# MPC Controller

Simulate model predictive controller

**Library:**Model Predictive Control Toolbox

## Description

The MPC Controller block receives the current measured output signal
(`mo`

), reference signal (`ref`

), and optional measured
disturbance signal (`md`

). The block computes the optimal manipulated
variable (`mv`

) by solving a quadratic programming problem using either the
default KWIK solver or a custom QP solver. For more information, see QP Solvers.

To use the block in simulation and code generation, you must specify an
`mpc`

object, which defines a model predictive controller. This
controller must have already been designed for the plant that it controls.

Because the MPC Controller block uses MATLAB Function
blocks, it requires compilation each time you change the MPC object and block. Also, because
MATLAB^{®} does not allow compiled code to reside in any MATLAB product folder, you must use a non-MATLAB folder to work on your Simulink^{®} model when you use MPC blocks.

## Ports

### Input

**Required Inputs**

`mo`

— Measured outputs

vector

Measured 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[k|k]** input port.

#### Dependencies

To enable this port, clear the **Use custom state estimation instead of
using the built-in Kalman filter** parameter.

`x[k|k]`

— Custom state estimate

vector

Custom state estimate, specified as a vector signal. The block uses the connected state
estimates instead of estimating the states using the built-in
estimator. If your controller uses custom state estimation, you must
connect the current state estimates to the **x[k|k]**
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 built-in estimator or when the states are fully measurable.

#### Dependencies

To enable this port, select the **Use custom state estimation instead of using the
built-in Kalman filter** parameter.

`ref`

— Model output reference values

row vector | matrix

Plant 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*is the number of output variables. Each element specifies the reference for an output variable.

_{y}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.

**Additional Inputs**

`md`

— input

row vector | matrix

If 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*is the number of manipulated variables. Each element specifies the value for a measured disturbance.

_{md}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.

#### Dependencies

To enable this port, select the **Measured disturbances**
parameter.

`ext.mv`

— Control signals used in plant at previous control interval

vector

Control signals used in the plant at the previous control interval, specified as a
vector signal of length *N _{mv}*, where

*N*is the number of manipulated variables. Use this input port to improve state estimation accuracy when:

_{mv}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*and

_{k–1}*t*. For example, if the MVs are actually varying over this interval, you might supply the time-averaged value evaluated at time

_{k}*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.

#### Dependencies

To enable this port, select the **External manipulated variable**
parameter.

`switch`

— Enable or disable optimization

scalar

To 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.

#### Dependencies

To enable this port, select the **Use external signal to enable or disable optimization** parameter.

`mv.target`

— Manipulated variable targets

vector

To specify manipulated variable targets, enable this input port, and connect a vector signal. To make a given manipulated variable track its specified target value, you must also specify a nonzero tuning weight for that manipulated variable.

The supplied **mv.target** values at run-time apply across the prediction
horizon.

#### Dependencies

To enable this port, select the **Targets for manipulated variables** parameter.

**Online Constraints**

`ymin`

— Minimum output variable constraints

vector | matrix

To specify run-time 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*is the number of plant outputs,

_{y}*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 ith 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, time-varying
bound) | ymin replaces the constant bound defined in
`OutputVariables(i).Min` with a time-varying
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, time-varying
bounds) | The `i` th column of ymin
replaces the constant bound defined in
`OutputVariables(i).Min` with a time-varying
bound. |

**Vector OutputVariables(i).Min in the mpc
object (a time-varying bound for the ith 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, time-varying
bound) | ymin replaces the time-varying 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, time-varying
bounds). | The `i` th column of ymin
replaces the time-varying bound defined in
`OutputVariables(i).Min` , and the original bound
profile is discarded. |

#### Dependencies

To enable this port, select the **Lower OV limits**
parameter.

`ymax`

— Maximum output variable constraints

vector | matrix

To specify run-time 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*is the number of plant outputs,

_{y}*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 ith 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, time-varying
bound) | ymax replaces the constant bound defined in
`OutputVariables(i).Max` with a time-varying
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, time-varying
bounds) | The `i` th column of ymax
replaces the constant bound defined in
`OutputVariables(i).Max` with a time-varying
bound. |

**Vector OutputVariables(i).Max in the mpc
object (a time-varying bound for the ith 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, time-varying
bound) | ymax replaces the time-varying 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, time-varying
bounds). | The `i` th column of ymax
replaces the time-varying bound defined in
`OutputVariables(i).Max` , and the original bound
profile is discarded. |

#### Dependencies

To enable this port, select the **Upper OV limits**
parameter.

