MPC Controller

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.

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.

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

To vary the references over the prediction horizon (previewing) from time k+1 to time k+p, connect ref to a matrix signal with N_y columns and up to p rows. Here, k is the current time and p is the prediction horizon. Each row contains the references for one prediction horizon step. If you specify fewer than p rows, the final references are used for the remaining steps of the prediction horizon.

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

To vary the disturbances over the prediction horizon (previewing) from time k to time k+p, connect md to a matrix signal with N_md columns and up to p+1 rows. Here, k is the current time and p is the prediction horizon. Each row contains the disturbances for one prediction horizon step. If you specify fewer than p+1 rows, the final disturbances are used for the remaining steps of the prediction horizon.

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 N_mv, where N_mv is the number of manipulated variables. Use this input port to improve state estimation accuracy when:

Controller state estimation assumes that the MVs are piecewise constant. Therefore, at time t_k, the ext.mv value must contain the effective MVs between times t_k–1 and t_k. For example, if the MVs are actually varying over this interval, you might supply the time-averaged value evaluated at time t_k.

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 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.

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_y is the number of plant outputs, k is the current time, and p is the prediction horizon. Each row contains the bounds for one prediction horizon step. If you specify fewer than p rows, the bounds in the final row apply for the remainder of the prediction horizon. If there is only one output variable, and a vector signal with no more than p entries is connected, then these entries are used across the prediction horizon.

The 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.

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 N_y columns and up to p rows. Here, N_y is the number of plant outputs, k is the current time, and p is the prediction horizon. Each row contains the bounds for one prediction horizon step. If you specify fewer than p rows, the bounds in the final row apply for the remainder of the prediction horizon. If there is only one output variable, and a vector signal with no more than p entries is connected, then these entries are used across the prediction horizon.

The 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.

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 N_mv columns and up to p rows. Here, N_mv is the number of manipulated variables, k is the current time, and p is the prediction horizon. Each row contains the bounds for one prediction horizon step. If you specify fewer than p rows, the bounds in the final row apply for the remainder of the prediction horizon. If there is only one manipulated variable, and a vector signal with no more than p entries is connected, then these entries are used across the prediction horizon.

The 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.

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 N_mv columns and up to p rows. Here, N_mv is the number of manipulated variables, k is the current time, and p is the prediction horizon. Each row contains the bounds for one prediction horizon step. If you specify fewer than p rows, the bounds in the final row apply for the remainder of the prediction horizon. If there is only one manipulated variable, and a vector signal with no more than p entries is connected, then these entries are used across the prediction horizon.

The 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.

Dependencies

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

Manipulated variable constraint matrix, specified as an N_c-by-N_mv matrix signal, where N_c is the number of mixed input/output constraints and N_mv is the number of manipulated variables.

If you define E in the mpc object, you must connect a signal to the E input port. Otherwise, connect a zero matrix with the correct size.

To specify 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.

Controlled output constraint matrix, specified as an N_c-by-N_y matrix signal, where N_c is the number of mixed input/output constraints and N_y is the number of plant outputs. If you define F in the mpc object, you must connect a signal to the F input port with same number of rows. Otherwise, connect a zero matrix with the correct size.

To specify 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.

Custom constraint vector, specified as a row vector signal of length N_c, where N_c is the number of mixed input/output constraints. If you define G in the mpc object, you must connect a signal to the G input port with same number of rows. Otherwise, connect a zero matrix with the correct size.

To specify 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.

Measured disturbance constraint matrix, specified as an N_c-by-n_N matrix signal, where N_c is the number of mixed input/output constraints, and N_v is the number of measured disturbances. If you define S in the mpc object, you must connect a signal to the S input port with same number of rows. Otherwise, connect a zero matrix with the correct size.

To specify 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.

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_y is the number of outputs. Each element specifies a nonnegative tuning weight for an output variable. For more information on specifying tuning weights, see Tune Weights.

To vary the tuning weights over the prediction horizon from time k+1 to time k+p, connect y.wt to a matrix signal with N_y columns and up to p rows. Here, k is the current time and p is the prediction horizon. Each row contains the tuning weights for one prediction horizon step. If you specify fewer than p rows, the tuning weights in the final row apply for the remainder of the prediction horizon. For more information on varying weights over the prediction horizon, see 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 N_mv elements, where N_mv is the number of manipulated variables. Each element specifies a nonnegative tuning weight for a manipulated variable. For more information on specifying tuning weights, see Tune Weights.

To vary the tuning weights over the prediction horizon from time k to time k+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.

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_mv is the number of manipulated variables. Each element specifies a nonnegative tuning weight for a manipulated variable rate. For more information on specifying tuning weights, see Tune Weights.

To vary the tuning weights over the prediction horizon from time k to time k+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.

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.

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:

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.

Optimal manipulated variable control action, output as a column vector signal of length N_mv, where N_mv is the number of manipulated variables.

If the solver converges to a local optimum solution (qp.status is positive), then mv contains the optimal solution.

If the solver fails (qp.status is negative), then mv remains at its most recent successful solution; that is, the controller output freezes.

If the solver reaches the maximum number of iterations without finding an optimal solution (qp.status is zero) and the Optimization.UseSuboptimalSolution property of the controller is:

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:

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 manipulated variable sequence, returned as a matrix signal with p+1 rows and N_mv columns, where p is the prediction horizon and N_mv is the number of manipulated variables.

The first p rows of mv.seq contain the calculated optimal manipulated variable values from current time k to time k+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 N_x columns, where p is the prediction horizon and N_x 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 N_y columns, where p is the prediction horizon and N_y is the number of output variables.

The first p rows of y.seq contain the calculated optimal output values from current time k to time k+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.

Specify an mpc object that defines an implicit MPC controller by entering the name of an mpc object from the MATLAB workspace.

Programmatic Use

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 state reflects the state of the plant at the start of your simulation, to the best of your knowledge. This initial state can differ from the nominal state defined in the mpc object.

If custom state estimation is enabled, the block ignores the Initial Controller State parameter.

Programmatic Use

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

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.

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.

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

Programmatic Use

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

Programmatic Use

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

Programmatic Use

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

Programmatic Use

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

Programmatic Use

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

Programmatic Use

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

Programmatic Use

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

Programmatic Use

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

Programmatic Use

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

Programmatic Use

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

Programmatic Use

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

Programmatic Use

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

Programmatic Use

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

Programmatic Use

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

For more information, see Constraints on Linear Combinations of Inputs and Outputs and Update Mixed Input/Output Constraints at Run Time.

Programmatic Use

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

Programmatic Use

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

Programmatic Use

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

Programmatic Use

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

Programmatic Use

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

Programmatic Use

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

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

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

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

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

Programmatic Use

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

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

Programmatic Use

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

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

Programmatic Use

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

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

Programmatic Use

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

Programmatic Use

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.

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

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

Programmatic Use