Option set for `mpcmove`

function

To specify options for the `mpcmove`

, `mpcmoveAdaptive`

, and `mpcmoveMultiple`

functions, use an `mpcmoveopt`

object.

Using this object, you can specify run-time values for a subset of controller properties,
such as tuning weights and constraints. If you do not specify a value for one of the
`mpcmoveopt`

properties, the value of the corresponding controller option
is used instead.

creates a default set
of options for the `options`

= mpcmoveopt`mpcmove`

function. To modify the property values,
use dot notation.

`OutputWeights`

— Output variable tuning weights`[]`

(default) | vector | arrayOutput variable tuning weights that replace the
`Weights.OutputVariables`

property of the controller at run time,
specified as a vector or array of nonnegative values.

To use the same weights across the prediction horizon, specify a row vector of length
*N _{y}*, where

To vary the tuning weights over the prediction horizon from time *k*+1 to time *k*+*p*, specify an array with *N _{y}* columns and up to

The format of `OutputWeights`

must match the format of the
`Weights.OutputVariables`

property of the controller object. For
example, you cannot specify constant weights across the prediction horizon in the
controller object, and then specify time-varying weights using
`mpcmoveopt`

.

`MVWeights`

— Manipulated variable tuning weights`[]`

(default) | vector | arrayManipulated variable tuning weights that replace the
`Weights.ManipulatedVariables`

property of the controller at run
time, specified as a vector or array of nonnegative values.

To use the same weights across the prediction horizon, specify a row vector of length
*N _{mv}*, where

To vary the tuning weights over the prediction horizon from time *k* to time *k*+*p*-1, specify an array with *N _{mv}* columns and up to

The format of `MVWeights`

must match the format of the
`Weights.ManipulatedVariables`

property of the controller object. For
example, you cannot specify constant weights across the prediction horizon in the
controller object, and then specify time-varying weights using
`mpcmoveopt`

.

`MVRateWeights`

— Manipulated variable rate tuning weights`[]`

(default) | vector | arrayManipulated variable rate tuning weights that replace the
`Weights.ManipulatedVariablesRate`

property of the controller at run
time, specified as a vector or array of nonnegative values.

To use the same weights across the prediction horizon, specify a row vector of length
*N _{mv}*, where

To vary the tuning weights over the prediction horizon from time *k* to time
*k*+*p*-1, specify
an array with *N _{mv}* columns
and up to

The format of `MVRateWeights`

must match the format of the
`Weights.ManipulatedVariablesRate`

property of the controller object.
For example, you cannot specify constant weights across the prediction horizon in the
controller object, and then specify time-varying weights using
`mpcmoveopt`

.

`ECRWeight`

— Slack variable tuning weight`[]`

(default) | positive scalarSlack variable tuning weight that replaces the `Weights.ECR`

property of the controller at run time, specified as a positive scalar.

`OutputMin`

— Output variable lower bounds`[]`

(default) | row vector | matrixOutput variable lower bounds, specified as a row vector of length
*N _{y}* or as a matrix with

If you did not specify the `OutputVariables(i).Min`

property of the
`mpc`

object, then specifying `OutputMin`

results in an error
when you execute `mpcmove`

.

To change the bounds over the prediction horizon from time *k*+1 to
time *k*+*p*, specify a matrix with
*N _{y}* columns and up to

`OutputMin(:,i)`

replaces the
`OutputVariables(i).Min`

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)**

`OutputMin` Dimension | Replacement Behavior |
---|---|

Scalar `OutputMin` (single output, constant bound) | `OutputMin` replaces the constant bound defined in
`OutputVariables(i).Min` |

Column vector `OutputMin` (single output, time-varying
bound) | `OutputMin` replaces the constant bound defined in
`OutputVariables(i).Min` with a time-varying bound. |

Row vector `OutputMin` (multiple outputs, constant
bounds) | `OutputMin(i)` replaces the constant bound defined in
`OutputVariables(i).Min` |

Matrix `OutputMin` (multiple outputs, time-varying
bounds) | `OutputMin(:,i)` 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)**

`OutputMin` Dimension | Replacement Behavior |
---|---|

Scalar `OutputMin` (single output, constant bound) | `OutputMin` 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 `OutputMin` (single output, time-varying
bound) | `OutputMin` replaces the time-varying bound defined in
`OutputVariables(i).Min` , and the original bound profile is
discarded. |

Row vector `OutputMin` (multiple outputs, constant
bounds) | `OutputMin(i)` 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 `OutputMin` (multiple outputs, time-varying
bounds). | `OutputMin(:,i)` replaces the time-varying bound defined
in `OutputVariables(i).Min` , and the original bound profile is
discarded. |

`OutputMax`

— Output variable upper bounds`[]`

(default) | row vector | matrixOutput variable upper bounds, specified as a row vector of length
*N _{y}* or as a matrix with

If you did not specify the `OutputVariables(i).Max`

property of the
`mpc`

object, then specifying `OutputMax`

results in an error
when you execute `mpcmove`

.

