Refinement

Specify custom disturbance models, custom state estimator, terminal weights, and custom constraints

Once you have created a model predictive controller for your plant, you can tune the system closed-loop response using the MPC Designer app or at the command line.

Functions

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MPC Properties

`get`	Get property values from MPC object
`getname`	Retrieve I/O signal names from MPC plant model
`set`	Set or modify MPC object properties
`setname`	Set I/O signal names in MPC plant model

Constraints and Weights

`getconstraint`	Obtain mixed input/output constraints from model predictive controller
`setconstraint`	Set mixed input/output constraints for model predictive controller
`setterminal`	Terminal weights and constraints

State Estimation

`getEstimator`	Obtain Kalman gains and model for estimator design
`setEstimator`	Modify a model predictive controller’s state estimator

Disturbance Models

`getindist`	Retrieve unmeasured input disturbance model
`getoutdist`	Retrieve unmeasured output disturbance model
`setindist`	Modify unmeasured input disturbance model
`setoutdist`	Modify unmeasured output disturbance model

Solvers Settings

`ActiveSet`	Options object for active-set QP solver used within an `mpc` object (Since R2024a)
`InteriorPoint`	Options object for interior point QP solver used in `mpc` object (Since R2024a)
`ADMM`	Options object for active set QP solver used in `mpc` object (Since R2024a)
`BranchBound`	Options object for branch and bound MIQP solver used in `mpc` object (Since R2024a)

Custom QP Applications

`mpcActiveSetSolver`	Solve quadratic programming problem using active-set algorithm (Since R2020a)
`mpcActiveSetOptions`	Create default option set for `mpcActiveSetSolver` (Since R2020a)
`mpcInteriorPointSolver`	Solve a quadratic programming problem using an interior-point algorithm (Since R2020a)
`mpcInteriorPointOptions`	Create default option set for `mpcInteriorPointSolver` (Since R2020a)
`setCustomSolver`	Configures an MPC object to use the QP solver from Optimization Toolbox as a custom solver (Since R2021b)

Apps

MPC Designer

Design and simulate model predictive controllers

Topics

Weights and Constraints

Setting Targets for Manipulated Variables
If your plant has more manipulated variables than outputs, you can hold the excess manipulated variables at target values for economical or operational reasons.
Constraints on Linear Combinations of Inputs and Outputs

You can design and simulate a model predictive controller with mixed input/output constraints.
- Use Custom Constraints in Blending Process
Terminal Weights and Constraints

To achieve infinite horizon control, you can use terminal weights at the final prediction horizon step. To ensure stability for constrained systems, you may have to also define terminal constraints at the end of the prediction horizon.
- Provide LQR Performance Using Terminal Penalty Weights

Disturbance Models and State Estimation

Adjust Disturbance and Noise Models
MPC controllers model unknown events using input and output disturbance models, and measurement noise models.
Custom State Estimation
You can override the default MPC controller state estimation method by changing the default Kalman gains or by supplying your own controller state estimates.
Implement Custom State Estimator Equivalent to Built-In Kalman Filter
Design a state estimator equivalent to the linear Kalman filter of an MPC controller.
Use MPC with Extended State Observer to Reject Unmeasured Output Disturbances
Use an extended state observer to reject unmeasured disturbance at the plant output.

Optimization Formulation and Solvers

Optimization Problem
Model predictive controllers compute optimal manipulated variable control moves by solving a quadratic program at each control interval.
QP Solvers
The model predictive controller QP solvers convert an MPC optimization problem to a general form quadratic programming problem.
Manipulated Variable Blocking
You can improve the robustness of your controller and smooth manipulated variable adjustments by dividing the prediction horizon into a series of blocking intervals.
Specifying Alternative Cost Function with Off-Diagonal Weight Matrices
You can specify an alternative cost function for your model predictive controller to minimize during optimization.
Control Quarter-Car Suspension Dynamics Using ADMM Solver
Design an MPC controller which uses the Alternating Direction Method of Multipliers (ADMM) as a solver to control the dynamics of the active suspension of a quarter-car suspension system.