• Automatic Control, Semester 1, position 1

Introducing of: nature of computer control systems (CCS) related to types of signal transfer; real CCS as mainly presented in the practice; choice of physical model of CCS; mathematical modeling of CCS. Mastering of: methods of determining of static and dynamic characteristics of CCS; real time computer control by discrete algorithms. "Offline" use of MATLAB and SIMULINK аs software standard of automatic control.

Exact but not approximate treatment of CCS according to their discrete nature. Scientific and engineering treatment of CCS as dominantly represented in practice. Applying the methods of analysis and synthesis of a controller in CCS, as well of whole CCS. Solving problems of calculation nature by means of computer and MATLAB and SIMULINK in the "offline" mode, related to the analysis or synthesis of CCS. Determining of dynamic and static characteristics of CCS.

Introduction in Computer Control (CC): specific nature of CCS, importance and examples. Samplers, quantization and coding: real and ideal samplers, mathematical description, technical realization, description of quantization and coding. Complex and frequency images of ideal sampler output: determination, Shannon's theorem. CCS transfer characteristics: definition in the frequency and s-domain. Systems for signal duration extension: definition, analysis and transfer characteristics. Z-transform: definition, transfer characteristics in z-domain. Block diagrams of CCS: аlgebra of s and z block diagrams. Modeling and analysis of CCS: classical mathematical modeling, static characteristics and types of action. State concept of CCS: modern mathematical modeling, properties and solving. Dynamic properties of CCS: definitions, determining, criteria.

PA: Graphical determination of the signal in the receiver. Analytical calculation of time discrete signal x*(t). Quantization and coding of signals. All three forms of the discrete complex X*(s) and frequency image X*(jω) of the output signal of the ideal sampler. Application of Shannon's theorem. Characteristics of the zero order hold. Z transformation. Analysis of z-images. Application of z-block algebra. Discretization of the differential equation of behavior. Determination of the discrete (difference) equation of state and output and their solutions. Examples of testing the controllability, observability and stability of the system. PL: Work in MATLAB and SIMULINK: simulation of types of signal transmission, determination of X*(s), X*(jω), frequency spectrum of input and output signal of ideal sampler and low-pass filter, determination of z-images. Simulation of discrete mathematical models in Simulink. Determination of dynamic properties. Computer control of a physical object in real time. PZ: Manipulation with mathematical models, examination of static and dynamic characteristics of discrete systems. Manipulation with mathematical models, examination of the characteristics of discrete systems in transient and stationary regime.

Basic knowledge of automatic control. Basic computer knowledge based on use of PC. Basic knowledge of undergraduate mathematics.

Script for Computer control (in Serbian). Modular educational real time control system with various control plants (DC servo motor, inverted pendulum, double inverted pendulum, heat flow experiment, coupled water tanks experiment), with acquisition hardware and software. Power source, function generator, oscilloscope, PCs. Siemens Simatic PLC.

Total assigned hours: 75

New material: 20
Elaboration and examples (recapitulation): 10

Auditory exercises: 16
Laboratory exercises: 7
Calculation tasks: 0
Seminar paper: 0
Project: 7
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 0
Review and grading of lab reports: 0
Review and grading of seminar papers: 0
Review and grading of the project: 5
Test: 5
Test: 0
Final exam: 5

Activity during lectures: 5
Test/test: 55
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 0
Project: 10
Final exam: 30
Requirement for taking the exam (required number of points): 21

Lj. Grujić, Discrete Systems (in Serbian), ISBN: 86-7083-180-5, Faculty of Mechanical Engineering, Belgrade 1991.; K. J. Astrom, B. Wittenmark, Computer-Controlled Systems: Theory and Design, ISBN: 7-302-05008-2, Prentice Hall, Hoboken, 1997.; C. L. Phillips, H. T. Nagle, A. Chakrabortty, Digital Control System Analysis and Design, ISBN: 1-292-06122-7, Pearson, Edinburgh Gate, 2015.; C. H. Houpis, G. B. Lamont, Digital control systems, ISBN: 0-07-030500-5, McGraw-Hill, New York, 1992.