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Control Systems Analysis

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code450-2034/05
Number of ECTS Credits Allocated4 ECTS credits
Type of Course Unit *Choice-compulsory type B
Level of Course Unit *First Cycle
Year of Study *Third Year
Semester when the Course Unit is deliveredWinter Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites
PrerequisitiesCourse Unit CodeCourse Unit Title
450-2019Cybernetics
Name of Lecturer(s)Personal IDName
PIE046Ing. Martin Pieš, Ph.D.
Summary
The course extends the knowledge of the subject Cybernetics and provides more detailed explanations of concepts from the field of control and deals with the properties of control systems. Students will gradually get acquainted with analysis of continuous and discrete linear dynamic systems, especially with their external and internal description. Regarding the properties of dynamic systems, it will discuss stability, controllability, reachability and observability. Students also get acquainted with the methods of identification of dynamical systems. It will be followed by analysis of linear control systems in both frequency and time domain. It also discusses the stability of control circuits, the static accuracy and quality control.
Learning Outcomes of the Course Unit
The aim of the course is to provide students with a broader basis of the analysis of dynamic systems and control circuits. This part of the theory of automatic control is required for the following master's degree. Students will be able to practically carry out dynamic system identification and to analyze properties of dynamical systems and control circuits using computer technology and simulation systems, in particular, Simulink and Matlab / Scilab.
Course Contents
Lectures:

1. Introduction to the analysis of control systems. The mathematical background necessary for systems analysis.
2. The basic dynamic systems - Proportional, Integral , Derivative , the inertia, the second order, transport delay. Basic types of discrete systems. Proportional system. Summator, derivative system, inertia. The oscillating systems of the first and the second order.
3. Couplings between systems. Solving equations of continuous systems. The transition matrix. Generators input functions. Diagram of state variables. State-space and input/output description of the system. The state equation and transmission matrix. Transfer between state-space and input/output description. Frobenius and Jordan canonical form.
4. Solving equations of discrete systems . The transition matrix. Generator of input functions. Diagram of state variables. State-space representations of discrete systems. State-space and input/output description of the system. The state equation and transmission matrix. Frobenius and Jordan canonical form.
5. Context of continuous and discrete system description. Discretization of continuous systems. Frequency analysis of sampling. Zero-order and first order hold systems.
6. The feedback loop - a detailed description of the functionality. Block diagram, standard transfer function defined for the circuit.
7. Static and dynamic properties of the controllers.
8. Analysis of the feedback circuits in the time domain. Stability, static accuracy and control quality. Integral criteria of control quality. Criteria for controllability, reachability, observability and reconstructability. Analysis of continuous and discrete control systems in state space.
9. Analysis of feedback circuits in the frequency domain. Stability. Analysis using the frequency characteristics. Root locus method.
10. Nonlinear control systems.
11. Methods of identification of the systems. Experimental identification. Identification using deterministic signals. Identification using stochastic signals.
12. Methods for online identification of systems parameters. Solving problems by least squares method. OE models, ARX, ARMAX, and their use in the identification of system parameters
13. Case Study Part 1 - Analysis of educational physical models in the time and frequency domains - laboratory task.
14. Case Study Part 2 - Analysis of educational physical models in the time and frequency domains - laboratory task.

Exercises:

1. Getting acquainted with the outline of the course and with the laboratory. Safety training.
2. The basic dynamic systems and their static and dynamic properties, demonstration in Matlab and Simulink /Scilab.
3. The state-space description of continuous systems, demonstration in Matlab and Simulink /Scilab
4. The internal state description of discrete systems, in Matlab and Simulink /Scilab.
5. Context of continuous and discrete system description, demonstration in Matlab and Simulink /Scilab - laboratory task.
6. Feedback control circuit, demonstration in Matlab and Simulink /Scilab.
7. Static and dynamic characteristics of the controllers, demonstration in Matlab and Simulink /Scilab - laboratory task.
8. Analysis of the feedback circuits in the time domain.
9. Analysis of feedback circuits in the frequency domain.
10. Analysis of nonlinear control circuits.
11. Identification systems, demonstration in Matlab and Simulink /Scilab - laboratory task.
12. Working on projects - practical part of offline identification.
13. Working on projects - practical part of online identification.
14. Credits, project control.

Projects:
Each student gets assignment of one project to be processed by PC. Time consumption: appx. 10 hours. The title of the project: Analysis of continuous and discrete cascade and multidimensional control circuits, static and dynamic optimization.
Recommended or Required Reading
Required Reading:
Ogata, K. (2010). Modern control engineering. Boston, Prentice Hall.
[1] Ožana, Š., Srovnal,V: Analýza regulačních systémů. Učební text a návody do cvičení. VŠB-TUO, FEI, 2012.
[2] Balátě, J. (2004). Automatické řízení. Praha, BEN - technická literatura.
[3] Vavřín,P.: Teorie automatického řízení I. Brno, VUT 1991.
Recommended Reading:
Franklin,G.F.,at all.:Digital Control of Dynamic Systems. Adison-Wesley 1992.
Ogata,K.:Discrete-time Control Systems.Prentice-Hall 1987.
Shinners,S.M.:Modern Control System Theory and Design. John Wiley&Sons 1992
Štecha,J: Teorie automatického řízení I. Praha, ČVUT 1990.
Vavřín,V.: Teorie dynamických systémů. Brno, VUT 1989.
Ogata, K. (2010). Modern control engineering. Boston, Prentice Hall.

Planned learning activities and teaching methods
Lectures, Tutorials, Project work
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit35 15
        ExaminationExamination65 16