Compute MPC control law
MPC Simulink Library
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 variables (mv
)
by solving a quadratic program (QP).
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 will control.
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.
The MPC Controller block has the following parameter groupings:
You must provide a traditional (implicit) mpc
object
that defines your controller using one of the following methods:
Enter the name of an mpc
object
in the MPC Controller edit box. This
object must be present in the MATLAB workspace.
If you want to modify the controller settings in a graphical environment, click Design to open the MPC Designer app. 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.
To see how well the controller works for the nonlinear plant, run a closed-loop Simulink simulation.
If you do not have an existing mpc
object
in the MATLAB workspace, leave the MPC
controller field empty. With the MPC Controller block
connected to the plant, click Design to
open the MPC Designer app. Using the app, linearize the Simulink model at a specified operating
point, and design your controller. For more information, see Design MPC Controller in Simulink and Linearize Simulink Models
Using MPC Designer.
To use this design approach, you must have Simulink Control Design™ software.
If you specified a controller in the MPC Controller field, click Review to review you design for run-time stability and robustness issues. For more information, see Review Model Predictive Controller for Stability and Robustness Issues.
Specifies the initial controller state. If this parameter is
left blank, the block uses the nominal values that are 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.
If your controller uses default state estimation, this inport
is labeled mo
. Connect this inport to the measured
signals from the plant.
If your controller uses custom state estimation, check Use
custom estimated states instead of measured outputs in
the General tab. Checking that option changes
the label on this inport to x[k|k]
. Connect a signal
providing the controller state estimates. (The controller state includes
the plant, disturbance, and noise model states.) The estimates supplied
at time t_{k} must be based
on the measurements and other data available at time t_{k}.
The ref
dimension must not change
from one control instant to the next. Each element must be a
real number.
When ref
is a 1-by-n_{y} signal,
where n_{y} is the number of
outputs, there is no reference signal previewing. All the current
values are applied across the prediction horizon.
To use signal previewing, specify ref
as
an N-by-n_{y} signal,
where N is the number of time steps for
which you are specifying reference values. Here, $$1<N\le p$$,
and p is the prediction horizon. Previewing
usually improves performance since the controller can anticipate future
reference signal changes. The first row of ref
specifies
the n_{y} references
for the first step in the prediction horizon (at the next control
interval k = 1),
and so on for N steps. If N < p,
the last row designates constant reference values for the remaining p - N steps.
For example, suppose n_{y} =
2 and p =
6. At a given control instant, the signal connected
to the ref
inport is:
[2 5 ← k=1 2 6 ← k=2 2 7 ← k=3 2 8] ← k=4
The signal informs the controller that:
Reference values for the first prediction horizon
step k = 1 are 2
and 5
.
The first reference value remains at 2
,
but the second increases gradually.
The second reference value becomes 8
at
the beginning of the fourth step k =
4 in the prediction horizon.
Both values remain constant at 2
and 8
respectively
for steps 5–6 of the prediction horizon.
mpcpreview
shows how to use reference previewing
in a specific case. For calculation details on the use of the reference
signal, see Optimization Problem.
The mv
outport provides a signal defining
the $${n}_{u}\ge 1$$ manipulated variables, which
are to be implemented in the plant. The controller updates its mv
outport
by solving a quadratic program at each control instant.
Add an inport (md
) to which you can connect
a measured disturbance signal.
The md
dimension must not change
from one control instant to the next. Each element must be a
real number.
When md
is a 1-by-n_{md} signal,
where $${n}_{md}\ge 1$$ is the number of measured disturbances
defined for your controller, there is no measured disturbance previewing.
All the current values are applied across the prediction horizon.
To use disturbance previewing, specify ref
as
an N-by-n_{md} signal,
where N is the number of time steps for
which the MD is known. Here, $$1<N\le p+1$$,
and p is the prediction horizon. Previewing
usually improves performance since the controller can anticipate future
disturbances. The first row of md
specifies the n_{md} current
disturbance values (k=1),
with other rows specifying disturbances for subsequent control intervals.
If N < p +
1, the last row designates constant reference
values for the remaining p - N +
1 steps.
For example, suppose n_{md} =
2 and p =
6. At a given control instant, the signal connected
to the md
inport is:
[2 5 ← k=0 2 6 ← k=1 2 7 ← k=2 2 8] ← k=3
This signal informs the controller that:
The current MD
values are 2
and 5
at k =
0.
The first MD
remains at 2
,
but the second increases gradually.
