate optimal states at time k+p, the final two rows of x.seq are identical.
To enable this port, select the Optimal state sequence parameter.
y.seq
— Optimal output variable sequenceOptimal output variable sequence, returned as a matrix signal with p+1 rows and N_{y} columns, where p is the prediction horizon and N_{y} is the number of output variables.
The first p rows of y.seq contain the calculated optimal output values from current time k to time k+p1. The first row of y.seq is computed based on the current estimated states and the current measured disturbances (first row of input md). Since the controller does not calculate optimal output values at time k+p, the final two rows of y.seq are identical.
To enable this port, select the Optimal output sequence parameter.
Adaptive MPC Controller
— Controller objectmpc
object nameSpecify an mpc
object that defines an MPC controller by
entering the name of an mpc
object designed at the nominal
operating point of the block. At run time, the controller replaces the original
prediction model (A
, B
, C
, and
D
) and nominal values (U
, Y
,
X
, and DX
) with the data specified in the
model input port at each control instant.
By default, the block assumes all other controller object properties (for example tuning weights, constraints) are constant. You can override this assumption using the options in the Online Features section.
The following restrictions apply to the mpc
controller object:
It must exist in the MATLAB^{®} workspace.
Its prediction model must be an LTI discretetime, statespace object with no
delays. Use the absorbDelay
command to convert
delays to discrete states. The dimensions of the A
,
B
, C
, and D
matrices in
the prediction determine the dimensions required by the model
inport signal.
Block Parameter:
mpcobj 
Type: string, character vector 
Default:
"" 
Initial Controller State
— Initial statempcstate
object nameSpecify the initial controller state. If you leave this parameter blank, the block uses the
nominal values defined in the Model.Nominal
property of the
mpc
object. To override the default, create an mpcstate
object in your workspace, and enter its name in the
field.
Use this parameter make the controller states reflect the true plant environment at
the start of your simulation to the best of your knowledge. This initial states can
differ from the nominal states defined in the mpc
object.
If custom state estimation is enabled, the block ignores Initial Controller State parameter.
Block Parameter: x0 
Type: string, character vector 
Default: "" 
Measured disturbance
— Add measured disturbance input porton
(default)  off
If your controller has measured disturbances, you must select this parameter to add the md output port to the block.
Block Parameter:
md_inport 
Type: string, character vector 
Values:
"off" , "on" 
Default:
"on" 
External manipulated variable
— Add external manipulated variable input portSelect this parameter to add the ext.mv input port to the block.
Block Parameter: mv_inport 
Type: string, character vector 
Values: "off" , "on" 
Default: "off" 
Targets for manipulated variables
— Add manipulated variable target input portSelect this parameter to add the mv.target input port to the block.
Block Parameter: uref_inport 
Type: string, character vector 
Values: "off" , "on" 
Default: "off" 
Optimal cost
— Odd optimal cost output portSelect this parameter to add the cost output port to the block.
Block Parameter: return_cost 
Type: string, character vector 
Values: "off" , "on" 
Default: "off" 
Optimization status
— Add optimization status output portSelect this parameter to add the qp.status output port to the block.
Block Parameter: return_qpstatus 
Type: string, character vector 
Values: "off" , "on" 
Default: "off" 
Estimated controller states
— Add estimated states output portSelect this parameter to add the est.state output port to the block.
Block Parameter: return_state 
Type: string, character vector 
Values: "off" , "on" 
Default: "off" 
Optimal control sequence
— Add optimal control sequence output portSelect this parameter to add the mv.seq output port to the block.
Block Parameter: return_mvseq 
Type: string, character vector 
Values: "off" , "on" 
Default: "off" 
Optimal state sequence
— Add optimal state sequence output portSelect this parameter to add the x.seq output port to the block.
Block Parameter: return_xseq 
Type: string, character vector 
Values: "off" , "on" 
Default: "off" 
Optimal output sequence
— Add optimal output sequence output portSelect this parameter to add the y.seq output port to the block.
Block Parameter:
return_ovseq 
Type: string, character vector 
Values: "off" , "on" 
Default: "off" 
Use custom state estimation instead of using the builtin Kalman filter
— Use custom state estimate input portSelect this parameter to remove the mo input port and add the x[kk] input port.
