Model predictive controller
A model predictive controller uses linear plant, disturbance, and noise models to estimate the controller state and predict future plant outputs. Using the predicted plant outputs, the controller solves a quadratic programming optimization problem to determine control moves.
For more information on the structure of model predictive controllers, see MPC Modeling.
mpcobj = mpc(plant)plant. The controller, mpcobj, inherits its
control interval from plant.Ts, and its time unit from
plant.TimeUnit. All other controller properties are default values.
After you create the MPC controller, you can set its properties using dot
notation.
If plant.Ts = -1, you must set the Ts
property of the controller to a positive value before designing and simulating your
controller.
mpcobj = mpc(plant,ts)Ts property of the controller. If plant is
a:
Continuous-time model, then the controller discretizes the model for prediction
using sample time ts
A discrete-time model with a specified sample time, the controller resamples the
plant for prediction using sample time ts
A discrete-time model with an unspecified sample time
(plant.Ts = –1), it inherits sample time
ts when used for predictions
mpcobj = mpc(plant,ts,P,M,W,MV,OV,DV)
P sets the PredictionHorizon
property.
M sets the ControlHorizon
property.
W sets the Weights property.
MV sets the ManipulatedVariables
property.
OV sets the OutputVariables
property.
DV sets the DisturbanceVariables
property.
mpcobj = mpc(model)model.Plant, must be a discrete-time
model. This syntax sets the Model property of the
controller.
mpcobj = mpc(model,ts)Ts property of the controller. If
model.Plant is a discrete-time LTI model with an unspecified
sample time (model.Plant.Ts = –1), it inherits
sample time ts when used for predictions.
mpcobj = mpc(model,ts,P,M,W,MV,OV,DV)
plant — Plant prediction modelPlant prediction model, specified as either an LTI model or a linear System Identification Toolbox™ model. The specified plant corresponds to the
Model.Plant property of the controller.
If you do not specify a sample time when creating your controller,
plant must be a discrete-time model.
For more information on MPC prediction models, see MPC Modeling.
Note
Direct feedthrough from manipulated variables to any output in
plant is not supported.
model — Prediction modelPrediction model, specified as a structure with the same format as the Model
property of the controller. If you do not specify a sample time when creating your
controller, model.Plant must be a discrete-time model.
For more information on MPC prediction models, see MPC Modeling.
Ts — Controller sample timeController sample time, specified as a positive finite scalar. The controller uses a
discrete-time model with sample time Ts for prediction.
PredictionHorizon — Prediction horizonPrediction horizon steps, specified as a positive integer. The product of
PredictionHorizon and Ts is the prediction
time; that is, how far the controller looks into the future.
ControlHorizon — Control horizon2 (default) | positive integer | vector of positive integersControl horizon, 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.
Vector of positive integers [m1,
m2, …], specifying the lengths of
blocking intervals. By default the controller computes M blocks
of free moves, where M is the number of blocking intervals. The
first free move applies to times k through
k+m1-1, the second
free move applies from time
k+m1 through
k+m1+m2-1,
and so on. Using block moves can improve the robustness of your controller. The sum
of the values in ControlHorizon must match the prediction
horizon p. If you specify a vector whose sum is:
Less than the prediction horizon, then the controller adds a blocking
interval. The length of this interval is such that the sum of the interval
lengths is p. For example, if
p=10 and you specify a control horizon
of ControlHorizon=[1 2 3], then the
controller uses four intervals with lengths [1 2 3 4].
Greater than the prediction horizon, then the intervals are truncated until
the sum of the interval lengths is equal to p. For example,
if p=10 and you specify a control horizon
of ControlHorizon= [1 2 3 6 7], then the
controller uses four intervals with lengths [1 2 3 4].
For more information on manipulated variable blocking, see Manipulated Variable Blocking.
Model — Prediction model and nominal conditionsPrediction model and nominal conditions, specified as a structure with the following fields. For more information on the MPC prediction model, see MPC Modeling and Controller State Estimation.