`umin`

— Minimum manipulated variable constraints

vector | matrix

To specify run-time 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*+*p*-1, connect **umin** to a
matrix signal with *N _{mv}* columns and up to

*p*rows. Here,

*N*is the number of manipulated variables,

_{mv}*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 ith 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, time-varying
bound) | umin replaces the constant bound defined in
`ManipulatedVariables(i).Min` with a time-varying
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, time-varying
bounds) | The `i` th column of umin
replaces the constant bound defined in
`ManipulatedVariables(i).Min` with a time-varying
bound. |

**Vector ManipulatedVariables(i).Min in the mpc
object (a time-varying bound for the ith 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, time-varying
bound) | umin replaces the time-varying 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, time-varying
bounds). | The `i` th column of umin
replaces the time-varying bound defined in
`ManipulatedVariables(i).Min` , and the original
bound profile is discarded. |

#### Dependencies

To enable this port, select the **Lower MV limits**
parameter.

`umax`

— Maximum manipulated variable constraints

vector | matrix

To specify run-time 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*+*p*-1, connect **umax** to a
matrix signal with *N _{mv}* columns and up to

*p*rows. Here,

*N*is the number of manipulated variables,

_{mv}*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 ith 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, time-varying
bound) | umax replaces the constant bound defined in
`ManipulatedVariables(i).Max` with a time-varying
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, time-varying
bounds) | The `i` th column of umax
replaces the constant bound defined in
`ManipulatedVariables(i).Max` with a time-varying
bound. |

**Vector ManipulatedVariables(i).Max in the mpc
object (a time-varying bound for the ith 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, time-varying
bound) | umax replaces the time-varying 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, time-varying
bounds). | The `i` th column of umax
replaces the time-varying bound defined in
`ManipulatedVariables(i).Max` , and the original
bound profile is discarded. |

#### Dependencies

To enable this port, select the **Upper MV limits**
parameter.

`E`

— Manipulated variable constraint matrix

matrix

Manipulated variable constraint matrix, specified as an
*N _{c}*-by-

*N*matrix signal, where

_{mv}*N*is the number of mixed input/output constraints and

_{c}*N*is the number of manipulated variables.

_{mv}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 run-time 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`

.#### Dependencies

To enable this port, select the **Custom constraints** parameter.

`F`

— Controlled output constraint matrix

matrix

Controlled output constraint matrix, specified as an
*N _{c}*-by-

*N*matrix signal, where

_{y}*N*is the number of mixed input/output constraints and

_{c}*N*is the number of plant outputs. If you define

_{y}`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 run-time 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`

.#### Dependencies

To enable this port, select the **Custom constraints** parameter.

`G`

— Custom constraint vector

row vector

Custom constraint vector, specified as a row vector signal of length
*N _{c}*, where

*N*is the number of mixed input/output constraints. If you define

_{c}`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 run-time 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`

.#### Dependencies

To enable this port, select the **Custom constraints** parameter.

`S`

— Measured disturbance constraint matrix

matrix

Measured disturbance constraint matrix, specified as an
*N _{c}*-by-

*n*matrix signal, where

_{N}*N*is the number of mixed input/output constraints, and

_{c}*N*is the number of measured disturbances. If you define

_{v}`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 run-time 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`

.#### Dependencies

To enable this port, select the **Custom constraints** parameter. This port is added only if the `mpc`

object has measured disturbances.

**Online Tuning Weights**

`y.wt`

— Output variable tuning weights

row vector | matrix

To specify run-time 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 time-varying 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*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.

_{y}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 Setting Time-Varying Weights and Constraints with MPC Designer.

#### Dependencies

To enable this port, select the **OV weights** parameter.

`u.wt`

— Manipulated variable tuning weights

row vector | matrix

To specify run-time 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 time-varying 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*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.

_{mv}To vary the tuning weights over the prediction horizon from time *k*
to time *k*+*p*-1, 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 Setting Time-Varying Weights and Constraints with MPC Designer.

#### Dependencies

To enable this port, select the **MV weights** parameter.

`du.wt`

— Manipulated variable rate tuning weights

row vector | matrix

To specify run-time 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 time-varying 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*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.

