# About

The term "system identification" shall be defined first.

## Definition of Identification

Identification is the experimental determination of the temporal behavior of a process or system. One uses measured signals and determines the temporal behavior within a class of mathematical models. The error (respectively deviation) between the real process or system and its mathematical model shall be as small as possible. However, this task is aggravated by the following implications:

## Problems

- The available measurement period is always limited, either due to economic reasons or due to time-variance of the process
- The maximum allowable change of the input signal is always limited, either due to technical reasons or due to the use of linearized models
- The maximum change of the output signal may also be limited, either due to technical reasons or due to the use of linearized models
- The noise and disturbances consist of different components, whose influence may or may not be limited respectively eliminated by the identification method.

## Topics of the Lecture

- Introduction into the determination of mathematical process models

based on measured data.
- Theoretical and experimental modeling of dynamic systems
- System identification using continuous time signals:

- Aperiodic signals:

- Fourier analysis

- Evaluation of characteristic values (step responses)

- Periodic signals:

- Frequency response analysis

- Correlation analysis
- System identification using discrete time signals:

- Deterministic and stochastic signals

- Basics in estimation theory

- Correlation analysis
- Parameter estimation techniques:

- Least-squares estimation

- Model structure determination

- Recursive estimation algorithms

- Instrumental variables estimation
- Identification with artificial neural networks
- Kalman Filter and Extended Kalman Filter
- Numerically efficient methods
- Implementation under MatLab
- Numerous examples with real experimental data