Aim
The aim of the course is to provide advanced knowledge and skills in mathematical modeling based on measurement data, including model structure selection, parameter estimation, model validation, prediction, simulation, and control.

Knowledge and understanding
For a passing grade the student must

• be able to define basic concepts for systems with multiple inputs and outputs

• be able to translate between different multivariable system descriptions, in particular time series models, transient responses, transfer function matrices, and state-space descriptions

• be able to derive dynamical mathematical models describing relations between inputs and outputs, including disturbance models

• understand the role of the experimental conditions for the accuracy and quality of the resulting mathematical model

• be able to approximate (reduce) multivariable mathemical models according to a given approximation accuracy

Skills and abilities
For a passing grade the student must

• be able to formulate control-oriented models of multivariable systems in the form of state-space models, time series models, transient responses, and transfer function

• be able to calculate dynamic mathematical models from experimental input and output signal measurements

• be able to validate a mathematical model in relation to experimental data using statistical analysis, model approximation, and simulation

• be able to translate control specifications to requirements on the mathematical model

Judgement and approach
For a passing grade the student must

• be able to understand relations and limitations when simplified models are used to describe a complex multivariable real system

• be able to draw conclusions about the plausibility and quality of a model based on system identification and mathematical modeling

• be able to evaluate the quality of experimental data

• show ability for teamwork and group collaboration during projects

Contents
Identification is a relevant topic for everyone that is working with analysis of experimental data and mathematical modeling. The topics of identification include measurement collection, signal conditioning, model selection, parameter estimation, and mathematical modeling. The course primarily covers physical models and dynamical models represented as differential equations, transfer functions, and difference equations. Identification is important in control, where mathematical models play an important role in decision-making, prediction, control, simulation, and optimization. Many control design methods assume the existence of transfer functions that describe the controlled process. The derivation of these transfer functions is one of the tasks of identification.

Lectures: Transient analysis; Spectral methods; Frequency analysis; Linear regression; Interactive programs; Model parameterizations; Prediction error methods; Instrument variable methods: Real-time identification; Recursive methods; Continuous-time models, Identification in closed loop; Structure selection; Model validation; Experiment design; Model reduction; Partitioned models; 2D-methods; Nonlinear systems; Subspace methods;

Laboratories: Frequency analysis, Interactive identification, Identification for control

Literature
Johansson R: System Modeling and Identification. Prentice Hall, 1993. ISBN 0-13-482308-7.