_{mv}To vary the tuning weights over the prediction horizon from time *k* to time *k*+*p*-1, 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 Setting Time-Varying Weights and Constraints with MPC Designer.

#### Dependencies

To enable this port, select the **MVRate weights** parameter.

`ecr.wt`

— Slack variable tuning weight

scalar

To specify a run-time 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 worst-case constraint violation.

#### Dependencies

To enable this port, select the **ECR weight** parameter.

**Online Horizons**

`p`

— Prediction horizon

positive integer

Prediction 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.

#### Dependencies

To enable this port, select the **Adjust prediction horizon and control horizon at run time** parameter.

`m`

— Control horizon

positive integer | vector

Control 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.

#### Dependencies

To enable this port, select the **Adjust prediction horizon and control horizon at run time** parameter.

### Output

**Required Output**

`mv`

— Optimal manipulated variable control action

column vector

Optimal manipulated variable control action, output as a column vector signal of length *N _{mv}*, where

*N*is the number of manipulated variables.

_{mv}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

**Additional Outputs**

`cost`

— Objective function cost

nonnegative scalar

Objective 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 offset-free and dimensionless.

The cost value is only meaningful when the **qp.status** output is nonnegative.

#### Dependencies

To enable this port, select the **Optimal cost** parameter.

`qp.status`

— Optimization status

integer

Optimization 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 ill-conditioned QP problem. In this case, the block holds its**mv**output at the most recent successful solution.

In a real-time application, you can use **qp.status** to set an alarm or take other special action.

#### Dependencies

To enable this port, select the **Optimization status** parameter.

`est.state`

— Estimated controller states

vector

Estimated 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[k|k]** input signal.

#### Dependencies

To enable this port, select the **Estimated controller states**
parameter.

**Optimal Sequences**

`mv.seq`

— Optimal manipulated variable sequence

matrix

Optimal manipulated variable sequence, returned as a matrix signal with *p*+1 rows and *N _{mv}* columns, where

*p*is the prediction horizon and

*N*is the number of manipulated variables.

_{mv}The first *p* rows of **mv.seq** contain the
calculated optimal manipulated variable values from current time *k* to
time *k*+*p*-1. 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.

#### Dependencies

To enable this port, select the **Optimal control sequence** parameter.

`x.seq`

— Optimal prediction model state sequence

matrix

Optimal 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*is the number of states.

_{x}The first row of **x.seq** contains the current estimated state
values, either from the built-in state estimator or from the custom state estimation
block input **x[k|k]**. The next *p* rows of
**x.seq** contain the calculated optimal state values from time
*k*+1 to time *k*+*p*.

#### Dependencies

To enable this port, select the **Optimal state sequence** parameter.

`y.seq`

— Optimal output variable sequence

matrix

Optimal output variable sequence, returned as a matrix signal with *p*+1 rows and *N _{y}* columns, where

*p*is the prediction horizon and

*N*is the number of output variables.

_{y}The first *p* rows of **y.seq** contain the
calculated optimal output values from current time *k* to time
*k*+*p*-1. 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.

#### Dependencies

To enable this port, select the **Optimal output sequence** parameter.

## Parameters

`MPC Controller`

— Controller object

`mpc`

object name

Specify an `mpc`

object that defines an implicit MPC
controller by entering the name of an `mpc`

object from the
MATLAB workspace.

#### Programmatic Use

Block Parameter:
`mpcobj` |

Type: string, character vector |

Default:
`""` |

`Initial Controller State`

— Initial state

`mpcstate`

object name

Specify 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 to make sure that 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 the **Initial
Controller State** parameter.

#### Programmatic Use

Block Parameter: `x0` |

Type: string, character vector |

Default: `""` |

`Design`

— Interactively design controller

button

To interactively modify the controller specified using the **MPC
Controller** parameter, open the **MPC
Designer** app by clicking **Design**. For example, you
can:

Import a new prediction model.

Change horizons, constraints, and weights.

Evaluate MPC performance with a linear plant.

Export the updated controller to the MATLAB workspace.

If you have an existing `mpc`

object in the MATLAB workspace, specify the name of that object using the **MPC
Controller** parameter.

If you do not have an existing `mpc`

object in the MATLAB workspace, leave the **MPC Controller** parameter empty.
With the MPC Controller block connected to the plant, open **MPC
Designer** by clicking **Design**. Using the app,
linearize the Simulink model at a specified operating point, and design your controller. To use
this design approach, you must have Simulink
Control Design™ software. For more information, see Design MPC Controller in Simulink and Linearize Simulink Models Using MPC Designer.