To change the bounds over the prediction horizon from time *k*+1 to
time *k*+*p*, specify a matrix with
*N _{y}* columns and up to

`OutputMax(:,i)`

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)**

`OutputMax` Dimension | Replacement Behavior |
---|---|

Scalar `OutputMax` (single output, constant bound) | `OutputMax` replaces the constant bound defined in
`OutputVariables(i).Max` |

Column vector `OutputMax` (single output, time-varying
bound) | `OutputMax` replaces the constant bound defined in
`OutputVariables(i).Max` with a time-varying bound. |

Row vector `OutputMax` (multiple outputs, constant
bounds) | `OutputMax(i)` replaces the constant bound defined in
`OutputVariables(i).Max` |

Matrix `OutputMax` (multiple outputs, time-varying
bounds) | `OutputMax(:,i)` 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)**

`OutputMax` Dimension | Replacement Behavior |
---|---|

Scalar `OutputMax` (single output, constant bound) | `OutputMax` 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 `OutputMax` (single output, time-varying
bound) | `OutputMax` replaces the time-varying bound defined in
`OutputVariables(i).Max` , and the original bound profile is
discarded. |

Row vector `OutputMax` (multiple outputs, constant
bounds) | `OutputMax(i)` 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 `OutputMax` (multiple outputs, time-varying
bounds). | `OutputMax(:,i)` replaces the time-varying bound defined
in `OutputVariables(i).Max` , and the original bound profile is
discarded. |

`MVMin`

— Manipulated variable lower bounds`[]`

(default) | row vector | matrixManipulated variable lower bounds, specified as a row vector of length
*N _{mv}* or as a matrix with

If you did not specify the `ManipulatedVariables(i).Min`

property
of the `mpc`

object, then specifying
`MVMin`

results in an error when you execute `mpcmove`

.

To change the bounds over the prediction horizon from time *k* to
time *k*+*p*-1, specify a matrix with
*N _{mv}* columns and up to

`MVMin(:,i)`

replaces the
`ManipulatedVariables(i).Min`

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)**

`MVMin` Dimension | Replacement Behavior |
---|---|

Scalar `MVMin` (single output, constant bound) | `MVMin` replaces the constant bound defined in
`ManipulatedVariables(i).Min` |

Column vector `MVMin` (single output, time-varying
bound) | `MVMin` replaces the constant bound defined in
`ManipulatedVariables(i).Min` with a time-varying
bound. |

Row vector `MVMin` (multiple outputs, constant
bounds) | `MVMin(i)` replaces the constant bound defined in
`ManipulatedVariables(i).Min` |

Matrix `MVMin` (multiple outputs, time-varying
bounds) | `MVMin(:,i)` 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)**

`MVMin` Dimension | Replacement Behavior |
---|---|

Scalar `MVMin` (single output, constant bound) | `MVMin` 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 `MVMin` (single output, time-varying
bound) | `MVMin` replaces the time-varying bound defined in
`ManipulatedVariables(i).Min` , and the original bound profile
is discarded. |

Row vector `MVMin` (multiple outputs, constant
bounds) | `MVMin(i)` 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 `MVMin` (multiple outputs, time-varying
bounds). | `MVMin(:,i)` replaces the time-varying bound defined in
`ManipulatedVariables(i).Min` , and the original bound profile
is discarded. |

`MVMax`

— Manipulated variable upper bounds`[]`

(default) | row vector | matrixManipulated variable upper bounds, specified as a row vector of length
*N _{mv}* or as a matrix with

If you did not specify the `ManipulatedVariables(i).Max`

property
of the `mpc`

object, then specifying
`MVMax`

results in an error when you execute `mpcmove`

.

