SYSTEMS ENGINEERING | FRT110 |

**Aim**

The course is mandatory for students in year 2 of the Engineering Nano-Science progamme (N) and year 3 of the Environmental Engineering programme (W). The aim of the course is to give an overview of systems engineering, in particular control engineering, and its concepts, methods, and application areas. The course also develops the skills in using computer-based analysis and simulation tools.

Control plays a major role in most parts of our society. In earlier courses the students have learnt how to model and understand system behaviour. The aim of this course is to learn the students how to make a system operate more reliable, in a more environment-friendly way, with better precision, or in a more economical way, in spite of external disturbances acting on the system. The word system has a very general interpretation. It can, for example, be an atomic energy microscope or a waste water treatment plant.. The course teaches a systems-oriented way of thinking which the students can make use of in their future careers, independent of the actual application area.

*Knowledge and understanding*

For a passing grade the student must

- understand what a linear time-invariant dynamical systems is
- be able to grasp the basic concepts of control
- understand how a dynamical system can be modelled using different model representations, for example transient responses, transfer functions, differential equations on state-space form and input-output form, and frequency responses described using Bode or Nyquist diagrams
- have knowledge about the concepts that are used to describe the performance of a dynamical system, for example stability and stationary characteristics
- have knowledge about the most common controller types and their mathematical basis
- understand the advantages and disadvantages of different controller structures

*Skills and abilities*

For a passing grade the student must

- be able to use the basic concepts of control correctly both in speaking and writing
- be able to approximate a nonlinear dynamical system using linearization
- be able to describe a dynamical systems using different representations, including transient responses, transfer functions, state-space model, and differential equations on state-space form and input-output signal form
- be able to compute the relationships between different model representations
- be able to analyse dynamical systems and reason about ther behaviour
- be able to design controllers and controller structures from given specifications
- be able to use modern computer tools for control
- be able to write simple sequence control programs
- be able to perform smaller experiments on laboratory setups to derive a system that behaves according to a given specification

*Judgement and approach*

For a passing grade the student must

- be capable of solving new previously unknown controller problems of smaller size
- be able to communicate in a professional way with persons working with control
- show ability for teamwork and group collaboration in laboratory exercises
- be able to read and give feedback on project reports, and be able to produce written reports of the solutions to the hand-in problems

**Contents**

The course gives insight in the use of systems engineerings-based analysis methods and dynamical models for feedback systems. It also provides tools for the design of simple controllers.

Important areas are mathemical models of simple control loops and analysis of their dynamics. Computer tools are used for analysis, synthesis, and implementation.

Lectures: Introduction to transient responses and feedback; Basic modelling and analysis of the dynamics of both natural and engineering processes; Analysis of the properties of simple control loops; Concepts and tools for analysis of dynamical systems, e.g., linearisation, the solutions to differential equations, and stability.

The course contains computer-based exercises and laboratory experiments on real model processes.

*Course modules*: Introduction, Modelling, Dynamical systems, Feedback, PID design, Controller structures, Frequency domain analysis

**Literature**

Feedback Systems, an Introduction to Scientists and Engineers, Karl Johan Åström and Richard Murray