11. Examples

• 11.1. How to
  • 11.1.1. Basic Example
  • 11.1.2. How to Incorporate Preview Information in the MPC Problem
    • 11.1.2.1. Introduction
    • 11.1.2.2. Use preview information in the MATLAB® interface
    • 11.1.2.3. Comparison of MPC with Preview and Standard MPC
  • 11.1.3. HOW TO: Implement an MPC Controller with a Time-Varying Dynamics
    • 11.1.3.1. Introduction
    • 11.1.3.2. Implementation
    • 11.1.3.3. Comparison of the two approaches
  • 11.1.4. How to Implement 1-Norm and Infinity-Norm Cost Functions
    • 11.1.4.1. Introduction
    • 11.1.4.2. 1-norm reformulation
    • 11.1.4.3. \(\infty\)-norm formulation
  • 11.1.5. HOW TO: Implement Rate Constraints
    • 11.1.5.1. Problem formulation
    • 11.1.5.2. Implementation
    • 11.1.5.3. Simulation Results
  • 11.1.6. Binary MPC Example
    • 11.1.6.1. Simulation result
    • 11.1.6.2. Details on problem reformulation
• 11.2. Y2F interface: Basic example
  • 11.2.1. Defining the problem data
  • 11.2.2. Defining the MPC problem
  • 11.2.3. Generating a solver
  • 11.2.4. Calling the generated solver
  • 11.2.5. Simulation
  • 11.2.6. Results
  • 11.2.7. Variation 1: Parametric cost
  • 11.2.8. Variation 2: Time-varying dynamics
  • 11.2.9. Variation 3: Time-varying constraints
• 11.3. Y2F interface: Trajectory Optimization for Quadrotor Flight
  • 11.3.1. Defining the problem parameters
  • 11.3.2. Defining the MPC problem
  • 11.3.3. Generating a solver
  • 11.3.4. Calling the generated solver
  • 11.3.5. Results
• 11.4. Low-level interface: Active Suspension Control
  • 11.4.1. Introduction
  • 11.4.2. Disturbance Model: Speed Bump
  • 11.4.3. Implementation of Preview Information
  • 11.4.4. Comparison of Passive Vehicle and Active Suspension Control Using Preview Information
• 11.5. Low-level interface: Robust estimation (Kalman filter)
  • 11.5.1. System Description
  • 11.5.2. Robust Kalman filter
  • 11.5.3. Simulation and Comparison
• 11.6. Low-level interface: Spacecraft Rendezvous
  • 11.6.1. Introduction
  • 11.6.2. Model
  • 11.6.3. Constraints
  • 11.6.4. Objective
  • 11.6.5. Spacecraft Rendezvous Maneuvers with and without 1-Norm Cost
• 11.7. Low-level interface: DC/DC converter
  • 11.7.1. Example Overview
  • 11.7.2. Special Requirements
  • 11.7.3. Introduction - Control of a DC/DC Converter
  • 11.7.4. Control Objective by Using Model Predictive Control
  • 11.7.5. Model Predictive Control Design via FORCESPRO MATLAB® Interface
  • 11.7.6. Simulation of the PLECS® Model with Model Predictive Control
  • 11.7.7. Comparison of Model Predictive Control and PI Control
• 11.8. High-level interface: Basic example
  • 11.8.1. Defining the problem data
  • 11.8.2. Defining the MPC problem
  • 11.8.3. Generating a solver
  • 11.8.4. Calling the generated solver
  • 11.8.5. Simulation
  • 11.8.6. Results
• 11.9. High-level interface: Obstacle avoidance (MATLAB & Python)
  • 11.9.1. Defining the MPC Problem
    • 11.9.1.1. Objective
    • 11.9.1.2. Matrix equality constraints
    • 11.9.1.3. Runtime Parameters
    • 11.9.1.4. Inequality constraints
    • 11.9.1.5. Dimensions
    • 11.9.1.6. Initial conditions
  • 11.9.2. Generating a solver
  • 11.9.3. Calling the generated solver
  • 11.9.4. Results
  • 11.9.5. Variation: External functions
• 11.10. High-level interface: Indoor localization (MATLAB & Python)
  • 11.10.1. Time of flight measurements
  • 11.10.2. Estimation error
  • 11.10.3. Minimize the error
  • 11.10.4. Implementation
• 11.11. High-level interface: Path tracking example (MATLAB)
  • 11.11.1. Defining the MPC Problem
    • 11.11.1.1. Objective
