Model Predictive Control

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.

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 $H_p$. The Lyapunov function
• Stability of MPC Exercise 6.2 $H_p=2$, $H_u=2$, $H_p=2$, $H_u=1$.
• 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: $H_p$, $H_u$, $Q$, $R$
• 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

Book: Predictive Control: With Constraints by Jan Maciejowski