 Saverio Mascolo Professore Ordinario (Full Professor) IEEE Fellow

## Model Predictive Control (6 CFU)

The course describes the main properties of Model Predictive Control (MPC), the most widely used and successful control method in the process industry and nowadays also applied in distribution networks, coordination of autonomous systems, automotive, and in many other fields of application.

## Prerequisites

Knowledge of Automatic Control, Dynamical Systems Theory and Estimation and Control of Dynamical Systems.

## Examination method

A final project consists of:

1. studying some papers, notes or documentation on a specific subject
2. performing simulations or numerical tests on a software platform
3. writing a report
4. giving a presentation

Students are encouraged to contact directly the lab assistants to decide the project to be carried out. Further information regarding the proposed projects is given in the following pages. More detailed information, references, and tools will be given once the project has been assigned.

## Contents

The MPC framework Prediction horizon, control horizon. Mathematical formulation of the MPC problem as an optimization problem

Case studies Autonomous guided vehicles Drones Active suspension

MPC with constraints Mathematical formulation of MPC with constraints. Examples.

MPC with Matlab Instructions: mpc Examples: tuning Q and R and constraints

MPC design Extended example: the paper machine

MPC with disturbance MPC formulation with disturbance Observer Disturbance model with augmented state Example: the Cesna aircraft model

Solving MPC problems Solving MPC problems. The unconstrained problem as a least square problem Constrained problems. Lagrange multiplier. Solving QP problems: - Active set method - Interior points method.

paper machine case Extended analysis using matlab MPC

The case of Cesna Aircraft Extended analysis using MPC in matlab

case studies Inverted pendulum using MPC+VREP

Stabiliy analysis The stability analysis of the MPC controller Example by changing Hp The Lyapunov function

Stability of MPC Exercise 6.2 Hp=2 Hu=2 Hp=2 Hu=1

Projects Illustration of possible projects

Stabilty Stability proof using infinite horizon Terminal constraints

Inverted pendulum nonlinear model of an inverted pendulum position and angle control Swing up with MPC

MPC tuning Tuning: Hp, Hu, Q, R

Sensitivity for MIMO systems Sensitivity function for MIMO systems SVD decomposition

Projects the case of a mobile robot. Path planning, odometry

MPC for photovoltaic panel MPC for the photovoltaic panel. identification of the linearized model and mpc design

Robust MPC Robust MPC Small gain theorem SVD ||k(z)S(z)D||<1

simulink MPC for a photovoltaic panel The case of a ship model variables: rudder angle and propeller speed MPC: edit scenario

Multiple MPC design

Libro di testo: Predictive Control: With Constraints by Jan Maciejowski

## Further Information

C3Lab, Department of Electrical and Information Engineering, Polytechnic of Bari
Prof. Saverio Mascolo
Email: mascolo at poliba dot it

Lab. Assistant:
Dott. Vito Andrea Racanelli
Per ricevimenti: https://calendly.com/vitoandrearacanelli

Email:  Saverio Mascolo Professore Ordinario (Full Professor) IEEE Fellow

## Model Predictive Control (6 CFU)

The course describes the main properties of Model Predictive Control (MPC), the most widely used and successful control method in the process industry and nowadays also applied in distribution networks, coordination of autonomous systems, automotive, and in many other fields of application.

## Prerequisites

Knowledge of Automatic Control, Dynamical Systems Theory and Estimation and Control of Dynamical Systems.

## Examination method

A final project consists of:

1. studying some papers, notes or documentation on a specific subject
2. performing simulations or numerical tests on a software platform
3. writing a report
4. giving a presentation

Students are encouraged to contact directly the lab assistants to decide the project to be carried out. Further information regarding the proposed projects is given in the following pages. More detailed information, references, and tools will be given once the project has been assigned.

## Contents

The MPC framework Prediction horizon, control horizon. Mathematical formulation of the MPC problem as an optimization problem

Case studies Autonomous guided vehicles Drones Active suspension

MPC with constraints Mathematical formulation of MPC with constraints. Examples.

MPC with Matlab Instructions: mpc Examples: tuning Q and R and constraints

MPC design Extended example: the paper machine

MPC with disturbance MPC formulation with disturbance Observer Disturbance model with augmented state Example: the Cesna aircraft model

Solving MPC problems Solving MPC problems. The unconstrained problem as a least square problem Constrained problems. Lagrange multiplier. Solving QP problems: - Active set method - Interior points method.

paper machine case Extended analysis using matlab MPC

The case of Cesna Aircraft Extended analysis using MPC in matlab

case studies Inverted pendulum using MPC+VREP

Stabiliy analysis The stability analysis of the MPC controller Example by changing Hp The Lyapunov function

Stability of MPC Exercise 6.2 Hp=2 Hu=2 Hp=2 Hu=1

Projects Illustration of possible projects

Stabilty Stability proof using infinite horizon Terminal constraints

Inverted pendulum nonlinear model of an inverted pendulum position and angle control Swing up with MPC

MPC tuning Tuning: Hp, Hu, Q, R

Sensitivity for MIMO systems Sensitivity function for MIMO systems SVD decomposition

Projects the case of a mobile robot. Path planning, odometry

MPC for photovoltaic panel MPC for the photovoltaic panel. identification of the linearized model and mpc design

Robust MPC Robust MPC Small gain theorem SVD ||k(z)S(z)D||<1

simulink MPC for a photovoltaic panel The case of a ship model variables: rudder angle and propeller speed MPC: edit scenario

Multiple MPC design

Libro di testo: Predictive Control: With Constraints by Jan Maciejowski

## Further Information

C3Lab, Department of Electrical and Information Engineering, Polytechnic of Bari
Prof. Saverio Mascolo
Email: mascolo at poliba dot it

Lab. Assistant:
Dott. Vito Andrea Racanelli
Per ricevimenti: https://calendly.com/vitoandrearacanelli

Email: 