## Advanced Control

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)

Exercises and their solutions, as well as additional material, will be available for download.

In addition to the problems which are solved in the regular exercise course, a set of additional problems is offered for homework. The solutions of the homework are discussed in the additional exercise course (optional).