| Beschreibung |
After the course, students will be able to describe dynamical systems using state-space and input-output representations, and to analyse their stability using eigenvalue-based methods. They will understand the structure and purpose of feedback control loops and will be able to design linear controllers (including PID) and assess their performance using frequency-domain tools. Through a project-based laboratory component, students will gain hands-on experience with a physical control system (Quanser Qube Servo), encompassing system identification, controller synthesis, and experimental validation. Students will document and present their results, demonstrating both technical competence and the ability to communicate engineering solutions clearly. |
| Literatur |
K. J. Åström and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Princeton University Press, 2nd ed., 2021 |
| Bemerkung |
The course provides an introduction to dynamical systems and feedback control, motivated throughout by engineering applications. Topics include: mathematical modelling of continuous-time dynamical systems (differential equations, state-space representation, linearisation around equilibria); essential linear algebra (vectors, matrices, eigenvalues and eigenvectors, matrix exponential, their role in system behaviour); stability analysis via eigenvalues; the feedback control loop (plant, controller, sensor, disturbance); state feedback and pole placement; optimal state feedback via Linear Quadratic Regulation (LQR); state estimation and the Kalman filter (linear quadratic estimator); output feedback via the combination of LQR and Kalman filter (LQG control). PID control is discussed as a practically widespread special case. Frequency-domain tools (transfer functions, Bode plots, gain and phase margin) are introduced as complementary analysis methods. Applications are drawn from structural engineering (active vibration damping, tuned mass dampers, structural health monitoring) and digital engineering (cyber-physical systems, embedded control). A central element of the course is a laboratory project in which student groups design, implement, and experimentally validate a controller for the Quanser Qube Servo3 hardware platform. Results are documented in a written report+poster and presented publicly at the end of the semester at the annual summaery event. Key topics: - Dynamical systems: models, simulation, qualitative behaviour
- Linear algebra essentials: eigenvalues, eigenvectors, matrix exponential
- Stability and linearisation
- Feedback control: block diagrams, state feedback, pole placement
- Optimal control: Linear Quadratic Regulator (LQR)
- State estimation: Kalman filter and Linear Quadratic Estimator (LQE)
- Output feedback: LQG control
- PID control as a practical special case
- Frequency domain: transfer functions and Bode diagrams (overview)
- Engineering applications: structural vibration control, cyber-physical systems
- Outlook: Model predictive control
- Laboratory project: Quanser Qube Servo3 (system identification, controller design, implementation, presentation)
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