Control Engineering

Objectives General Objectives: This course introduces students to energy-based modeling and control methods for lumped-parameter multi-physical systems (electrical, mechanical, thermodynamical), focusing on: 1) port-based modeling using bond graphs; 2) energy-based modeling and port-Hamiltonian control methods; and 3) an introduction to geometric control on Lie groups. Specific Objectives: Knowledge and Understanding: Students will expand their knowledge and understanding of linear algebra and differential geometry. including concepts such as dual spaces, tensors, manifolds and tangent spaces. They will acquire knowledge beyond standard signal-based system modeling. The students will understand the bottom-up modeling of systems using the concept of power ports and how to classify atomic subsystems based on energy, regardless of the specific physical domain. They will learn about Dirac structures and how to derive the port-Hamiltonian model of a system. The students will also learn key control design methods using the port-Hamiltonian structure of systems, such as energy shaping, energy balancing, passivity-based control, and IDA-PBC. Finally, they will learn the basics of Lie groups and the energetic modeling of rigid bodies, along with some key geometric control strategies for controlling single and multi-body systems. Applying Knowledge and Understanding: The students will apply their knowledge and understanding to the modeling and analysis of multi-physical systems from an energy-based perspective using bond graphs. They will also apply this knowledge to the synthesis of controllers using key energy-based control methods and geometric control techniques. Critical and Judgment Skills: The students will learn how to represent and analyze content related to the modeling and control of multi-physical systems. The course will improve their critical and analytical capabilities by using visual representations, such as bond graphs, to illustrate system dynamics, and by employing coordinate-free descriptions of systems and controller synthesis. Communication Skills: The course will equip students with the ability to present and discuss technical problems and solutions related to port-based modeling and geometric control, using advanced mathematical and visual tools. Learning Ability: The course promotes independent learning by encouraging students to engage with theoretical foundations, analyze scientific literature, and implement advanced control strategies in real-world scenarios.