Advanced topics in digital processing, 7.5 ECTS Credits

Learning Outcomes

Upon completion of the course, students should be able to

-describe and analyse discrete-time signals and systems mathematically

-use these mathematical descriptions to design and analyse digital filters meeting specified

requirements

-implement the digital filters.

Content and Form of Instruction

Methods to describe and analyse discrete-time signals and systems and to design and analyse

digital filters are discussed theoretically in lectures (see components below). The digital filters

are implemented in supervised laboratory work.

Discrete-time signals and systems and how these can be described and analysed mathematically

using impulse response and discrete Fourier transform. Description and analysis of multifrequent

signals and systems.

Design and analysis of digital filters of finite and infinite impulse response type.

Implementation and analysis of digital filters which amongst others includes number

quantisation and quick algorithms for calculating the discrete Fourier transform.

Modulation Theory, 7.5 ECTS Credits

Learning Outcomes

After the course the student should be able to:

- describe with word and equations the basic analog and digital modulation methods, with

emphasis on signal format, frequency content and bandwidth.

- describe the basic principles for analog and digital demodulation methods, superheterodyne

receivers, and the phase locked loop used as frequency stabilizer and FM-demodulator.

- describe the basic concepts, components and building blocks of an electronic communication

system.

- do calculations using Friis' transmission equation and link budget on simple communication

links.

- do calculations on thermal noise, noise factor, equivalent noise temperature and signal-to-noise

ratio (S/N) in a system with cascaded components.

- describe the basic FM radio and TV techniques.

Content and Form of Instruction

Instruction is in the form of lectures, calculation exercises and obligatory assignments.

Analog modulation and demodulation methods (AM and FM).

Pulse modulation methods (PAM, PWM and PPM).

Digital modulation and demodulation methods (ASK, FSK, PSK and QAM).

Communication systems with transmitter and receiver. Phase locked loop.

Friis' transmission equation and the link budget.

Thermal noise and signal-to-noise ratio (S/N).

Mixers and up- and down-converting. The superheterodyne receiver.

Introduction to signal theory.

Introduction to satellite communication and access methods.

Basic FM radio and TV techniques.

Model Based Control Systems, 7.5 ECTS Credits

Learning Outcomes

Upon completion of the course a student should be able to

- describe stability theory for linear and nonlinear industrial systems

Upon completion of the course a student should be able to

- describe stability theory for linear and nonlinear industrial systems

- analyze industrial systems with respect to stability, controllability and observability

- describe polynomial methods and state feedback, and use such methods in control design for

industrial systems

- design controllers based on direct pole placement, but also to design controllers based on the

optimality criteria minimum variance control, linear quadratic control and model predictive

control

- describe and use methods for state estimation, and use them in state space based control design

- use modern software to implement, simulate and analyze control loops for industrial systems

- independently by literary search obtain deepened knowledge within the area of automatic

control

Content and Form of Instruction

Theory for model based control systems are discussed during lectures, and are illustrated and

investigated through exercises.

The course content includes

-state space models

-linear and nonlinear systems

-stability, controllability and observability

-state space feedback and observer based on pole placement

-linear quadratic state feedback

-estimation with Kalman filter

-model predictive control

-control based on pole placement with polynomial methods

- minimum variance control

-simulation

Optimal Control, 7.5 ECTS Credits

Learning Outcomes

Upon completion of the course, students should be able to

-describe an optimal control problem mathematically

-use mathematical tools to solve the optimal control problem

-implement and evaluate the solution to the optimal control problem

Content and Form of Instruction

Mathematical description of an optimal control problem and mathematical methods to solve such

a problem are treated in lectures. The theory is then illustrated and tested in supervised exercises.

Course content covers calculus of variations and optimal control, linear quadratic optimal control

systems, Pontryagin's minimum principle, the Hamilton-Jacobi-Bellman equation and optimal

control systems with restrictions.

Robotics and Embedded Control, 7.5 ECTS

The topics of the course are the fundamental theory of robots, embedded control systems and

practical aspects of real-time controllers of robotic platforms.

System Identification, 7.5 ECTS Credits

Learning Outcomes

Upon completion of the course a student should be able to:

- carry out the different steps, from identification experiment to model validation, in the process

of identifying a dynamic system, and

- combine these steps for identifying a dynamic system and presenting a mathematical model.

Content and Form of Instruction

The procedure of identifying a system is discussed theoretically in lectures, and is then illustrated

and investigated in supervised computer exercises.

The course content includes experiment design, models for linear time-invariant systems, choice

of model structure, prediction, non-parametric and parametric identification methods, prediction

error methods, accuracy analysis, and model validation.

Scientific Computing, 7.5 ECTS Credits

Learning Outcomes

The aim of the course is that students acquire an understanding of the importance of numerical

computation methods and basic principles for the construction and use of numerical algorithms.

Upon completion of the course a student should be able to

- identify mathematical problems in science and technology that are impossible to solve with

analytical methods and, if needed, rewrite the problems in a form suitable for a numerical

solution method,

- use numerical methods for problems in linear algebra, optimization problems, and differential

equations and describe the advantages and disadvantages of the methods,

- analyze and use results from numerical library routines,

- implement numerical algorithms for large scale computations in MATLAB or in a suitable

programming language such as C or Fortran.

Content and Form of Instruction

Each course module below treats the numerical algorithms that are discussed and illustrated in

lectures, and implementation tasks that are performed individually or in small groups under

supervision. The actual numerical methods treated can vary from term to term. Students analyze

and evaluate the results of numerical experiments in a written report which is also presented

orally at a seminar.

Course module 1, Linear algebra: Direct and iterative numerical solution of systems of linear

equations, solution of least-squares problems, numerical solution of eigenvalue and singular

value problems.

Course module 2, Optimization: Numerical solution of non-linear equations, constrained and

unconstrained optimization, numerical solution of non-linear least-squares problems, linear

programming.

Course module 3, Differential equations: Numerical solution of initial and boundary value

problems.

Parameter Estimation, 7.5 ECTS Credits

Learning Outcomes

Upon completion of the course a student should be able to:

- describe statistical models of observations

- use Fisher information and the Cramér-Rao lower bound to judge the quality of parameter

estimators, and for experiment design

- use the maximum likelihood method and the least squares method for parameter estimation

- use numerical methods for implementation of parameter estimation methods

- solve practical parameter estimation problems in engineering and science

Content and Form of Instruction

Mathematical tools and methods for parameter estimation are discussed theoretically during

lectures, and are illustrated and investigated through exercises.

The course content includes

-parametric models and distributions of observations

-Fisher information

-the Cramér-Rao lower bound

-the maximum likelihood method

-the least squares method

-numerical methods for parameter estimation