mpcmoveopt
Option set for mpcmove
function
Description
To specify options for the mpcmove
, mpcmoveAdaptive
, and mpcmoveMultiple
functions, use an mpcmoveopt
object.
Using this object, you can specify runtime 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.
Creation
Syntax
Description
creates a default set
of options for the options
= mpcmoveoptmpcmove
function. To modify the property values,
use dot notation.
Properties
OutputWeights
— Output variable tuning weights
[]
(default)  vector  array
Output 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 N_{y} is the number of output variables.
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 p rows. Here, k is the current time and p is the prediction horizon. Each row contains the output variable tuning weights for one prediction horizon step. If you specify fewer than p rows, the weights in the final row are used for the remaining steps of the prediction horizon.
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 timevarying weights using
mpcmoveopt
.
MVWeights
— Manipulated variable tuning weights
[]
(default)  vector  array
Manipulated 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 N_{mv} is the number of manipulated variables.
To vary the tuning weights over the prediction horizon from time k to time k+p1, specify an array 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 manipulated variable tuning weights for one prediction horizon step. If you specify fewer than p rows, the weights in the final row are used for the remaining steps of the prediction horizon.
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 timevarying weights using
mpcmoveopt
.
MVRateWeights
— Manipulated variable rate tuning weights
[]
(default)  vector  array
Manipulated 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 N_{mv} is the number of manipulated variables.
To vary the tuning weights over the prediction horizon from time k to time k+p1, specify an array 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 manipulated variable rate tuning weights for one prediction horizon step. If you specify fewer than p rows, the weights in the final row are used for the remaining steps of the prediction horizon.
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 timevarying weights using
mpcmoveopt
.
ECRWeight
— Slack variable tuning weight
[]
(default)  positive scalar
Slack 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  matrix
Output variable lower bounds, specified as a row vector of length N_{y} or as a matrix with N_{y} columns, where N_{y} is the number of output variables.
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 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 are used for the remaining steps of the prediction horizon.
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 i
th 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, timevarying
bound)  OutputMin replaces the constant bound defined in
OutputVariables(i).Min with a timevarying bound. 
Row vector OutputMin (multiple outputs, constant
bounds)  OutputMin(i) replaces the constant bound defined in
OutputVariables(i).Min 
Matrix OutputMin (multiple outputs, timevarying
bounds)  OutputMin(:,i) replaces the constant bound defined in
OutputVariables(i).Min with a timevarying bound. 
Vector OutputVariables(i).Min
in the mpc
object (a timevarying bound for the i
th 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, timevarying
bound)  OutputMin replaces the timevarying 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, timevarying
bounds).  OutputMin(:,i) replaces the timevarying bound defined
in OutputVariables(i).Min , and the original bound profile is
discarded. 
OutputMax
— Output variable upper bounds
[]
(default)  row vector  matrix
Output variable upper bounds, specified as a row vector of length N_{y} or as a matrix with N_{y} columns, where N_{y} is the number of output variables.
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 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 are used for the remaining steps of the prediction horizon.
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 i
th plant output to be applied to
all prediction steps)
OutputMax Dimension  Replacement Behavior 