The second MD
becomes 8
at
the beginning of the third stepk =
3 in the prediction horizon.
Both values remain constant at 2
and 8
respectively
for steps 4–6 of the prediction horizon.
mpcpreview
shows how to use MD
previewing
in a specific case.
For calculation details, see MPC Modeling and QP Matrices.
Add an inport (ext.mv
), which you can connect
to the actual manipulated variables (MV) used in the plant. The block
uses these to update its internal state estimates.
Controller state estimation assumes that the MV is piecewise
constant. At time t_{k}, the ext.mv
value
must be the effective MV between times t_{k–1} and t_{k}.
For example, if the MV is actually varying over this interval, you
might supply the time-averaged value evaluated at time t_{k}.
The following example, from the model mpc_bumpless
,
includes a switch that can override the controller's output
with a signal supplied by the operator. Also, the controller output
may saturate. Feeding back the actual MV used in the plant (labeled u(t)
in
the example) improves the accuracy of controller state estimates.
If the external MV option is inactive or the ext.mv
inport
in unconnected, the controller assumes that its MV output is used
in the plant without modification.
Note
There is direct feed through from the |
Add an outport (cost
) that provides the optimal
quadratic programming objective function value at the current time
(a nonnegative scalar). If the optimization problem is infeasible,
however, the value is meaningless. (See qp.status
.)
Add an outport (mv.seq
) that provides the
computed optimal MV
sequence for the entire prediction
horizon from k=0
to k = p-1
.
If n_{u} is the number of MVs
and p is the length of the prediction horizon,
this signal is a p by n_{u} matrix.
The first row represents k=0
and duplicates the
block's MV outport.
The following block diagram (from Analysis of Control Sequences
Optimized by MPC on a Double Integrator System) illustrates
how to use this option. The diagram shows how to collect diagnostic
data and send it to the To Workspace2 block, which
creates the variable, useq
, in the workspace. Run
the example to see how the optimal sequence evolves with time.
Add an outport (qp.status
) that allows you
to monitor the status of the QP solver.
If a QP problem is solved successfully at 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. Thus,
a large value means a relatively slow block execution at this time
interval.
The QP solver may 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.
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 OV outside its specified
bounds.
qp.status = -2
— The QP
solver has encountered numerical difficulties in solving a severely
ill-conditioned QP problem.
For all the previous three failure modes, the MPC
Controller block holds its mv
output at
the most recent successful solution. In a real-time application, you
can use status indicator to set an alarm or take other special action.
The next diagram shows how to use the status indicator to monitor the MPC Controller block in real time. See Monitoring Optimization Status to Detect Controller Failures for more details.
Add an outport (est.state
) to receive the
controller state estimates, x[k|k]
, at each control
instant. These include the plant, disturbance and noise model states.
Replace mo
with the x[k|k]
inport
for custom state estimation as described in Required Inports.
Add inports (umin
, umax
, ymin
, ymax
)
that you can connect to run-time constraint signals.
umin
andumax
are vectors
with n_{u} elements. ymin
andymax
are
vectors with n_{y} elements.
If any of these inports are unconnected, they are treated as
unbounded signals. The corresponding variable in the mpc
object
must also be unbounded.
For connected inports, the following rules apply:
All connected signals must be finite. Simulink does not support infinite signals.
If a variable is unconstrained in the controller object, the connected value is ignored.
If this check box is not selected, the block uses the constant
constraint values stored within its mpc
object.
Note: You cannot specify time-varying constraints at run time using a matrix signal. |
A controller intended for real-time applications should have "knobs" you can use to tune its performance when it operates with the real plant. This group of optional inports serves that purpose.
The diagram shown below shows three of the MPC Controller tuning
inports. In this simulation context, the inports are tuned using pre-stored
signals (the ywt
, duwt
, and ECRwt
variables
in the From Workspace blocks). In practice, you would
connect a knob or similar manual adjustment.
Note: You cannot specify time-varying weights at run time using a matrix signal. |
Add an inport (y.wt
) for a vector signal
with n_{y} elements. Each element
specifies a nonnegative tuning weight for each controlled output variable
(OV). This signal overrides the MPCobj.Weights.OV
property
of the mpc
object, which establishes the relative
importance of OV reference tracking.
For example, if the preceding controller defined three OVs,
the signal connected to the y.wt
inport should
be a vector with three elements. If the second element is relatively
large, the controller would place a relatively high priority on making
OV(2) track the r(2)
reference signal. Setting
a y.wt
signal to zero turns off reference tracking
for that OV.