Plant — Plant prediction modelPlant prediction model, specified as either an LTI model or a linear System Identification Toolbox model.
Note
Direct feedthrough from manipulated variables to any output in
plant is not supported.
Disturbance — Model describing expected unmeasured disturbancesModel describing expected unmeasured disturbances, specified as an LTI model.
This model is required only when the plant has unmeasured disturbances. You can
set this disturbance model directly using dot notation or using the setindist function.
By default, input disturbances are expected to be integrated white noise. To model the signal, an integrator with dimensionless unity gain is added for each unmeasured input disturbance, unless the addition causes the controller to lose state observability. In that case, the disturbance is expected to be white noise, and so, a dimensionless unity gain is added to that channel instead.
Noise — Model describing expected output measurement noiseModel describing expected output measurement noise, specified as an LTI model.
By default, measurement noise is expected to be white noise with unit variance. To model the signal, a dimensionless unity gain is added for each measured channel.
Nominal — Nominal operating point at which plant model is linearizedNominal operating point at which plant model is linearized, specified as a structure with the following fields.
| Field | Description | Default |
|---|---|---|
X | Plant state at operating point, specified as a column vector
with length equal to the number of states in
| zero vector |
U | Plant input at operating point, including manipulated variables
and measured and unmeasured disturbances, specified as a column vector
with length equal to the number of inputs in
| zero vector |
Y | Plant output at operating point, including measured and
unmeasured outputs, specified as a column vector with length equal to
the number of outputs in | zero vector |
DX | For continuous-time models, | zero vector |
ManipulatedVariables — Manipulated variable information, bounds, and scale factorsManipulated Variable (MV) information, bounds, and scale factors, specified as a
structure array with Nmv elements, where
Nmv is the number of manipulated
variables. To access this property, you can use the alias MV instead
of ManipulatedVariables.
Note
Rates refer to the difference Δu(k)=u(k)-u(k-1). Constraints and weights based on derivatives du/dt of continuous-time input signals must be properly reformulated for the discrete-time difference Δu(k), using the approximation du/dt ≅ Δu(k)/Ts.
Each structure element has the following fields.
Min — MV lower bound-Inf (default) | scalar | vectorMV lower bound, specified as a scalar or vector. By default, this lower bound is unconstrained.
To use the same bound across the prediction horizon, specify a scalar value.
To vary the bound over the prediction horizon from time k to time k+p-1, specify a vector of up to p values. Here, k is the current time and p is the prediction horizon. If you specify fewer than p values, the final bound is used for the remaining steps of the prediction horizon.
Max — MV upper boundInf (default) | scalar | vectorMV upper bound, specified as a scalar or vector. By default, this upper bound is unconstrained.
To use the same bound across the prediction horizon, specify a scalar value.
To vary the bound over the prediction horizon from time k to time k+p-1, specify a vector of up to p values. Here, k is the current time and p is the prediction horizon. If you specify fewer than p values, the final bound is used for the remaining steps of the prediction horizon.
MinECR — MV lower bound softness0 (default) | nonnegative scalar | vectorMV lower bound softness, where a larger equal concern for relaxation (ECR) value indicates a softer constraint, specified as a nonnegative scalar or vector. By default, MV lower bounds are hard constraints.
To use the same ECR value across the prediction horizon, specify a scalar value.
To vary the ECR value over the prediction horizon from time k to time k+p-1, specify a vector of up to p values. Here, k is the current time and p is the prediction horizon. If you specify fewer than p values, the final ECR value is used for the remaining steps of the prediction horizon.
MaxECR — MV upper bound0 (default) | nonnegative scalar | vectorMV upper bound softness, where a larger equal concern for relaxation (ECR) value indicates a softer constraint, specified as a nonnegative scalar or vector. By default, MV upper bounds are hard constraints.
To use the same ECR value across the prediction horizon, specify a scalar value.