    • 11.11.1.2. Equality constraints
    • 11.11.1.3. Bounds
    • 11.11.1.4. Dimensions
  • 11.11.2. Generating a solver
  • 11.11.3. Calling the generated solver
    • 11.11.3.1. Choosing the Path
  • 11.11.4. Results
  • 11.11.5. Using the SQP Fast solver
• 11.12. High-level interface: Legacy path tracking example (MATLAB & Python)
  • 11.12.1. Defining the MPC Problem
    • 11.12.1.1. Objective
    • 11.12.1.2. Matrix equality constraints
    • 11.12.1.3. Bounds
    • 11.12.1.4. Dimensions
    • 11.12.1.5. Initial conditions
  • 11.12.2. Generating a solver
  • 11.12.3. Calling the generated solver
  • 11.12.4. Results
• 11.13. High-level interface: Rate Constraints
  • 11.13.1. Implementation in MATLAB
  • 11.13.2. Results
• 11.14. High-level interface: Soft Constraints
  • 11.14.1. Implementation in MATLAB
  • 11.14.2. Results
• 11.15. Controlling a crane using a FORCESPRO NLP solver
  • 11.15.1. Defining the MPC problem
    • 11.15.1.1. Model dimensions and dynamics
    • 11.15.1.2. System constraints
    • 11.15.1.3. Objective function
  • 11.15.2. Generating a FORCESPRO interior point NLP solver
  • 11.15.3. Calling the crane solver
  • 11.15.4. Results
• 11.16. Real-time SQP Solver: Robotic Arm Manipulator (MATLAB & Python)
  • 11.16.1. Defining the MPC problem
    • 11.16.1.1. Tracking objective
    • 11.16.1.2. State and input constraints
    • 11.16.1.3. Initial condition and horizon length
  • 11.16.2. Generating a real-time SQP solver
  • 11.16.3. Calling the generated SQP solver
  • 11.16.4. Calling the dynamics used in the model directly in MATLAB/Python
  • 11.16.5. Results
• 11.17. Controlling a DC motor using a FORCESPRO SQP solver
  • 11.17.1. Defining the MPC problem
    • 11.17.1.1. The tracking objective function
    • 11.17.1.2. The dynamics
    • 11.17.1.3. Input and state constraints
    • 11.17.1.4. Generating the FORCESPRO SQP solver
    • 11.17.1.5. Calling the solver
    • 11.17.1.6. Results
• 11.18. Mixed-integer nonlinear solver: F8 Crusader aircraft
  • 11.18.1. Defining the problem data
    • 11.18.1.1. Objective
    • 11.18.1.2. Equality constraints
    • 11.18.1.3. Inequality constraints
    • 11.18.1.4. Initial and final conditions
  • 11.18.2. Defining the MPC problem
  • 11.18.3. Generating an MINLP solver
  • 11.18.4. Calling the generated MINLP solver
  • 11.18.5. Providing an initial guess at run-time
  • 11.18.6. Changing the parallelization strategy at run-time
  • 11.18.7. Results
• 11.19. High-level interface: Optimal EV charging and speed profile example (MATLAB & PYTHON)
  • 11.19.1. Problem Overview
    • 11.19.1.1. Vehicle Dynamics
    • 11.19.1.2. Vehicle Energetics
    • 11.19.1.3. Bounds
    • 11.19.1.4. MPC Formulation
    • 11.19.1.5. Model Parameters
  • 11.19.2. Defining the MPC Problem
    • 11.19.2.1. Objective function
    • 11.19.2.2. Equality constraints
    • 11.19.2.3. Inequality constraints
    • 11.19.2.4. Generating the FORCESPRO NLP solver
    • 11.19.2.5. Calling the solver
    • 11.19.2.6. Results
• 11.20. High-level interface: Extended optimal EV charging and speed profile example using a 2D motor efficiency map (MATLAB & PYTHON)
  • 11.20.1. Problem Overview
    • 11.20.1.1. Vehicle Dynamics
    • 11.20.1.2. Vehicle Energetics
    • 11.20.1.3. Bounds
    • 11.20.1.4. MPC Formulation
    • 11.20.1.5. Model Parameters
  • 11.20.2. Defining the MPC Problem
    • 11.20.2.1. Scaling
    • 11.20.2.2. Objective function
    • 11.20.2.3. Equality constraints
    • 11.20.2.4. Inequality constraints
    • 11.20.2.5. Generating the FORCESPRO NLP solver
    • 11.20.2.6. Calling the solver
    • 11.20.2.7. Results