Explicit MPC Controller
Design and simulate explicit model predictive controller
Library
MPC Simulink Library
Description
The Explicit MPC Controller block uses the following input signals:
Measured plant outputs (
mo)Reference or setpoint (
ref)Measured plant disturbance (
md), if any
The key difference is that the Explicit MPC Controller block uses a table-lookup control law during each control interval rather than solving a quadratic program. The reduced online computational effort is advantageous in applications requiring a short control interval. The primary trade-off is a heavier offline computational effort to determine the control law and a larger memory footprint to store it. The combinatorial character of this computation restricts its use to applications with relatively few input, output, and state variables, a short prediction horizon, and few output constraints.
The Explicit MPC Controller supports only a subset of optional MPC features, as outlined in the following table.
| Supported Features | Unsupported Features |
|---|---|
|
|
Dialog Box
The Explicit MPC Controller block has the following parameter groupings:
Parameters
Explicit MPC Controller
An explicitMPC object
containing the control law to be used. It must exist in the workspace. Use the
generateExplicitMPC command to
create this object.
Initial Controller State
An optional mpcstate object specifying the
initial controller state. By default the block uses the
Model.Nominal property of the controller object.
Required Inports
- Measured output or State estimate
If your controller uses default state estimation, this inport is labeled
mo. Connect this inport to the measured plant output signals. The MPC controller uses measured plant outputs to improve its state estimates.To enable custom state estimation, in the General section, select the Use custom state estimation instead of using the built-in Kalman filter. Selecting this option changes the label on this inport to
x[k|k]. Connect a signal that provides estimates of the controller state (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.- Reference
At each control instant, the
refsignal must contain the current reference values (targets or setpoints) for the ny output variables, where ny is the total number of outputs, including measured and unmeasured outputs. Since this block does not support reference previewing,refcannot be defined as a matrix.
Required Outports
Manipulated Variables
The mv outport provides a signal defining the manipulated variables for controlling the plant. The
controller updates its mv outport at each control instant
using the control law contained in the explicit MPC controller object. If the
control law evaluation fails, this signal is unchanged; that is, it is held at
the previous successful result.
Additional Inports (General Section)
Measured disturbance
Add an inport (md) to which you can connect
a vector signal containing nmd elements,
where nmd is the number
of measured disturbances.
Since this block does not support measured disturbance previewing, md cannot
be defined as a matrix.
External manipulated variable
Add an inport (ext.mv) to which you connect a vector signal
that contains the actual manipulated variables (MV) used in the plant. The
controller uses this signal to update their controller state estimates at each
control interval. Using this inport improves state estimation accuracy when the
MVs used in the plant differ from the MVs calculated by the block, for example
due to signal saturation or an override condition.
Note
Using this option can cause an algebraic loop in the Simulink® model, since there is direct feedthrough from the
ext.mv inport to the mv outport.
To prevent such algebraic loops, insert a Memory block or
Unit Delay block.
For additional information, see the corresponding section of the MPC Controller block reference page.
Additional Outports (General Section)
Status of piecewise affine function evaluation
Add an outport (status) that indicates whether
the latest explicit MPC control-law evaluation succeeded. The outport
provides a scalar signal that has one of the following values:
1 — Successful explicit control law evaluation
0 — Failure: One or more control law parameters out of range.
–1 — Undefined: Control law parameters were within the valid range but an extrapolation was necessary.
If status is either 0 or –1, the mv outport
remains at the last known good value.
Region number of evaluated piecewise affine function
Add an outport (region) providing the index
of the polyhedral region used in the latest explicit control law evaluation
(a scalar). If the control law evaluation fails, the signal at this
outport equals zero.
Estimated plant, disturbance, and noise model states
Add an outport (est.state) for the controller
state estimates, x[k|k], at each control instant.
These estimates include the plant, disturbance, and noise model states.
State Estimation (General Section)
Use custom estimated states instead of measured outputs
Replace mo with the x[k|k] inport for
custom state estimation as described in Required Inports.
Others Section
Block data type
Specify the block data type of the manipulated variables as one of the following:
double— Double-precision floating point (default)single— Single-precision floating pointIf you are implementing the block on a single-precision target, specify the output data type as
single.
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.
Inherit sample time
Use 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 or Triggered Subsystem 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.
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 (Simulink).
Use external signal to enable controller evaluation
Add an inport (switch) whose input specifies whether the
controller evaluates its control law. If the input signal is zero, the
controller behaves normally. If the input signal is nonzero, the Explicit
MPC Controller block turns off controller evaluation. 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.
However, the controller continues to update its internal state estimates in the
usual way. Thus, it is ready to resume optimization calculations whenever the
switch signal returns to zero. While controller
evaluation is 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 the value it had when evaluation was disabled.