To vary the ECR value over the prediction horizon from time k to time k+p-1, specify a vector of up to p values. Here, k is the current time and p is the prediction horizon. If you specify fewer than p values, the final ECR value is used for the remaining steps of the prediction horizon.
RateMin — MV rate of change lower bound-Inf (default) | nonpositive scalar | vectorMV rate of change lower bound, specified as a nonpositive scalar or vector. The MV rate of change is defined as MV(k) - MV(k-1), where k is the current time. By default, this lower bound is unconstrained.
To use the same bound across the prediction horizon, specify a scalar value.
To vary the bound over the prediction horizon from time k to time k+p-1, specify a vector of up to p values. Here, k is the current time and p is the prediction horizon. If you specify fewer than p values, the final bound is used for the remaining steps of the prediction horizon.
RateMax — MV rate of change upper boundInf (default) | nonnegative scalar | vectorMV rate of change upper bound, specified as a nonnegative scalar or vector. The MV rate of change is defined as MV(k) - MV(k-1), where k is the current time. By default, this lower bound is unconstrained.
To use the same bound across the prediction horizon, specify a scalar value.
To vary the bound over the prediction horizon from time k to time k+p-1, specify a vector of up to p values. Here, k is the current time and p is the prediction horizon. If you specify fewer than p values, the final bound is used for the remaining steps of the prediction horizon.
RateMinECR — MV rate of change lower bound softness0 (default) | nonnegative finite scalar | vectorMV rate of change lower bound softness, where a larger equal concern for relaxation (ECR) value indicates a softer constraint, specified as a nonnegative finite scalar or vector. By default, MV rate of change lower bounds are hard constraints.
To use the same ECR value across the prediction horizon, specify a scalar value.
To vary the ECR values over the prediction horizon from time k to time k+p-1, specify a vector of up to p values. Here, k is the current time and p is the prediction horizon. If you specify fewer than p values, the final ECR values are used for the remaining steps of the prediction horizon.
RateMaxECR — MV rate of change upper bound softness0 (default) | nonnegative finite scalar | vectorMV rate of change upper bound softness, where a larger equal concern for relaxation (ECR) value indicates a softer constraint, specified as a nonnegative finite scalar or vector. By default, MV rate of change upper bounds are hard constraints.
To use the same ECR value across the prediction horizon, specify a scalar value.
To vary the ECR values over the prediction horizon from time k to time k+p-1, specify a vector of up to p values. Here, k is the current time and p is the prediction horizon. If you specify fewer than p values, the final ECR values are used for the remaining steps of the prediction horizon.
Name — MV nameMV name, specified as a string or character vector.
Units — MV units"" (default) | string | character vectorMV units, specified as a string or character vector.
ScaleFactor — MV scale factor1 (default) | positive finite scalarMV scale factor, specified as a positive finite scalar. In general, use the operating range of the manipulated variable. Specifying the proper scale factor can improve numerical conditioning for optimization. For more information, see Specify Scale Factors.
OutputVariables — Output variable information, bounds, and scale factorsOutput variable (OV) information, bounds, and scale factors, specified as a
structure array with Ny elements, where
Ny is the number of output variables. To
access this property, you can use the alias OV instead of
OutputVariables.
Each structure element has the following fields.
Min — OV lower bound-Inf (default) | scalar | vectorOV lower bound, specified as a scalar or vector. By default, this lower bound is unconstrained.
To use the same bound across the prediction horizon, specify a scalar value.
To vary the bound over the prediction horizon from time k+1 to time k+p, specify a vector of up to p values. Here, k is the current time and p is the prediction horizon. If you specify fewer than p values, the final bound is used for the remaining steps of the prediction horizon.
Max — OV upper boundInf (default) | scalar | vectorOV upper bound, specified as a scalar or vector. By default, this upper bound is unconstrained.
To use the same bound across the prediction horizon, specify a scalar value.
To vary the bound over the prediction horizon from time k+1 to time k+p, specify a vector of up to p values. Here, k is the current time and p is the prediction horizon. If you specify fewer than p values, the final bound is used for the remaining steps of the prediction horizon.
