Afterwards the student:
- is able to determine whether a system is linear, time-invariant or causal, and understands the notion of a state. And in case of a linear system, whether it is controllable, observable, stabilisable and/or detectable;
- Is able to design an observer and stabilizing controller based on a state description of the system;
- can determine and analyse transfer functions of complex systems, and use them to design stabilising controllers;
- can design LQ optimal controllers.
This course introduces several results from Systems and Control Theory.|
The focus is on dynamical systems with inputs and outputs, especially linear systems and their state representations. An important problem is the extent to which the dynamical behaviour can be controlled by choice of input. In contrast to standard ODEs, we may be able to turn unstable ODEs into stable ones by carefully choosing the input. For this type of analysis we need the notions of controllability, detectability and observability. We design observers to estimate the state of a system, and we design dynamical stabilising controllers using static state feedback in combination with observers. Finally, we analyse systems in the frequency domain, and we use transfer functions to construct controllers and analyse complex interconnected systems.