If you do not connect a signal to the y.wt
inport,
the block uses the OV weights specified in your MPC object, and these
values remain constant.
Add an inport (u.wt
), whose input is a vector
signal defining n_{u} nonnegative
weights, where n_{u} is the
number of manipulated variables (MVs). The input overrides the MPCobj.Weights.MV
property
of the mpc
object, which establishes the relative
importance of MV target tracking.
For example, if your controller defines four MVs and the second u.wt
element
is relatively large, the controller would try to keep MV(2) close
to its specified target (relative to other control objectives).
If you do not connect a signal to the u.wt
inport,
the block uses the Weights.MV
weights property
specified in your mpc
object, and these values
remain constant.
Add an inport (du.wt
), for a vector signal
defining n_{u} nonnegative
weights, where n_{u} is the
number of manipulated variables (MVs). The input overrides the MPCobj.Weights.MVrate
property
of the mpc
object, which establishes the relative
importance of MV changes.
For example, if your controller defines four MVs and the second du.wt
element
is relatively large, the controller would use relatively small changes
in the second MV. Such move suppression makes
the controller less aggressive. However, too much suppression makes
it sluggish.
If you do not connect a signal to the du.wt
inport,
the block uses the Weights.MVrate
property specified
in your mpc
object, and these values remain constant.
Add an inport (ECR.wt
), for a scalar nonnegative
signal that overrides the mpc
controller's MPCobj.Weights.ECR
property.
This inport 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.
You may not be able to avoid violations of an output variable
constraint. Thus, increasing the ECR.wt
value is
often counterproductive. Such an increase causes the controller to
pay less attention to its other objectives and does not help reduce
constraint violations. You usually need to tune ECR.wt
to
achieve the proper balance in relation to the other control objectives.
If you want one or more manipulated variable (MV) to track a
target value that changes with time, use this option to add an mv.target
inport
to which you can connect the target signal (dimension n_{u},
where n_{u} is the number of
MVs).
For this to be effective, the corresponding MV(s) must have nonzero penalty weights (these weights are zero by default).
Specify the default block sample time and signal dimensions
for performing simulation, trimming, or linearization. In these
cases, the mv
output signal remains at zero. You
must specify default condition values that are compatible with your Simulink model
design.
Note: These default conditions apply only if the MPC Controller field is empty. If you specify a controller from the MATLAB workspace, the sample time and signal sizes from the specified controller are used. |
Specify the default controller sample time.
Specify the default signal dimensions for the following input signal types:
Manipulated variables
Unmeasured disturbances
Measured disturbances
Note: You can specify the measured disturbances signal dimension only if, on the General tab, in the Additional Inports section, the Measured disturbance option is selected. |
Specify the default signal dimensions for the following output signal types:
Measured outputs
Unmeasured outputs
Specify the block data type as one of the following:
double
— Double-precision
floating point (default).
single
— Single-precision
floating point.
Specify the output data type as single
if
you are implementing the MPC Controller block on a
single-precision target.
For an example of double-precision and single-precision simulation and code generation for an MPC controller, see Simulation and Code Generation Using Simulink Coder.
To view the port data types in a model, in the Simulink Editor, select Display > Signals & PortsPort Data Types.
Use the sample time inherited from the parent subsystem as the MPC Controller block's sample time.
Inheriting the sample time allows you to conditionally execute the MPC Controller block inside the Function-Call Subsystem or Triggered Subsystem blocks. For an example, see Using MPC Controller Block Inside Function-Call and Triggered Subsystems.
Note: When you place an MPC controller block inside a Function-Call Subsystem or Triggered Subsystem block, you must execute the subsystem at the controller's design sample rate. You may see unexpected results if you use an alternate sample rate. |
To view the sample time of a block, in the Simulink Editor, select Display > Sample Time. Select Colors, Annotations, or All. For more information, see View Sample Time Information.
Add an inport (switch
) whose input specifies
whether the controller performs optimization calculations. If the
input signal is zero, the controller behaves normally. If the input
signal becomes nonzero, the MPC Controller block turns
off the controller optimization calculations. This action reduces
computational effort when the controller output is not needed, such
as when the system is operating manually or another controller has
taken over. The controller, however, continues to update its internal
state estimate in the usual way. Thus, it is ready to resume optimization
calculations whenever the switch
signal returns
to zero. While the controller optimization is turned off, the MPC
Controller 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 whatever value it
had when the optimization was disabled.
mpc
| MPC Designer | mpcstate
| Multiple
MPC Controllers