MinECR — OV lower bound softness1 (default) | nonnegative finite scalar | vectorOV lower bound softness, where a larger equal concern for relaxation (ECR) value indicates a softer constraint, specified as a nonnegative finite scalar or vector. By default, OV upper bounds are soft constraints.
To avoid creating an infeasible optimization problem at run time, it is best practice to use soft OV bounds.
To use the same ECR value across the prediction horizon, specify a scalar value.
To vary the ECR value over the prediction horizon from time k+1 to time k+p, specify a vector of up to p values. Here, k is the current time and p is the prediction horizon. If you specify fewer than p values, the final ECR value is used for the remaining steps of the prediction horizon.
MaxECR — OV upper bound softness1 (default) | nonnegative finite scalar | vectorOV upper bound softness, where a larger equal concern for relaxation (ECR) value indicates a softer constraint, specified as a nonnegative finite scalar or vector. By default, OV lower bounds are soft constraints.
To avoid creating an infeasible optimization problem at run time, it is best practice to use soft OV bounds.
To use the same ECR value across the prediction horizon, specify a scalar value.
To vary the ECR value over the prediction horizon from time k+1 to time k+p, specify a vector of up to p values. Here, k is the current time and p is the prediction horizon. If you specify fewer than p values, the final ECR value is used for the remaining steps of the prediction horizon.
Name — OV nameOV name, specified as a string or character vector.
Units — OV units"" (default) | string | character vectorOV units, specified as a string or character vector.
ScaleFactor — OV scale factor1 (default) | positive finite scalarOV scale factor, specified as a positive finite scalar. In general, use the operating range of the output variable. Specifying the proper scale factor can improve numerical conditioning for optimization. For more information, see Specify Scale Factors.
DisturbanceVariables — Input disturbance variable information and scale factorsDisturbance variable (DV) information and scale factors, specified as a structure
array with Nd elements, where
Nd is the total number of measured and
unmeasured disturbance inputs. The order of the disturbance signals within
DisturbanceVariables is the following: the first
Nmd entries relate to measured input
disturbances, the last Nud entries relate to
unmeasured input disturbances.
To access this property, you can use the alias DV instead of
DisturbanceVariables.
Each structure element has the following fields.
Name — DV nameDV name, specified as a string or character vector.
Units — OV units"" (default) | string | character vectorOV units, specified as a string or character vector.
ScaleFactor — DV scale factor1 (default) | positive finite scalarDV scale factor, specified as a positive finite scalar. Specifying the proper scale factor can improve numerical conditioning for optimization. For more information, see Specify Scale Factors.
Weights — Standard cost function tuning weightsStandard cost function tuning weights, specified as a structure. The controller applies these weights to the scaled variables. Therefore, the tuning weights are dimensionless values.
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.
Weights has the following fields. The values of these fields
depend on whether you use the standard or alternative cost function. For more
information on these cost functions, see Optimization Problem.
ManipulatedVariables — Manipulated variable tuning weightsManipulated variable tuning weights, which penalize deviations from MV
targets, specified as a row vector or array of nonnegative values. The default
weight for all manipulated variables is 0.
To use the same weights across the prediction horizon, specify a row vector of length Nmv, where Nmv is the number of manipulated variables.
To vary the tuning weights over the prediction horizon from time k to time k+p-1, specify an array with Nmv 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.
If you use the alternative cost function, specify
Weights.ManipulatedVariables as a cell array that contains
the
Nmv-by-Nmv
Ru matrix. For example,
mpcobj.Weights.ManipulatedVariables = {Ru}.
Ru must be a positive semidefinite
matrix. Varying the Ru matrix across the
prediction horizon Is not supported. For more information, see Alternative Cost Function.
ManipulatedVariablesRate — Manipulated variable rate tuning weightsManipulated variable rate tuning weights, which penalize large changes in
control moves, specified as a row vector or array of nonnegative values. The
default weight for all manipulated variable rates is
0.1.