To change the bounds over the prediction horizon from time *k* to
time *k*+*p*-1, specify a matrix with
*N _{mv}* columns and up to

`MVMax(:,i)`

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)**

`MVMax` Dimension | Replacement Behavior |
---|---|

Scalar `MVMax` (single output, constant bound) | `MVMax` replaces the constant bound defined in
`ManipulatedVariables(i).Max` |

Column vector `MVMax` (single output, time-varying
bound) | `MVMax` replaces the constant bound defined in
`ManipulatedVariables(i).Max` with a time-varying
bound. |

Row vector `MVMax` (multiple outputs, constant
bounds) | `MVMax(i)` replaces the constant bound defined in
`ManipulatedVariables(i).Max` |

Matrix `MVMax` (multiple outputs, time-varying
bounds) | `MVMax(:,i)` 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)**

`MVMax` Dimension | Replacement Behavior |
---|---|

Scalar `MVMax` (single output, constant bound) | `MVMax` 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 `MVMax` (single output, time-varying
bound) | `MVMax` replaces the time-varying bound defined in
`ManipulatedVariables(i).Max` , and the original bound profile
is discarded. |

Row vector `MVMax` (multiple outputs, constant
bounds) | `MVMax(i)` 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 `MVMax` (multiple outputs, time-varying
bounds). | `MVMax(:,i)` replaces the time-varying bound defined in
`ManipulatedVariables(i).Max` , and the original bound profile
is discarded. |

`CustomConstraint`

— Custom mixed input/output constraints`[]`

(default) | structureCustom mixed input/output constraints, specified as a structure with the following
fields. These constraints replace the mixed input/output constraints previously set
using `setconstraint`

.

`E`

— Manipulated variable constraint constantarray of zeros (default) |

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

`F`

— Controlled output constraint constantarray of zeros (default) |

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

`G`

— Mixed input/output constraint constantcolumn vector of zeros (default) | column vector of length

Mixed input/output constraint constant, specified as a column vector of length *N _{c}*.

`S`

— Measured disturbance constraint constantarray of zeros (default) |

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

`OnlyComputeCost`

— Flag indicating whether to calculate the optimal control sequence`0`

(default) | `1`

Flag indicating whether to calculate the optimal control sequence, specified as one of the following:

`0`

— Controller returns the predicted optimal control moves in addition to the objective function cost value.`1`

— Controller returns the objective function cost only, which saves computational effort.

`MVused`

— Manipulated variable values used in the plant during the previous control interval`[]`

(default) | row vectorManipulated variable values used in the plant during the previous control interval,
specified as a row vector of length *N _{mv}*, where

`MVused`

, the
`mpvmove`

uses the `LastMove`

property of its
current controller state input argument, `x`

.`MVTarget`

— Manipulated variable targets`[]`

(default) | row vectorManipulated variable targets, specified as a row vector of length
*N _{mv}*, where

`MVTarget(i)`

replaces the
`ManipulatedVariables(i).Target`

property of the controller at run
time.`PredictionHorizon`

— Prediction horizon`[]`

(default) | positive integerPrediction horizon, which replaces the `PredictionHorizon`

property
of the controller at run time, specified as a positive integer. If you specify
`PredictionHorizon`

, you must also specify
`ControlHorizon`

.

Specifying `PredictionHorizon`

changes the:

Number of rows in the optimal sequences returned by the

`mpcmove`

and`mpcmoveAdaptive`

functionsMaximum dimensions of the

`Plant`

and`Nominal`

input arguments of`mpcmoveAdaptive`

This parameter is ignored by the `mpcmoveMultiple`

function.

`ControlHorizon`

— Control horizon`[]`

(default) | positive integer | vector of positive integersControl horizon, which replaces the `ControlHorizon`

property of
the controller at run time, specified as one of the following:

Positive integer,

*m*, between`1`

and*p*, inclusive, where*p*is equal to`PredictionHorizon`

. In this case, the controller computes*m*free control moves occurring at times*k*through*k*+*m*-1, and holds the controller output constant for the remaining prediction horizon steps from*k*+*m*through*k*+*p*-1. Here,*k*is the current control interval. For optimal trajectory planning set*m*equal to*p*.Vector of positive integers, [

*m*_{1},*m*_{2}, …], where the sum of the integers equals the prediction horizon,*p*. In this case, the controller computes*M*blocks of free moves, where*M*is the length of the`ControlHorizon`

vector. The first free move applies to times*k*through*k*+*m*_{1}-1, the second free move applies from time*k*+*m*_{1}through*k*+*m*_{1}+*m*_{2}-1, and so on. Using block moves can improve the robustness of your controller compared to the default case.

If you specify `ControlHorizon`

, you must also specify
`PredictionHorizon`

.

This parameter is ignored by the `mpcmoveMultiple`

function.

`mpcmove` | Compute optimal control action |

`mpcmoveAdaptive` | Compute optimal control with prediction model updating |

`mpcmoveMultiple` | Compute gain-scheduling MPC control action at a single time instant |

Vary a manipulated variable upper bound during a simulation.

