Module number: MW1420

Duration: 1 Semester

Recurrence: Winter semester

Language: English

Number of ECTS: 5

## Staff

Professor in charge: PD Dr.-Ing. habil. Paul Kotyczka

## Amount of work

Class attendance: 60

Private study: 90

Total: 150

## Course work and exam formalities

Written exam at the end of the module, 90 min.

## Description

- Modeling of dynamical systems in state space

- Linearization

- Solution of the linear state differential equations

- The concepts of eigenvalues, poles and zeros

- Canonical forms of the state representation

- System properties: stability, controllability, observability

- Effects of pole-zero cancellations

- Relations between system representation the time and frequency domain

- Design of linear state feedback controllers in a two-degrees-of-freedom structure

- Design of linear state observers

- Methods for disturbance attenuation

- Introduction to flatness-based feedforward control at the example of linear systems

## Learning outcome

At the end of the lecture the students are able to:

- model real-world dynamical systems in the state-space representation and linearize them to achieve a linear state space model

- compute the solutions of linear state differential equations and analyze the dynamical system for stability, oberservability and controllability

- understand the purpose and advantage of a two-degrees-of-freedom controller structure

- design a state-feedback controller using the pole placement method and as a Linear Quadratic Regulator (LQR)

- design a Luenberger state-observer and a Linear Quadratic Estimator (LQE) to calculate the non measurable states of the system

- further modify the closed-loop system by adding measures to cope with the different disturbances acting on the system

- have a basic knowledge about flatness-based feedforward control

## Prerequisites

-  A basic course in automatic control dealing with the analysis of dynamical systems (transfer function, impulse response, poles and zeros, stability, Laplace Transform and basic control loops (P, PI, PID))

- Mathematical background: Basic linear algebra (matrix computations, eigenvalues, determinants,...) and complex numbers' theory.

## Media

The lecture will be written on the blackboard and supplemented with slides and computer simulations. Exercises and their solutions as well as simulation codes will be available for download.

## Literature

The lecture is self-contained: However, the following textbooks are recommended for the interested reader:

1. Dorf, R.C., Bishop, R.H.: Modern Control Systems. Prentice Hall (Pearson) 2008.

2. Franklin, G.F., Powell, J.D., Emami-Naeini, A.: Feedback Control of Dynamic Systems, 5th Edition, Prentice Hall (Pearson) 2006.

3. Kailath, T.: Linear Systems, Prentice Hall, 1980. Dorf, R.C., Bishop, R.H.: Modern Control Systems. Prentice Hall (Pearson) 2008.

4. Antsaklis, P.J., Michel, A.N.: Linear Systems. Birkhäuser, 2006.

5. Ogata, K.: Model Control Engineering, 5th Edition, Prentice Hall, 2009.

6. Ogata, K.: MATLAB for Control Engineers, 1st Edition, Prentice Hall, 2007.

## Teaching and studying methods

Weekly courses:

- 90 min. lecture

- 45 min. exercise course

- 90 min. additional excercise course (optional)