To use the same weights across the prediction horizon, specify a row vector of length Nmv, where Nmv is the number of manipulated variables.
To vary the tuning weights over the prediction horizon from time k to time k+p-1, specify an array with Nmv 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.
Note
It is best practice to use nonzero manipulated variable rate weights.
To improve the numerical robustness of the optimization problem, the
software adds the quantity 10*sqrt(eps) to each zero-valued
weight.
Note
It is best practice to use nonzero manipulated variable rate weights. If all
manipulated variable rate weights are strictly positive, the resulting QP
problem is strictly convex. If some weights are zero, the QP Hessian could be
positive semidefinite. To keep the QP problem strictly convex, when the
condition number of the Hessian matrix
KΔU is larger than
1012, the quantity 10*sqrt(eps)
is added to each diagonal term. See Cost Function.
If you use the alternative cost function, specify
Weights.ManipulatedVariablesRate as a cell array that
contains the
Nmv-by-Nmv
RΔu matrix. For example,
mpcobj.Weights.ManipulatedVariablesRate = {Rdu}.
RΔu must be a positive semidefinite
matrix. Varying the RΔu matrix across
the prediction horizon Is not supported. For more information, see Alternative Cost Function.
OutputVariables — Output variable tuning weightsOutput variable tuning weights, which penalize deviation from output
references, specified as a row vector or array of nonnegative values. The default
weight for all output variables is 1.
To use the same weights across the prediction horizon, specify a row vector of length Ny, where Ny 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 Ny 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.
If you use the alternative cost function, specify
Weights.OutputVariables as a cell array that contains the
Ny-by-Ny
Q matrix. For example, mpcobj.Weights.OutputVariables
= {Q}. Q must be a positive semidefinite matrix.
Varying the Q matrix across the prediction horizon Is not
supported. For more information, see Alternative Cost Function.
ECR — Slack variable tuning weight1e5 (default) | positive scalarSlack variable tuning weight, specified as a positive scalar. Increase or decrease the equal concern for relaxation (ECR) weight to make all soft constraints harder or softer, respectively.
Optimizer — QP optimization parametersQP optimization parameters, specified as a structure with the following fields. For more information on the supported QP solvers, see QP Solvers.
Algorithm — QP solver algorithm'active-set' (default) | 'interior-point'QP solver algorithm, specified as one of the following:
'active-set' — Solve the QP problem using the KWIK
active-set algorithm.
'interior-point' — Solve the QP problem using a
primal-dual interior-point algorithm with Mehrotra predictor-corrector.
ActiveSetOptions — Active-set QP solver settingsActive-set QP solver settings, specified as a structure. These settings apply
only when Algorithm is
'active-set'.
If CustomSolver or
CustomSolverGodeGen is true, the
controller does not require the custom solver to honor these settings.
You can specify the following active-set optimizer settings.
MaxIterations — Maximum number of iterations'default' (default) | positive integerMaximum number of iterations allowed when computing the QP solution, specified as one of the following:
'default' — The MPC controller automatically
computes the maximum number of QP solver iterations as , where:
nc is the total number of constraints across the prediction horizon.
nv is the total number of optimization variables across the control horizon.
The default MaxIterations value has a lower
bound of 120.
Positive integer — The QP solver stops after the specified number of iterations. If the solver fails to converge in the final iteration, the controller:
Freezes the controller movement if
UseSuboptimalSolution is
false.
Applies the suboptimal solution reached after the final
iteration if UseSuboptimalSolution is
true.
Note
The default MaxIterations value can be very large
for some controller configurations, such as those with large prediction
and control horizons. When simulating such controllers, if the QP solver
cannot find a feasible solution, the simulation can appear to stop
responding, since the solver continues searching for
MaxIterations iterations.
ConstraintTolerance — Tolerance used to verify that inequality constraints are satisfied1e-6 (default) | positive scalarTolerance used to verify that inequality constraints are satisfied by
the optimal solution, specified as a positive scalar. A larger
ConstraintTolerance value allows for larger
constraint violations.