Scalar 

Column vector 

Row vector 

Matrix 

Vector OutputVariables(i).Max
in the mpc
object (a timevarying bound for the i
th 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, timevarying
bound)  OutputMax replaces the timevarying 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, timevarying
bounds).  OutputMax(:,i) replaces the timevarying bound defined
in OutputVariables(i).Max , and the original bound profile is
discarded. 
MVMin
— Manipulated variable lower bounds
[]
(default)  row vector  matrix
Manipulated variable lower bounds, specified as a row vector of length N_{mv} or as a matrix with N_{mv} columns, where N_{mv} is the number of output variables.
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+p1, specify a matrix 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 are used for the remaining steps of the prediction horizon.
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 i
th 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, timevarying
bound)  MVMin replaces the constant bound defined in
ManipulatedVariables(i).Min with a timevarying
bound. 
Row vector MVMin (multiple outputs, constant
bounds)  MVMin(i) replaces the constant bound defined in
ManipulatedVariables(i).Min 
Matrix MVMin (multiple outputs, timevarying
bounds)  MVMin(:,i) replaces the constant bound defined in
ManipulatedVariables(i).Min with a timevarying
bound. 
Vector ManipulatedVariables(i).Min
in the mpc
object (a timevarying bound for the i
th 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, timevarying
bound)  MVMin replaces the timevarying 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, timevarying
bounds).  MVMin(:,i) replaces the timevarying bound defined in
ManipulatedVariables(i).Min , and the original bound profile
is discarded. 
MVMax
— Manipulated variable upper bounds
[]
(default)  row vector  matrix
Manipulated variable upper bounds, specified as a row vector of length N_{mv} or as a matrix with N_{mv} columns, where N_{mv} is the number of output variables.
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+p1, specify a matrix 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 are used for the remaining steps of the prediction horizon.
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 i
th 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, timevarying
bound)  MVMax replaces the constant bound defined in
ManipulatedVariables(i).Max with a timevarying
bound. 
Row vector MVMax (multiple outputs, constant
bounds)  MVMax(i) replaces the constant bound defined in
ManipulatedVariables(i).Max 
Matrix MVMax (multiple outputs, timevarying
bounds)  MVMax(:,i) replaces the constant bound defined in
ManipulatedVariables(i).Max with a timevarying
bound. 
Vector ManipulatedVariables(i).Max
in the mpc
object (a timevarying bound for the i
th 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, timevarying
bound)  MVMax replaces the timevarying 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, timevarying
bounds).  MVMax(:,i) replaces the timevarying bound defined in
ManipulatedVariables(i).Max , and the original bound profile
is discarded. 
CustomConstraint
— Custom mixed input/output constraints
[]
(default)  structure
Custom 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 constant
array of zeros (default)  N_{c}byN_{mv}
array
Manipulated variable constraint constant, specified as an N_{c}byN_{mv} array, where N_{c} is the number of constraints, and N_{mv} is the number of manipulated variables.
F
— Controlled output constraint constant
array of zeros (default)  N_{c}byN_{y}
array
Controlled output constraint constant, specified as an N_{c}byN_{y} array, where N_{y} is the number of controlled outputs (measured and unmeasured).
G
— Mixed input/output constraint constant
column vector of zeros (default)  column vector of length N_{c}
Mixed input/output constraint constant, specified as a column vector of length N_{c}.
S
— Measured disturbance constraint constant
array of zeros (default)  N_{c}byN_{md}
array
Measured disturbance constraint constant, specified as an N_{c}byN_{md} array, where N_{md} is the number of measured disturbances.
OnlyComputeCost
— Option to return only the value of the cost function in the solution details structure
0
(default)  1
Option to return only the value of the cost function in the info
solution details output
structure returned by mpcmove
. Specify it as one of the
following:
0
—mpcmove
returns all the detailed solution information in its second output argument.1
—mpcmove
returns only the predicted value of the cost function. This saves some computational effort as the predicted optimal plant state and output sequences do not need to be calculated. Note that ifmpcmove
is not called with a second output argument these sequences are not calculated either.
MVused
— Manipulated variable values used in the plant during the previous control interval
[]
(default)  row vector
Manipulated variable values used in the plant during the previous control interval,
specified as a row vector of length N_{mv}, where
N_{mv} is the number of manipulated
variables. If you do not specify MVused
, the
mpvmove
uses the LastMove
property of its
current controller state input argument, x
.
MVTarget
— Manipulated variable targets
[]
(default)  row vector
Manipulated variable targets, specified as a row vector of length
N_{mv}, where
N_{mv} is the number of manipulated
variables. MVTarget(i)
replaces the
ManipulatedVariables(i).Target
property of the controller at run
time.
PredictionHorizon
— Prediction horizon
[]
(default)  positive integer
Prediction 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
andmpcmoveAdaptive
functionsMaximum dimensions of the
Plant
andNominal
input arguments ofmpcmoveAdaptive
This parameter is ignored by the mpcmoveMultiple
function.
ControlHorizon
— Control horizon
[]
(default)  positive integer  vector of positive integers
Control 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 toPredictionHorizon
. In this case, the controller computes m free control moves occurring at times k through k+m1, and holds the controller output constant for the remaining prediction horizon steps from k+m through k+p1. 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.
Object Functions
mpcmove  Compute optimal control action and update controller states 
mpcmoveAdaptive  Compute optimal control with prediction model updating 
mpcmoveMultiple  Compute gainscheduling MPC control action at a single time instant 
Examples
Simulation with Varying Controller Property
Vary a manipulated variable upper bound during a simulation.
Define the plant, which includes a 4second input delay. Convert to a delayfree, discrete, statespace model using a 2second 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);
>"PredictionHorizon" is empty. Assuming default 10. >"ControlHorizon" is empty. Assuming default 2. >"Weights.ManipulatedVariables" is empty. Assuming default 0.00000. >"Weights.ManipulatedVariablesRate" is empty. Assuming default 0.10000. >"Weights.OutputVariables" 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;
Preallocate 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 #1 is integrated white noise. >"Model.Noise" is empty. Assuming white noise on each measured output.
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 horizonvarying constraint. The known input delay makes it impossible for the controller to satisfy an OV constraint prior to the third predictionhorizon 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 #1 is integrated white noise. >"Model.Noise" is empty. Assuming white noise on each measured output.
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.
Tips
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.
Version History
Introduced in R2018b
Apri esempio
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