Block Parameter: state_inport 
Type: string, character vector 
Values: "off" , "on" 
Default: "off" 
Linear TimeVarying (LTV) plants
— Use custom state estimate input portTo operate your controller in timevarying MPC mode, select this option. When operating in this mode, connect a 3–dimensional bus signal to the model input port
For an example, see TimeVarying MPC Control of a TimeVarying Plant.
Block Parameter:
isltv_plant 
Type: string, character vector 
Values:
"off" , "on" 
Default:
"off" 
Lower OV limits
— Add minimum OV constraint input portSelect this parameter to add the ymin input port to the block.
Block Parameter: ymin_inport 
Type: string, character vector 
Values: "off" , "on" 
Default: "off" 
Upper OV limits
— Add maximum OV constraint input portSelect this parameter to add the ymax input port to the block.
Block Parameter: ymax_inport 
Type: string, character vector 
Values: "off" , "on" 
Default: "off" 
Lower MV limits
— Add minimum MV constraint input portSelect this parameter to add the umin input port to the block.
Block Parameter: umin_inport 
Type: string, character vector 
Values: "off" , "on" 
Default: "off" 
Upper MV limits
— Add maximum MV constraint input portSelect this parameter to add the umax input port to the block.
Block Parameter: umax_inport 
Type: string, character vector 
Values: "off" , "on" 
Default: "off" 
Custom constraints
— Add custom constraints input portsSelect this parameter to add the E, F, G, and S input ports to the block.
Block Parameter: cc_inport 
Type: string, character vector 
Values: "off" , "on" 
Default: "off" 
OV weights
— Add OV tuning weights input portSelect this parameter to add the y.wt input port to the block.
Block Parameter: ywt_inport 
Type: string, character vector 
Values: "off" , "on" 
Default: "off" 
MV weights
— Add MV tuning weights input portSelect this parameter to add the u.wt input port to the block.
Block Parameter: uwt_inport 
Type: string, character vector 
Values: "off" , "on" 
Default: "off" 
MVRate weights
— Add MV rate tuning weights input portSelect this parameter to add the du.wt input port to the block.
Block Parameter: duwt_inport 
Type: string, character vector 
Values: "off" , "on" 
Default: "off" 
Slack variable weight
— Add ECR tuning weight input portSelect this parameter to add the ecr.wt input port to the block.
Block Parameter: rhoeps_inport 
Type: string, character vector 
Values: "off" , "on" 
Default: "off" 
Adjust prediction horizon and control horizon at run time
— Add horizon input portsSelect this parameter to add the p and m input port to the block.
Block Parameter: pm_inport 
Type: string, character vector 
Values: "off" , "on" 
Default: "off" 
Maximum prediction horizon
— Add horizon input ports10
(default)  positive integerSelect this parameter to add the p and m input port to the block.
To enable this parameter, select the Adjust prediction horizon and control horizon at run time parameter.
Block Parameter: MaximumP 
Type: string, character vector 
Default: "10" 
Inherit sample time
— Inherit block sample time from parent subsystemoff
(default)  on
Select this parameter to inherit the sample time of the parent subsystem as the block sample time. Doing so allows you to conditionally execute this block inside FunctionCall Subsystem (Simulink) or Triggered Subsystem (Simulink) blocks. For an example, see Using MPC Controller Block Inside FunctionCall and Triggered Subsystems.
Note
You must execute FunctionCall Subsystem or Triggered Subsystem blocks at the sample rate of the controller. Otherwise, you can see unexpected results.
If you clear this parameter, the sample time of the block is inherited from the controller object.
To view the sample time of a block, in the Simulink model window, on the Debug tab, under Information Overlays, select either colors or Text. For more information, see View Sample Time Information (Simulink).
Block Parameter:
SampleTimeInherited 
Type: string, character vector 
Values:
"off" , "on" 
Default:
"off" 
Use external signal to enable or disable optimization
— Add switch input portSelect this parameter to add the switch input port to the block.
Block Parameter: switch_inport 
Type: string, character vector 
Values: "off" , "on" 
Default: "off" 
mv.seq
output port signal dimensions have changedBehavior changed in R2018b
The signal dimensions of the mv.seq
output port of the
Adaptive MPC Controller block have changed. Previously, this signal was a
pbyN_{mv} matrix, where
p is the prediction horizon and
N_{mv} is the number of manipulated variables. Now,
mv.seq
is a
(p+1)byN_{mv} matrix, where
row p+1 duplicates row p.
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