UseWarmStart — Flag indicating whether to warm start each QP solver iterationtrue (default) | falseFlag indicating whether to warm start each QP solver iteration by passing in a list of active inequalities from the previous iteration, specified as a logical value. Inequalities are active when their equal portion is true.
InteriorPointOptions — Interior-point QP solver settingsInterior-point QP solver settings, specified as a structure. These settings
apply only when Algorithm is
'interior-point'.
If CustomSolver or
CustomSolverGodeGen is true, the
controller does not require the custom solver to honor these settings.
You can specify the following interior-point optimizer settings.
MaxIterations — Maximum number of iterations50 (default) | positive integerMaximum number of iterations allowed when computing the QP solution, specified as a positive integer. The QP solver stops after the specified number of iterations. If the solver fails to converge in the final iteration, the controller:
Freezes the controller movement if
UseSuboptimalSolution is
false.
Applies the suboptimal solution reached after the final iteration if
UseSuboptimalSolution is
true.
ConstraintTolerance — Tolerance used to verify that equality and inequality constraints are satisfied1e-6 (default) | positive scalarTolerance used to verify that equality and inequality constraints are
satisfied by the optimal solution, specified as a positive scalar. A larger
ConstraintTolerance value allows for larger
constraint violations.
OptimalityTolerance — Termination tolerance for first-order optimality (KKT dual residual)1e-6 (default) | positive scalarTermination tolerance for first-order optimality (KKT dual residual), specified as a positive scalar.
ComplementarityTolerance — Termination tolerance for first-order optimality (KKT average complementarity residual)1e-8 (default) | positive scalarTermination tolerance for first-order optimality (KKT average complementarity residual), specified as a positive scalar. Increasing this value improves robustness, while decreasing this value increases accuracy.
StepTolerance — Termination tolerance for decision variables1e-8 (default) | positive scalarTermination tolerance for decision variables, specified as a positive scalar.
MinOutputECR — Minimum value allowed for output constraint ECR values0 (default) | nonnegative scalarMinimum value allowed for output constraint equal concern for relaxation (ECR)
values, specified as a nonnegative scalar. A value of 0
indicates that hard output constraints are allowed. If either of the
OutputVariables.MinECR or
OutputVariables.MaxECR properties of an MPC controller are
less than MinOutputECR, a warning is displayed and the value
is raised to MinOutputECR during computation.
UseSuboptimalSolution — Flag indicating whether a suboptimal solution is acceptablefalse (default) | trueFlag indicating whether a suboptimal solution is acceptable, specified as a
logical value. When the QP solver reaches the maximum number of iterations without
finding a solution (the exit flag is 0), the controller:
Freezes the MV values if UseSuboptimalSolution is
false
Applies the suboptimal solution found by the solver after the final
iteration if UseSuboptimalSolution is
true
To specify the maximum number of iterations, depending on the value of
Algorithm, use either
ActiveSetOptions.MaxIterations or
InteriorPointOptions.MaxIterations.
CustomSolver — Flag indicating whether to use a custom QP solver for simulationfalse (default) | trueFlag indicating whether to use a custom QP solver for simulation, specified as
a logical value. If CustomSolver is true,
the user must provide an mpcCustomSolver function on the
MATLAB® path.
This custom solver is not used for code generation. To generate code for a
controller with a custom solver, use
CustomSolverCodeGen.
If CustomSolver is true, the
controller does not require the custom solver to honor the settings in either
ActiveSetOptions or
InteriorPointOptions.
For more information on using a custom QP solver see, Custom QP Solver.
CustomSolverCodeGen — Flag indicating whether to use a custom QP solver for code generationfalse (default) | trueFlag indicating whether to use a custom QP solver for code generation,
specified as a logical value. If CustomSolverCodeGen is
true, the user must provide an
mpcCustomSolverCodeGen function on the MATLAB path.