`Review`

— Review controller for stability and robustness issues

button

Once you specify a controller using the **MPC Controller**
parameter, you can review your design for run-time stability and robustness issues by
clicking **Review**. For more information, see Review Model Predictive Controller for Stability and Robustness Issues.

**General Tab**

`Measured disturbance`

— Add measured disturbance input port

`on`

(default) | `off`

If your controller has measured disturbances, you must select this parameter to add
the **md** output port to the block.

#### Programmatic Use

Block Parameter:
`md_inport` |

Type: string, character vector |

Values:
`"off"` , `"on"` |

Default:
`"on"` |

`External manipulated variable`

— Add external manipulated variable input port

`off`

(default) | `on`

Select this parameter to add the **ext.mv** input port to the block.

#### Programmatic Use

Block Parameter: `mv_inport` |

Type: string, character vector |

Values: `"off"` , `"on"` |

Default: `"off"` |

`Targets for manipulated variables`

— Add manipulated variable target input port

`off`

(default) | `on`

Select this parameter to add the **mv.target** input port to the block.

#### Programmatic Use

Block Parameter: `uref_inport` |

Type: string, character vector |

Values: `"off"` , `"on"` |

Default: `"off"` |

`Optimal cost`

— Add optimal cost output port

`off`

(default) | `on`

Select this parameter to add the **cost** output port to the
block.

#### Programmatic Use

Block Parameter:
`return_cost` |

Type: string, character vector |

Values:
`"off"` , `"on"` |

Default:
`"off"` |

`Optimization status`

— Add optimization status output port

`off`

(default) | `on`

Select this parameter to add the **qp.status** output port to the block.

#### Programmatic Use

Block Parameter: `return_qpstatus` |

Type: string, character vector |

Values: `"off"` , `"on"` |

Default: `"off"` |

`Estimated controller states`

— Add estimated states output port

`off`

(default) | `on`

Select this parameter to add the **est.state** output port to the block.

#### Programmatic Use

Block Parameter: `return_state` |

Type: string, character vector |

Values: `"off"` , `"on"` |

Default: `"off"` |

`Optimal control sequence`

— Add optimal control sequence output port

`off`

(default) | `on`

Select this parameter to add the **mv.seq** output port to the block.

#### Programmatic Use

Block Parameter: `return_mvseq` |

Type: string, character vector |

Values: `"off"` , `"on"` |

Default: `"off"` |

`Optimal state sequence`

— Add optimal state sequence output port

`off`

(default) | `on`

Select this parameter to add the **x.seq** output port to the block.

#### Programmatic Use

Block Parameter: `return_xseq` |

Type: string, character vector |

Values: `"off"` , `"on"` |

Default: `"off"` |

`Optimal output sequence`

— Add optimal output sequence output port

`off`

(default) | `on`

Select this parameter to add the **y.seq** output port to the block.

#### Programmatic Use

Block Parameter:
`return_ovseq` |

Type: string, character vector |

Values: `"off"` , `"on"` |

Default: `"off"` |

`Use custom state estimation instead of using the built-in Kalman filter`

— Use custom state estimate input port

`off`

(default) | `on`

Select this parameter to remove the **mo** input port and add the **x[k|k]** input port.

#### Programmatic Use

Block Parameter: `state_inport` |

Type: string, character vector |

Values: `"off"` , `"on"` |

Default: `"off"` |

**Online Features Tab**

`Lower OV limits`

— Add minimum OV constraint input port

`off`

(default) | `on`

Select this parameter to add the **ymin** input port to the block.

#### Programmatic Use

Block Parameter: `ymin_inport` |

Type: string, character vector |

Values: `"off"` , `"on"` |

Default: `"off"` |

`Upper OV limits`

— Add maximum OV constraint input port

`off`

(default) | `on`

Select this parameter to add the **ymax** input port to the block.

#### Programmatic Use

Block Parameter: `ymax_inport` |

Type: string, character vector |

Values: `"off"` , `"on"` |

Default: `"off"` |

`Lower MV limits`

— Add minimum MV constraint input port

`off`

(default) | `on`

Select this parameter to add the **umin** input port to the block.

