Module Description

Module: Control Systems Theory and Design


Control Systems Theory and DesignLecture2Winter Semester
Control Systems Theory and DesignRecitation Section (small)2Winter Semester

Module Responsibility:

Prof. Herbert Werner

Admission Requirements:


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
  • 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. 


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:



Written exam

Workload in Hours:

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

Course: Control Systems Theory and Design


Herbert Werner




Winter Semester


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


  • 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
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