# Getting Started with Model Predictive Control Toolbox – Video – MATLAB

Model Predictive Control Toolbox supports monitoring run-time controller performance and adjusting run-time weights and constraints. Monitoring Run-Time Controller Performance Model predictive controllers formulate and solve a QP optimization problem at each computation step. The toolbox lets you monitor optimization status at run time. You can access the optimization status signal to detect rare occasions when an optimization may fail to converge and then decide if a backup control strategy should be used. The MPC Controller block also lets you access the optimal cost and control sequence at each computation step.

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Model Predictive Control Toolbox supports monitoring run-time controller performance and adjusting run-time weights and constraints. Monitoring Run-Time Controller Performance Model predictive controllers formulate and solve a QP optimization problem at each computation step.

The toolbox lets you monitor optimization status at run time. You can access the optimization status signal to detect rare occasions when an optimization may fail to converge and then decide if a backup control strategy should be used. The MPC Controller block also lets you access the optimal cost and control sequence at each computation step.

You can use these signals to analyze controller performance and develop custom control strategies. For example, you can use optimal cost information for switching between two model predictive controllers whose outputs are restricted to discrete values. Simulink model that uses the optimal cost signal to switch between two model predictive controllers whose outputs are restricted to discrete values. You can compare the reference signal top right, red and plant output top right, blue to evaluate controller performance.

You can plot the manipulated variable—the controller output bottom right, green —to see when the control strategy switches between controllers. Adjusting Weights and Constraints at Run Time The toolbox lets you adjust the run-time weights and constraints of your model predictive controller to optimize its performance at run time without redesigning or reimplementing it. To perform run-time controller tuning in Simulink, you would configure the MPC Controller block to accept the appropriate weights.

Model Predictive Control Toolbox provides access to the following run-time tuning parameters: Weights on plant outputs Weights on manipulated variable rates Weight on overall constraint softening To adjust constraints at run time, you would configure the MPC Controller block to accept the appropriate signals.

The block provides you with the ability to change the following constraints at run time: Minimum and maximum values for manipulated variables Minimum and maximum values for output variables Custom constraints on linear combinations of manipulated and output variables Simulink model for run-time tuning of model predictive controller parameters.

Model Predictive Control Toolbox enables run-time tuning by changing weights on plant outputs, weights on manipulated variables, manipulated variable rates, and the weight on overall constraint softening. You can design an adaptive model predictive controller or implement a gain-scheduled model predictive controller. You can use an adaptive MPC controller to control a nonlinear plant across a wide operating range through run-time changes to an internal linear plant model.

The toolbox also provides a built-in linear time-varying LTV Kalman filter with asymptotic stability guarantee for state estimation in adaptive model predictive controllers. You can continuously estimate a linear plant model at run time with the online parameter estimation capabilities of System Identification Toolbox. You can then use the estimated model for run-time updates to an internal plant model in an adaptive MPC controller.

This approach lets you design controllers that can adapt to changes in plant dynamics as these changes happen. Adaptive MPC Control of Nonlinear Chemical Reactor Using Online Model Estimation If you can predict how the plant and nominal conditions vary in the future, you can specify an internal plant model that changes over the prediction horizon.

Such an LTV model is useful when controlling periodic systems or nonlinear systems that are linearized around a time-varying nominal trajectory. Adaptive MPC Controller block red for controlling nonlinear models over a wide operating range through run-time changes to an internal plant model.

Use System Identification Toolbox blocks to estimate a linear plant model at run time. With this block you can design a model predictive controller for each operating point and switch between model predictive controllers at run time. The Multiple MPC Controllers block ensures bumpless control transfer from one model predictive controller to another.

You can create linear plant models for controller design at each operating point either by linearizing a Simulink model with Simulink Control Design or by specifying the plant model directly. Multiple MPC Controllers block red for controlling nonlinear models over a wide operating range using multiple model predictive controllers with bumpless control transfer. By using optimal solutions precomputed offline, explicit MPC controllers require fewer computations than traditional implicit model predictive controllers and are, therefore, useful for applications with fast sample times.

You are able to generate an explicit MPC controller from a traditional model predictive controller, as well as simplify a generated explicit MPC controller for a reduced memory footprint. The toolbox also provides a function and a Simulink block for simulating and implementing a generated explicit model predictive controller in MATLAB and Simulink, respectively.

Implementing Fast Model Predictive Controllers Model Predictive Control Toolbox enables you to design, simulate, and deploy model predictive controllers with guaranteed worst-case execution time. You can use this capability to deploy model predictive controllers in applications with limited computational throughput budget. To accomplish this, the toolbox provides an option to limit the number of iterations for solving a QP optimization problem and two choices for specifying what the algorithm will do once that maximum number of iterations is reached: Use an approximate suboptimal solution from the last iteration of the QP solver, provided this approximate solution meets specified constraints.

Use manipulated variable values from the previous computation time. The approximate solution often will provide acceptable performance, but there is no guarantee this will always be the case.

Therefore, it is recommended that you simulate your controller performance with both options and choose the one with the best simulation results.

For some applications, the convergence of QP optimization can be accelerated by using a custom QP solver. The toolbox enables you to use such custom QP solvers instead of the built-in KWIK solver for both simulation and code generation.

The approximate solution provides no significant deterioration in performance lower left , while only using 3 or fewer iterations lower right. Simulating Economic Model Predictive Controllers Model Predictive Control Toolbox supports economic MPC; that is, the ability to optimize the controller for an arbitrary cost function under arbitrary nonlinear constraints, as can be the case with electricity prices fluctuating throughout the day.

Model Predictive Control Toolbox lets you provide your custom nonlinear cost function and custom nonlinear constraints. When you simulate economic MPC using the specified arbitrary cost function and arbitrary constraints, the MPC controller: Still uses a linear prediction model. Uses the arbitrary cost function you provided instead of the built-in quadratic cost function.

Applies the nonlinear constraints you provide in addition to any linear constraints. Computes optimal control moves by solving a nonlinear optimization problem using the SQP algorithm in the fmincon function from Optimization Toolbox. Deploying Model Predictive Controllers Model Predictive Control Toolbox provides several ways to deploy a controller in an application. You can: The toolbox provides a diagnostic function for estimating data memory size used by the deployed controller at run time.

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For Use with MATLAB®. User’s Guide. Version 2. Model Predictive Control. Toolbox. Alberto Bemporad. Manfred Morari. N. Lawrence Ricker. Dear all, I have came across various types of MPCs like DMC, GPC and MAC etc. I am using MPC toolbox of MATLAB and I was wondering exactly which type of. Request PDF on ResearchGate | On Jan 1, , A Bemporad and others published Model Predictive Control Toolbox.

## Getting Started with Model Predictive Control Toolbox

This video walks you through the design process of an MPC controller. In this control problem, we want the car to follow a reference trajectory. So, what we need to control here is the lateral position and the yaw angle. The reference values for the lateral position and yaw angle are calculated with respect to the horizontal axis. For more information, check out the link given in the video description, which will take you to this Model Predictive Control Toolbox example.

### Model Predictive Control Toolbox: Getting Started Guide, The Math Works

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### HOWTO VIDEO: Getting Started with Model Predictive Control Toolbox

For Use with MATLAB®. User’s Guide. Version 2. Model Predictive Control. Toolbox. Alberto Bemporad. Manfred Morari. N. Lawrence Ricker. Request PDF on ResearchGate | On Jan 1, , A Bemporad and others published Model Predictive Control Toolbox. Semantic Scholar extracted view of “Model Predictive Control Toolbox-for use with MATLAB” by Alberto Bemporad et al.

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