Course detail

Control of Linear Time-Invariant Systems

FSI-VA1Acad. year: 2026/2027

The course focuses on control design methods for dynamic systems in the continuous and discrete domains. It covers the structure of control loops, including MIMO and branched systems, their stability, autonomy, and methods for disturbance and transport delay compensation. The instruction includes state-space control, controllability, observability, the design of state controllers and observers, the pole-placement method, and LQR and LQG controllers. The course also introduces the principles of Model Predictive Control (MPC), evolutionary control design methods, and fuzzy control. Control of nonlinear systems is mentioned briefly.

Language of instruction

Czech

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

doc. Ing. Pavel Škrabánek, Ph.D.

Department

Institute of Automation and Computer Science (ÚAI)

Entry knowledge

Knowledge of basic principles and concepts in automation, knowledge of the mathematical foundations (differential and integral calculus, differential equations), and the ability to work with Matlab and its Simulink extension.

Rules for evaluation and completion of the course

Credit requirements: The basic condition for obtaining the credit is active participation in all laboratory exercises and successful defense of the semester project. The examination consists of a written and an oral part.

Attendance and activity at the seminars are required. One absence can be compensated for by attending a seminar with another group in the same week, or by the elaboration of substitute tasks. Longer absence can be compensated for by the elaboration of compensatory tasks assigned by the tutor.

Aims

The aim of the course is to introduce students to control design principles in continuous and discrete control loops. Students will gain the knowledge needed to design and evaluate MIMO and branched control structures, including disturbance and transport delay compensation. The course covers state-space control, the design of state controllers and observers, and modern methods such as LQR, LQG, and Model Predictive Control. It also provides an introduction to fuzzy control, nonlinear system control, and the basics of evolutionary design methods.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

ASTRÖM, K., HÄGGLUND, T. Advanced PID Control. ISA – Instrumentation, Systems, and Automation Society, Research Triangle Park, NC, 2006, ISBN 1-55617-942-1. (EN)
DORF, R. C., BISHOP, R. H. Modern Control Systems. Tenth Edition. Upper Saddle River – New Jersey: Pearson Prentice Hall, 2004, ISBN 0-13-145733-0.  (EN)
FRANKLIN, G. F., POWELL, J. D., Emami-Naeini, A. Feedback Control of Dynamic Systems. Fourth Edition. Prentice Hall, Upper Sadle River, 2002, ISBN 0-13-032393-4 . (EN)
GOODWIN G. C., GRAEBE, S. F., SALGADO, M. E. Control System Design. Pearson Education, Singapore, 2001, ISBN 81-297-0002-6 (EN)
OGATA,K.: Modern Control Engineering, Prentice Hall , fourth edition, New Jersey 2002, ISBN 0-13-043245-8 (EN)
ŠULC, B., VÍTEČKOVÁ, M. 2004. Teorie a praxe návrhu regulačních obvodů. Vydavatelství ČVUT, Praha, 2004, ISBN 80-01-03007-5 (CS)
VÍTEČKOVÁ, M., VÍTEČEK, A. Vybrané metody seřizování regulátorů. VŠB – TU Ostrava, Ostrava, 2011, ISBN 978-80-248-2503-8 (CS)

Recommended reading

Bernard Friedland: Control System Design: An Introduction to State-Space Methods. Dover Publications, 2005. (EN)
Morris, K.: Introduction to Feedback Control. Academic Press, London, 2002. (EN)
Švarc, I., Matoušek, R., Šeda, M., Vítečková, M.: Automatizace-Automatické řízení, skriptum VUT FSI v Brně, CERM 2011. (CS)
Švarc, I.: Teorie automatického řízení, podpory FSI, www stránky fakulty 2003. (CS)

Classification of course in study plans

  • Programme N-AIŘ-P Master's 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

39 hod., optionally

Teacher / Lecturer

doc. Ing. Pavel Škrabánek, Ph.D.

Syllabus

  1. Fundamentals of control theory and an overview of advanced control design methods. External and internal representations of a dynamic system in continuous and discrete domains.

  2. Auxiliary controlled and auxiliary manipulated variables. Control loops with disturbance measurement – loop invariance. Compensation of transport delay.

  3. Multivariable (MIMO) control loops. Their stability and autonomy. Multidimensional controllers. Branched control loops.

  4. State-space representation. State-feedback control. Controllability. Observability. Continuous and discrete formulations.

  5. Design of a state controller, influence of disturbances. Pole-placement method.

  6. Generalization of state-space control design, suitable structures for state-space control. Concept and design of state observers.

  7. LQR and LQG controllers.

  8. Model Predictive Control.

  9. Fundamentals of controller design using evolutionary methods.

  10. Fuzzy sets, fuzzy relations and their composition, fuzzy logic, linguistic variables, engineering fuzzy implication, approximate reasoning.

  11. Mamdani and Sugeno fuzzy logic systems, fuzzification, inference, defuzzification, knowledge-based fuzzy controllers, creation of a fuzzy rule base using empirical knowledge of system behavior, creation of a fuzzy rule base using general meta-rules.

  12. Control of nonlinear systems.

  13. Case study.

Laboratory exercise

8 hod., compulsory

Teacher / Lecturer

doc. Ing. Pavel Škrabánek, Ph.D.

Computer-assisted exercise

18 hod., compulsory

Teacher / Lecturer

doc. Ing. Pavel Škrabánek, Ph.D.

Syllabus

  1. Dynamic properties of a system, stability analysis. System properties. PID controller.
  2. Simulation of a branched control loop with disturbance measurement – control response without and with disturbance measurement.
  3. Modeling of a multivariable control loop. Practical ensuring of loop autonomy.
  4. State-space representation of a system.
  5. Pole-placement method.
  6. State observer.
  7. LQR and LQG controllers.
  8. MPC 1
  9. MPC 2
  10. Fuzzy controller.
  11. Control of nonlinear systems.
  12. Controller design using evolutionary methods.
  13. Credit (assessment).