This custom solver is not used for simulation. To simulate a controller with a
custom solver, use CustomSolver.
If CustomSolverCodeGen is true, the
controller does not require the custom solver to honor the settings in either
ActiveSetOptions or
InteriorPointOptions.
For more information on using a custom QP solver see, Custom QP Solver.
Notes — User notes{} (default) | cell array of character vectorsUser notes associated with the MPC controller, specified as a cell array of character vectors.
UserData — User data[] (default) | any MATLAB dataUser data associated with the MPC controller, specified as any MATLAB data, such as a cell array or structure.
History — Controller creation date and timeThis property is read-only.
Controller creation date and time, specified as a vector with the following elements:
History(1) — Year
History(2) — Month
History(3) — Day
History(4) — Hours
History(5) — Minutes
History(6) — Seconds
review | Examine MPC controller for design errors and stability problems at run time |
mpcmove | Compute optimal control action |
sim | Simulate closed-loop/open-loop response to arbitrary reference and disturbance signals for implicit or explicit MPC |
mpcstate | MPC controller state |
getCodeGenerationData | Create data structures for mpcmoveCodeGeneration |
generateExplicitMPC | Convert implicit MPC controller to explicit MPC controller |
Create a plant model with the transfer function .
Plant = tf([1 1],[1 2 0]);
The plant is SISO, so its input must be a manipulated variable and its output must be measured. In general, it is good practice to designate all plant signal types using either the setmpcsignals command, or the LTI InputGroup and OutputGroup properties.
Specify a sample time for the controller.
Ts = 0.1;
Define bounds on the manipulated variable, , such that .
MV = struct('Min',-1,'Max',1);
MV contains only the upper and lower bounds on the manipulated variable. In general, you can specify additional MV properties. When you do not specify other properties, their default values apply.
Specify a 20-interval prediction horizon and a 3-interval control horizon.
p = 20; m = 3;
Create an MPC controller using the specified values. The fifth input argument is empty, so default tuning weights apply.
MPCobj = mpc(Plant,Ts,p,m,[],MV);
-->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.
To minimize computational overhead, model predictive controller creation occurs in two
phases. The first happens at creation when you use the
mpc function, or when you change a controller property. Creation
includes basic validity and consistency checks, such as signal dimensions and nonnegativity of
weights.
The second phase is initialization, which occurs when you use the object for the first time in a simulation or analytical procedure. Initialization computes all constant properties required for efficient numerical performance, such as matrices defining the optimal control problem and state estimator gains. Additional, diagnostic checks occur during initialization, such as verification that the controller states are observable.
By default, both phases display informative messages in the command window. You can turn
these messages on or off using the mpcverbosity function.
You can also create model predictive controllers using the MPC Designer app.
Errors starting in R2018b
Support for implementing economic MPC using a linear MPC controller has been removed. Implement economic MPC using a nonlinear MPC controller instead. For more information on nonlinear MPC controllers, see Nonlinear MPC.
If you previously saved a linear MPC object configured with custom cost or constraint
functions, the software generates a warning when the object is loaded and an error if it
is simulated. To suppress the error and warning messages and continue using your linear
MPC controller, mpcobj, without the custom costs and constraints, set
the IsEconomicMPC flag to false.
mpcobj.IsEconomicMPC = false;
To implement your economic MPC controller using a nonlinear MPC object:
Create an nlmpc
object.
Convert your custom cost function to the format required for nonlinear MPC. For more information on nonlinear MPC cost functions, see Specify Cost Function for Nonlinear MPC.
Convert your custom constraint function to the format required for nonlinear MPC. For more information on nonlinear MPC constraints, see Specify Constraints for Nonlinear MPC.
Implement your linear prediction model using state and output functions. For more information on nonlinear MPC prediction models, see Specify Prediction Model for Nonlinear MPC.
get | mpcprops | mpcverbosity | set | setmpcsignals
You have a modified version of this example. Do you want to open this example with your edits?