Course detail
Theory of Dynamic Systems
FEKT-MPC-TDSAcad. year: 2022/2023
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
Czech
Number of ECTS credits
7
Mode of study
Not applicable.
Guarantor
Learning outcomes of the course unit
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
- 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
Prerequisites
The subject knowledge on the Bachelor´s degree level is requested.
Co-requisites
Not applicable.
Planned learning activities and teaching methods
Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations. Materials for lectures and exercises are available for students from web pages of the course. Students have to write a single project/assignment during the course.
Assesment methods and criteria linked to learning outcomes
Numerical Exercises - Max 15 points.
Individual project - Max. 15 points.
Final Exam - Max. 70 points.
Individual project - Max. 15 points.
Final Exam - Max. 70 points.
Course curriculum
1. Dynamic system definition and subdivision.
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, recapitulation.
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, recapitulation.
Work placements
Not applicable.
Aims
The aim of the course is to introduce general system theory and its application to dynamic systems and systemic approach towards control tasks solution.
Specification of controlled education, way of implementation and compensation for absences
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.
Recommended optional programme components
Not applicable.
Prerequisites and corequisites
Not applicable.
Basic literature
Blaha, P., Bortlík, P., Veselý, L.: Teorie dynamických systémů - sbírka úloh. Skriptum VUT, 2016. (CS)
Štecha, J., Havlena, V.:Teorie dynamických systémů. Vydavatelství ČVUT, Praha, 1999. (CS)
Štecha, J., Havlena, V.:Teorie dynamických systémů. Vydavatelství ČVUT, Praha, 1999. (CS)
Recommended reading
Not applicable.
Elearning
eLearning: currently opened course
Classification of course in study plans
- Programme MPC-KAM Master's 1 year of study, winter semester, compulsory
Type of course unit
Lecture
39 hod., optionally
Teacher / Lecturer
Syllabus
1. Dynamic systems - definition and subdivision.
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.
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
14 hod., compulsory
Teacher / Lecturer
Syllabus
1. Different descriptions of dynamic systems, state space descripaztion, input function generators.
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.
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
12 hod., compulsory
Teacher / Lecturer
Syllabus
1. Recapitulation of the possibilities of entering dynamic systems in MATLAB and Simulink. Using a Symbolic Toolbox to calculate Laplace transform and Z transform.
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.
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
eLearning: currently opened course