Course detail
Theory of Dynamic Systems
FEKT-MPC-TDSAcad. year: 2024/2025
Systems theory, systemic approach, cybernetics. I/O and state space approach to the analysis and design of dynamic systems, mutual conversions. Continuous, discrete, linear, non-linear, time invariant and time variant systems. System stability. System decomposition. SISO and MIMO systems. Controllability, reachability, observability, reconstructability and realizability of systems. State observers and state feedback. Deterministic and stochastic systems. Bayesian approach to estimation. Kalman filter.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Entry knowledge
Rules for evaluation and completion of the course
Individual project - Max. 15 points.
Final Exam - Max. 70 points.
The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.
Aims
After passing the course, the student is able to:
- demonstrate and explain the difference between state space and input output description of the system
- explain the concept of causality, realizability, reachability, controlability, observability and reconstructability of the system
- identify and approximate basic types of dynamic systems and discretize the system
- apply the principles of block algebra and Mason’s gain rule for the evaluation of the system’s transfer function
- design the state observer and state feedback
- explain Bayesian approach to estimation and the principle of Kalman filter
Study aids
Prerequisites and corequisites
Basic literature
Štecha, J., Havlena, V.:Teorie dynamických systémů. Vydavatelství ČVUT, Praha, 1999. (CS)
Recommended reading
Elearning
Classification of course in study plans
- Programme MPC-KAM Master's 1 year of study, winter semester, compulsory
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
2. Different types of system description: input-output, transfer function, frequency response, polynomials.
3. State space description, state equations, their solution. Modeling of dynamical systems in MATLAB Simulink.
4. Model realization: serial, parallel, direct programming. Canonical forms.
5. Controllability, reachability, observability, reconstruct-ability of systems.
6. Block algebra. Masons’s gain rule for transfer function computation.
7. State feedback. State observers.
8. Methods of continuous time system discretization.
9. Stability of linear and nonlinear systems, stability of interval polynomials.
10. Multi input multi output systems.
11. Bayesian approach to parameter estimation.
12. Kalman filter.
13. Reserve, review.
Fundamentals seminar
Teacher / Lecturer
Syllabus
2. Conversion of block diagram to signal flow graph. Utilization of Mason’s gain rule. Determination of observability index for the system with two inputs.
3. State feedback design. Design of identity observer with required dynamics.
4. Computation of discrete equivalents of continuous time systems – system with zero order hold, Euler and Tustin approximation, method of equivalent zeros and poles.
5. Determination of stability. Interval polynomial stability.
6. Description and control of MIMO systems. Decoupling of cross-couplings in MIMO systems.
7. Work on the project.
Exercise in computer lab
Teacher / Lecturer
Syllabus
2. Canonical forms of state space description implementation in MATLAB Simulink. State space description as Level 2 MATLAB S-function (continuous / discrete).
3. Calculation of the controllability, reachability, observability and reconstructability of the system using MATLAB functions. Creation of input function generators in Simulink. Transformation of state space descriptions.
4. State feedback using acker, place and reg commands, implementation of state controller in Simulink environment, commands for connecting systems described by state space equations.
5. estim command, state observer testing in Simulink, state feedback from state observer output. Different types of discretization of continuous time systems.
6. Testing the stability of linear and nonlinear dynamic systems. Multi-dimensional systems in MATLAB Simulink.
Elearning