This webpage concerns a lecture held by Prof. Werner until Winter 2023/24. Maybe the contents are outdated.

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Module Description

Control Systems Theory and Design

Courses:

Title	Type	Hrs/Week	Period
Control Systems Theory and Design	Lecture	2	Winter Semester
Control Systems Theory and Design	Recitation Section (small)	2	Winter Semester

Module Responsibility:

Prof. Herbert Werner

Admission Requirements:

None

Recommended Previous Knowledge:

Introduction to Control Systems

Educational Objectives:

Professional Competence

Theoretical Knowledge

Students can explain how linear dynamic systems are represented as state space models; they can interpret the system response to initial states or external excitation as trajectories in state space
They can explain the system properties controllability and observability, and their relationship to state feedback and state estimation, respectively
They can explain the significance of a minimal realisation
They can explain observer-based state feedback and how it can be used to achieve tracking and disturbance rejection
They can extend all of the above to multi-input multi-output systems
They can explain the z-transform and its relationship with the Laplace Transform
They can explain state space models and transfer function models of discrete-time systems
They can explain the experimental identification of ARX models of dynamic systems, and how the identification problem can be solved by solving a normal equation
They can explain how a state space model can be constructed from a discrete-time impulse response

Capabilities

Students can transform transfer function models into state space models and vice versa
They can assess controllability and observability and construct minimal realisations
They can design LQG controllers for multivariable plants
They can carry out a controller design both in continuous-time and discrete-time domain, and decide which is appropriate for a given sampling rate
They can identify transfer function models and state space models of dynamic systems from experimental data
They can carry out all these tasks using standard software tools (Matlab Control Toolbox, System Identification Toolbox, Simulink)

Personal Competence

Social Competence

Students can work in small groups on specific problems to arrive at joint solutions.

Autonomy

Students can obtain information from provided sources (lecture notes, software documentation, experiment guides) and use it when solving given problems.

They can assess their knowledge in weekly on-line tests and thereby control their learning progress.

ECTS-Credit Points Module:

6 ECTS

Examination:

Written exam

Workload in Hours:

Independent Study Time: 124, Study Time in Lecture: 56

Course: Control Systems Theory and Design

Lecturer:

Herbert Werner

Language:

English

Period:

Winter Semester

Content:

State space methods (single-input single-output)

• State space models and transfer functions, state feedback
• Coordinate basis, similarity transformations
• Solutions of state equations, matrix exponentials, Caley-Hamilton Theorem
• Controllability and pole placement
• State estimation, observability, Kalman decomposition
• Observer-based state feedback control, reference tracking
• Transmission zeros
• Optimal pole placement, symmetric root locus
Multi-input multi-output systems
• Transfer function matrices, state space models of multivariable systems, Gilbert realization
• Poles and zeros of multivariable systems, minimal realization
• Closed-loop stability
• Pole placement for multivariable systems, LQR design, Kalman filter

Digital Control
• Discrete-time systems: difference equations and z-transform
• Discrete-time state space models, sampled data systems, poles and zeros
• Frequency response of sampled data systems, choice of sampling rate

System identification and model order reduction
• Least squares estimation, ARX models, persistent excitation
• Identification of state space models, subspace identification
• Balanced realization and model order reduction

Case study
• Modelling and multivariable control of a process evaporator using Matlab and Simulink
Software tools
• Matlab/Simulink

Literature:

Werner, H., Lecture Notes „Control Systems Theory and Design“
T. Kailath "Linear Systems", Prentice Hall, 1980
K.J. Astrom, B. Wittenmark "Computer Controlled Systems" Prentice Hall, 1997
L. Ljung "System Identification - Theory for the User", Prentice Hall, 1999

ECTS-Credit Points Course: