Course detail

Control of Linear Time-Invariant Systems

FSI-VA1 Acad. year: 2026/2027 Winter semester

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.

Supervisor

doc. Ing. Pavel Škrabánek, Ph.D.

Department

Institute of Automation and Computer Science

Learning outcomes of the course unit

Prerequisites

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.

Planned learning activities and teaching methods

Assesment methods and criteria linked to learning outcomes

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.

Language of instruction

Czech

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.

Specification of controlled education, way of implementation and compensation for absences

The study programmes with the given course

Programme N-AIŘ-P: Applied Computer Science and Control, Master's
branch ---: no specialisation, 6 credits, compulsory

Type of course unit

 

Lecture

39 hours, optionally

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.

Computer-assisted exercise

26 hours, compulsory

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).