Advanced Control

The module "Advanced Control" introduces to the state-space approach for controller and observer design of linear dynamical systems. Based on typical control tasks, we introduce the two degrees of freedom (2DOF) control structure. In a unified framework, we consider the design of feedforward and feedback controllers and use different canonical state representations for state feedback and observer design. As an alternative to eigenvalue placement, we introduce the LQR approach for optimal design of state-feedback controllers and extend our controller structure to take measures to counteract external disturbances and improve the transient response of the control loop.

The course, taught in English in the winter semester, is a master's module. It corresponds to the lecture "Moderne Methoden der Regelungstechnik 1", which is held in German. The exam can only be validated in one of these courses (Advanced Control or Moderne Methoden der Regelungstechnik 1). After passing the exam you will receive 5 ECTS.

The module consists of a lecture and an exercise course. Furthermore, we offer an optional additional exercise to recapitulate the prerequisites (e. g., for the analysis of linear systems in the time and frequency domain) or to work on solutions to additional tasks. The optional revision exercise give you the opportunity to clarify open questions about the lecture content. In addition, they allow discussion of topics and advanced questions beyond the scope of the course.

Contents

1. State space models of linear time-invariant (LTI) dynamical systems
- Mathematical modeling of lumped dynamical systems from physical laws
- Control tasks and controller structures
- Equilibria and stability
- Linearization
- Stability criteria for linear systems

2. Design of linear state feedback controllers in a two-degrees-of-freedom structure
- Eigenvalue placement
- Controllability and controller canonical form
- Ackermann's formula and parametric state feedback
- LQR optimal control

3. Design of linear state observers
- Observability and observer canonical form
- Duality between controller and observer design
- Separation principle
- Decoupling control and effect of zeros

4. Methods for disturbance rejection
- Disturbance model and disturbance observer
- Constant disturbance feedback
- Disturbance decoupling
- Effect of integral action

5. Extended controller structures
- Extensions of the 2 DOF controller structure, e.g. by dynamic feedforward control

6. Input-output linearization for SISO systems
- Relative degree
- Lie derivative
- Internal dynamics and stability