Simulate adaptive and time-varying model predictive controllers

• Library:
• Model Predictive Control Toolbox

## Description

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 (time-varying 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 linear-time-varying (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 linear-time-varying 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.

Adaptation approachUpdate prediction model for a single controller as operating conditions changeSwitch between multiple controllers designed for different operating regions
• Only need to design a single controller offline

• Less run-time computational effort and smaller memory footprint

• More robust to real-life changes in plant conditions

• No need for online estimation of plant model

• Controllers can have different sample time, horizons, and weights

• Prediction models can have different orders or time domains

• Finite set of candidate controllers can be tested thoroughly

## Ports

### Input

expand all

Required Inputs

Updated 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 discrete-time state-space object with no delays. The following command extracts the state-space 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:

• Anx-by-nx matrix signal, where nx is the number of plant model states.

• Bnx-by-nu matrix signal, where nu is the total number of plant model inputs (i.e., manipulated variables, measured disturbances, and unmeasured disturbances).

• Cny-by-nx matrix signal, where ny is the number of plant model outputs.

• Dny-by-nu matrix signal.

• X — Vector signal of length nx, replacing the controller Model.Nominal.X property.

• Y — Vector signal of length ny, replacing the controller Model.Nominal.Y property.

• U — Vector signal of length nu, replacing the controller Model.Nominal.U property.

• DX — Vector signal of length nx, replacing the controller Model.Nominal.DX property. It must be appropriate for use with a discrete-time model of the assumed control interval. For more information, see Adaptive MPC.

To compute DX values, use the discrete-time state update function (f) for your model. Here, uk and xk are the respective input and state values for the current time step.

$DX=f\left({u}_{k},{x}_{k}\right)-{x}_{k}$

• Time-varying MPC mode, the bus you connect to the model inport must contain the following 3–dimensional bus signals:

• Anx-by-nx-by-(p+1) matrix signal

• Bnx-by-nu-by-(p+1) matrix signal

• Cny-by-nx-by-(p+1)

• Dny-by-nu-by-(p+1) matrix signal

• Xnx-by-(p+1) matrix signal

• Yny-by-(p+1) matrix signal

• Unu-by-(p+1) matrix signal

• DXnx-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 Time-Varying MPC.

One way to form the bus is to use a Bus Creator (Simulink) block.

#### Dependencies

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 Time-Varying (LTV) plants parameter

• Time-varying MPC mode, select the Linear Time-Varying (LTV) plants parameter

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 NY elements, where Ny 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 Ny 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.

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 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.

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.

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 Nmd elements, where Nmd 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 Nmd 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.

Control signals used in the plant at the previous control interval, specified as a vector signal of length Nmv, where Nmv 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 tk, the ext.mv value must contain the effective MVs between times tk–1 and tk. For example, if the MVs are actually varying over this interval, you might supply the time-averaged value evaluated at time tk.

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.

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.

To 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 Nmv elements, where Nmv 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+p-1, connect mv.target to a matrix signal with Nmv 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.

#### Dependencies

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

Online Constraints

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 Ny columns and up to p rows. Here, Ny 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 ith column of the ymin signal corresponds to the ith 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 DimensionReplacement 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 ith element of ymin replaces the constant bound defined in OutputVariables(i).Min
Matrix ymin (multiple outputs, time-varying bounds)The ith 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 DimensionReplacement 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 ith 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 ith 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.

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 Ny columns and up to p rows. Here, Ny 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 ith column of the ymax signal corresponds to the ith 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 DimensionReplacement 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 ith element of ymax replaces the constant bound defined in OutputVariables(i).Max
Matrix ymax (multiple outputs, time-varying bounds)The ith 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 DimensionReplacement 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 ith 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 ith 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.

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 Nmv columns and up to p rows. Here, Nmv 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 ith column of the umin signal corresponds to the ith 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 DimensionReplacement 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 ith element of umin replaces the constant bound defined in ManipulatedVariables(i).Min
Matrix umin (multiple outputs, time-varying bounds)The ith 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 DimensionReplacement 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 ith 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 ith 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.

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 Nmv columns and up to p rows. Here, Nmv 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 ith column of the umax signal corresponds to the ith 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 DimensionReplacement 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 ith element of umax replaces the constant bound defined in ManipulatedVariables(i).Max
Matrix umax (multiple outputs, time-varying bounds)The ith 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 DimensionReplacement 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 ith 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 ith 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.

Manipulated variable constraint matrix, specified as an Nc-by-Nmv matrix signal, where Nc is the number of mixed input/output constraints and Nmv 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 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, Nc must match the number of rows in the E matrix you specified using setconstraint.

#### Dependencies

To enable this port, select the Custom constraints parameter.

Controlled output constraint matrix, specified as an Nc-by-Ny matrix signal, where Nc is the number of mixed input/output constraints and Ny 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 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, Nc must match the number of rows in the F matrix you specified using setconstraint.

#### Dependencies

To enable this port, select the Custom constraints parameter.

Custom constraint vector, specified as a row vector signal of length Nc, where Nc 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 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, Nc must match the number of rows in the G matrix you specified using setconstraint.

#### Dependencies

To enable this port, select the Custom constraints parameter.

Measured disturbance constraint matrix, specified as an Nc-by-nN matrix signal, where Nc is the number of mixed input/output constraints, and Nv 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 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, Nc 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

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 Ny elements, where Ny 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 Ny 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.

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 Nmv elements, where Nmv 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+p-1, connect u.wt to a matrix signal with Nmv 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.

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 Nmv elements, where Nmv 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+p-1, connect du.wt to a matrix signal with Nmv 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.

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

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.

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

expand all

Required Output

Optimal manipulated variable control action, output as a column vector signal of length Nmv, where Nmv 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

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.

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.

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

Optimal manipulated variable sequence, returned as a matrix signal with p+1 rows and Nmv columns, where p is the prediction horizon and Nmv 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+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.

Optimal prediction model state sequence, returned as a matrix signal with p+1 rows and Nx columns, where p is the prediction horizon and Nx is the number of states.

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.

Optimal output variable sequence, returned as a matrix signal with p+1 rows and Ny columns, where p is the prediction horizon and Ny 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+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

expand all

Specify 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 discrete-time, state-space 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.

#### Programmatic Use

 Block Parameter: mpcobj Type: string, character vector Default: ""

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 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.

#### Programmatic Use

 Block Parameter: x0 Type: string, character vector Default: ""
General Tab

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"

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"

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"

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"

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"

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"

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"

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"

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"

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

To operate your controller in time-varying 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 Time-Varying MPC Control of a Time-Varying Plant.

#### Programmatic Use

 Block Parameter: isltv_plant Type: string, character vector Values: "off", "on" Default: "off"

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"

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"

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"

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"

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"

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"

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"

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"

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"

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"

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"
Others Tab

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.

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).

#### Programmatic Use

 Block Parameter: SampleTimeInherited Type: string, character vector Values: "off", "on" Default: "off"

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"

## Compatibility Considerations

expand all

Behavior changed in R2018b

## Extended Capabilities

### Functions

Introduced in R2014b