#### Programmatic Use

Block Parameter: `umin_inport` |

Type: string, character vector |

Values: `"off"` , `"on"` |

Default: `"off"` |

`Upper MV limits`

— Add maximum MV constraint input port

`off`

(default) | `on`

Select this parameter to add the **umax** input port to the block.

#### Programmatic Use

Block Parameter: `umax_inport` |

Type: string, character vector |

Values: `"off"` , `"on"` |

Default: `"off"` |

`Custom constraints`

— Add custom constraints input ports

`off`

(default) | `on`

Select this parameter to add the **E**, **F**, **G**, and **S** input ports to the block.

#### Programmatic Use

Block Parameter: `cc_inport` |

Type: string, character vector |

Values: `"off"` , `"on"` |

Default: `"off"` |

`OV weights`

— Add OV tuning weights input port

`off`

(default) | `on`

Select this parameter to add the **y.wt** input port to the block.

#### Programmatic Use

Block Parameter: `ywt_inport` |

Type: string, character vector |

Values: `"off"` , `"on"` |

Default: `"off"` |

`MV weights`

— Add MV tuning weights input port

`off`

(default) | `on`

Select this parameter to add the **u.wt** input port to the block.

#### Programmatic Use

Block Parameter: `uwt_inport` |

Type: string, character vector |

Values: `"off"` , `"on"` |

Default: `"off"` |

`MVRate weights`

— Add MV rate tuning weights input port

`off`

(default) | `on`

Select this parameter to add the **du.wt** input port to the block.

#### Programmatic Use

Block Parameter: `duwt_inport` |

Type: string, character vector |

Values: `"off"` , `"on"` |

Default: `"off"` |

`Slack variable weight`

— Add ECR tuning weight input port

`off`

(default) | `on`

Select this parameter to add the **ecr.wt** input port to the block.

#### Programmatic Use

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 ports

off (default) | on

Select this parameter to add the **p** and **m** input port to the block.

#### Programmatic Use

Block Parameter: `pm_inport` |

Type: string, character vector |

Values: `"off"` , `"on"` |

Default: `"off"` |

`Maximum prediction horizon`

— Add horizon input ports

`10`

(default) | positive integer

Select this parameter to add the **p** and **m** input port to the block.

#### Dependencies

To enable this parameter, select the **Adjust prediction horizon and control horizon at run time** parameter.

#### Programmatic Use

Block Parameter: `MaximumP` |

Type: string, character vector |

Default: `"10"` |

**Default Conditions Tab**

`Sample time`

— Default block sample time

`1`

(default) | positive scalar

Default block sample time for performing simulation, trimming, or linearization
using the **MPC Designer** app. You must specify a sample time that is compatible
with your Simulink model design.

#### Dependencies

This parameter applies only when the **MPC Controller** parameter
is empty and you open **MPC Designer** using the **Design**
button.

#### Programmatic Use

Block Parameter:
`n_ts` |

Type: string, character vector |

Default:
`"1"` |

`Prediction horizon`

— Default prediction horizon

`10`

(default) | positive integer

Default prediction horizon for performing simulation, trimming, or linearization
using the **MPC Designer** app. You must specify a prediction horizon that is
compatible with your Simulink model design.

#### Dependencies

This parameter applies only when the **MPC Controller** parameter
is empty and you open **MPC Designer** using the **Design**
button.

#### Programmatic Use

Block Parameter:
`n_p` |

Type: string, character vector |

Default:
`"10"` |

`Number of manipulated variables`

— Default number of manipulated variables

`1`

(default) | positive integer

Default number of manipulated variables for performing simulation, trimming, or
linearization using the **MPC Designer** app. You must specify a value that is
compatible with your Simulink model design.

#### Dependencies

This parameter applies only when the **MPC Controller** parameter
is empty and you open **MPC Designer** using the **Design**
button.

#### Programmatic Use

Block Parameter:
`n_mv` |

Type: string, character vector |

Default:
`"1"` |

`Number of measured disturbances`

— Default number of measured disturbances

`1`

(default) | nonnegative integer

Default number of measured disturbances for performing simulation, trimming, or
linearization using the **MPC Designer** app. You must specify a value that is
compatible with your Simulink model design.