Define the plant, which includes a 4-second input delay. Convert to a delay-free, discrete, state-space model using a 2-second control interval. Create the corresponding default controller, and specify MV bounds at +/-2.

```
Ts = 2;
Plant = absorbDelay(c2d(ss(tf(0.8,[5 1],'InputDelay',4)),Ts));
MPCobj = mpc(Plant,Ts);
```

-->The "PredictionHorizon" property of "mpc" object is empty. Trying PredictionHorizon = 10. -->The "ControlHorizon" property of the "mpc" object is empty. Assuming 2. -->The "Weights.ManipulatedVariables" property of "mpc" object is empty. Assuming default 0.00000. -->The "Weights.ManipulatedVariablesRate" property of "mpc" object is empty. Assuming default 0.10000. -->The "Weights.OutputVariables" property of "mpc" object is empty. Assuming default 1.00000.

MPCobj.MV(1).Min = -2; MPCobj.MV(1).Max = 2;

Create an empty `mpcmoveopt`

object. During simulation, you can set properties of the object to specify controller parameters.

options = mpcmoveopt;

Pre-allocate storage and initialize the controller state.

v = []; t = [0:Ts:20]; N = length(t); y = zeros(N,1); u = zeros(N,1); x = mpcstate(MPCobj);

-->Assuming output disturbance added to measured output channel #1 is integrated white noise. -->The "Model.Noise" property of the "mpc" object is empty. Assuming white noise on each measured output channel.

Use `mpcmove`

to simulate the following:

Reference (setpoint) step change from initial condition

*r*= 0 to*r*= 1 (servo response)MV upper bound step decrease from 2 to 1, occurring at

*t*= 10

r = 1; for i = 1:N y(i) = Plant.C*x.Plant; if t(i) >= 10 options.MVMax = 1; end [u(i),Info] = mpcmove(MPCobj,x,y(i),r,v,options); end

As the loop executes, the value of `options.MVMax`

is reset to 1 for all iterations that occur after *t* = 10. Prior to that iteration, `options.MVMax`

is empty. Therefore, the controller's value for `MVMax`

is used, `MPCobj.MV(1).Max = 2`

.

Plot the results of the simulation.

[Ts,us] = stairs(t,u); plot(Ts,us,'b-',t,y,'r-') legend('MV','OV') xlabel(sprintf('Time, %s',Plant.TimeUnit))

From the plot, you can observe that the original MV upper bound is active until *t* = 4. After the input delay of 4 seconds, the output variable (OV) moves smoothly to its new target of *r* = 1. reaching the target at *t* = 10. The new MV bound imposed at *t* = 10 becomes active immediately. This forces the OV below its target, after the input delay elapses.

Now assume that you want to impose an OV upper bound at a specified location relative to the OV target. Consider the following constraint design command:

MPCobj.OV(1).Max = [Inf,Inf,0.4,0.3,0.2];

This is a horizon-varying constraint. The known input delay makes it impossible for the controller to satisfy an OV constraint prior to the third prediction-horizon step. Therefore, a finite constraint during the first two steps would be poor practice. For illustrative purposes, the previous constraint also decreases from 0.4 at step 3 to 0.2 at step 5 and thereafter.

The following commands produce the same results shown in the previous plot. The OV constraint is never active because it is being varied in concert with the setpoint, *r*.

x = mpcstate(MPCobj);

-->Assuming output disturbance added to measured output channel #1 is integrated white noise. -->The "Model.Noise" property of the "mpc" object is empty. Assuming white noise on each measured output channel.

OPTobj = mpcmoveopt; for i = 1:N y(i) = Plant.C*x.Plant; if t(i) >= 10 OPTobj.MVMax = 1; end OPTobj.OutputMax = r + 0.4; [u(i),Info] = mpcmove(MPCobj,x,y(i),r,v,OPTobj); end

The scalar value *r* + 0.4 replaces the first finite value in the `MPCobj.OV(1).Max`

vector, and the remaining finite values adjust to maintain the original profile, that is, the numerical difference between these values is unchanged. *r* = 1 for the simulation, so the previous use of the `mpcmoveopt`

object is equivalent to the command

MPCobj.OV(1).Max = [Inf, Inf, 1.4, 1.3, 1.2];

However, using the `mpcmoveopt`

object involves much less computational overhead.

If a variable is unconstrained in the initial controller design, you cannot constrain it using

`mpcmoveopt`

. The controller ignores any such specifications.You cannot remove a constraint from a variable that is constrained in the initial controller design. However, you can change it to a large (or small) value such that it is unlikely to become active.

`mpc`

| `mpcmove`

| `setconstraint`

| `setterminal`

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