#### Dependencies

**MPC Controller**parameter is empty and you open**MPC Designer**using the**Design**button.To use this parameter, you must select the

**Measured disturbance**parameter.

#### Programmatic Use

Block Parameter:
`n_md` |

Type: string, character vector |

Default:
`"1"` |

`Number of unmeasured disturbances`

— Default number of unmeasured disturbances

`0`

(default) | nonnegative integer

Default number of unmeasured disturbances for performing simulation, trimming, or
linearization using the **MPC Designer** app. You must specify a value that is
compatible with your Simulink model design.

#### Dependencies

**MPC Controller** parameter
is empty and you open **MPC Designer** using the **Design**
button.

#### Programmatic Use

Block Parameter:
`n_ud` |

Type: string, character vector |

Default:
`"0"` |

`Number of measured outputs`

— Default number of measured outputs

`1`

(default) | positive integer

Default number of measured outputs for performing simulation, trimming, or
linearization using the **MPC Designer** app. You must specify a value that is
compatible with your Simulink model design.

#### Dependencies

**MPC Controller** parameter
is empty and you open **MPC Designer** using the **Design**
button.

#### Programmatic Use

Block Parameter:
`n_mo` |

Type: string, character vector |

Default:
`"1"` |

`Number of unmeasured outputs`

— Default number of unmeasured outputs

`0`

(default) | nonnegative integer

Default number of unmeasured outputs for performing simulation, trimming, or
linearization using the **MPC Designer** app. You must specify a value that is
compatible with your Simulink model design.

#### Dependencies

**MPC Controller** parameter
is empty and you open **MPC Designer** using the **Design**
button.

#### Programmatic Use

Block Parameter:
`n_uo` |

Type: string, character vector |

Default:
`"0"` |

**Others Tab**

`Block data type`

— Specify data type of manipulated variables

`double`

(default) | `single`

| `data type expression`

Specify the block data type of the manipulated variables as one of the following:

`double`

— Double-precision floating point`single`

— Single-precision floating pointIf you are implementing the block on a single-precision target, specify the output data type as

`single`

.`data type expression`

— An expression that evaluates to either`double`

or`single`

. For more information, see Control Data Types of Signals (Simulink).

#### Programmatic Use

Block Parameter: `BlockDataType` |

Type: string, character vector |

Values:
`"double"` , `"single"` , ```
data type
expression
``` |

Default: `"double"` |

`Inherit sample time`

— Inherit block sample time from parent subsystem

`off`

(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 Function-Call Subsystem (Simulink) or Triggered Subsystem (Simulink) blocks. For an example, see Using MPC Controller Block Inside Function-Call and Triggered Subsystems.

**Note**

You must execute Function-Call Subsystem or Triggered Subsystem blocks at the sample rate of the controller. Otherwise, you can see unexpected results for two reasons.

The first element of the MV rate vector (which is the difference between the current and the last value of the manipulated variable) is normally weighted and constrained assuming that the last MV value occurred in the past at the sample time specified in the MPC object, and when the block is executed with a different sample rate, this assumption no longer holds.

The built-in Kalman estimator uses the sample time specified in the MPC object to provide an estimation of the current state to the MPC optimization problem, so when the block is executed with a different sample time, the estimated state is no longer correct.

If you clear this parameter (default), 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).

#### Programmatic Use

Block Parameter:
`SampleTimeInherited` |

Type: string, character vector |

Values:
`"off"` , `"on"` |

Default:
`"off"` |

`Use external signal to enable or disable optimization`

— Add switch input port

`off`

(default) | `on`

Select this parameter to add the **switch** input port to the block.

#### Programmatic Use

Block Parameter: `switch_inport` |

Type: string, character vector |

Values: `"off"` , `"on"` |

Default: `"off"` |

## Model Examples

## Extended Capabilities

### C/C++ Code Generation

Generate C and C++ code using Simulink® Coder™.

### GPU Code Generation

Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

### PLC Code Generation

Generate Structured Text code using Simulink® PLC Coder™.

## Version History

**Introduced before R2006a**

### R2018b: MPC Simulink block `mv.seq`

output port signal dimensions have
changed

The signal dimensions of the `mv.seq`

output port of the MPC
Controller block have changed. Previously, this signal was a
*p*-by-*N _{mv}* matrix, where

*p*is the prediction horizon and

*N*is the number of manipulated variables. Now,

_{mv}`mv.seq`

is a
(*p*+1)-by-

*N*matrix, where row

_{mv}*p*+1 duplicates row

*p*.

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