•  PhD courses:
COMPUTER AND INFORMATION SCIENCES DEPARTMENT
Information Systems Track
1. Topics in Computer Science (Probability and Statistics)
2. Machine Learning
3. Text Mining and Natural Language Processing
4. Neural Computation
5. Programming Techniques
6. Computer Networks and Communication
7. Artificial Intelligence
8. Knowledge Discovery and Data Mining

•  US evaluation:
Postgraduate studies 1 year with GPA: 4.0
BS EE with GPA: 3.32

•  Online courses and Summer Shools:
2011
Stanford University Online Course: Introduction to Artificial Intelligence
2000 
Summer School in Aachen: Soft Computing in Medicine
RWTH Aachen in cooperation with Erudit
2000 
Postgraduate Course: Fuzzy Control, 2.5 ECTS Credits
Technical University of Danemark
Institution: Faculty of Electrical Engineering, University of Beograd

CONTROL SYSTEMS DIVISION
Control Curriculum
Explanation: 
(the grade scale ranges from 5 to 10 passing grades are from 6 to 10)
No. Course title ((lectures + teaching exercises + lab) hours per week) grade
1. Biomedical Instrumentation () 10
2. French () passed 
3. Selected Chapters on Sensors and Actuators () 10
4. Pattern Recognition () 10
5. Artificial Intelligence & Neural Networks () 10

•  Undergraduate Courses in detail:
Institution: Faculty of Electrical Engineering, University of Beograd

ELECTRONICS, TELECOMUNICATIONS AND CONTROL DIVISION
Control Curriculum
Explanation: 
(the grade scale ranges from 5 to 10 passing grades are from 6 to 10)
No. Course title ((lectures + teaching exercises + lab) hours per week) grade
I Year I II
1. Mathematics I (4+4) 9
Predicate calculus, formal theories. Theory of sets. Boolean algebra. Combinatorics and graph theory. General Algebra: groups, rings, fields, axiomes of real numbers. Complex numbers. Polinomials and rational functions. Linear algebra: vector spaces, systems of linear algebaric equations, determinants, matrices, eigenvectors, eigenvalues. Analitic geometry.
2. Mathematics II (4+4) 9
Limit processes: sequences and functions. Metric spaces. Ortonormal spaces. Differential calculus of one and more variables. Integral calculus: definite and indefinite integrals, improper integrals. Theory of series: numerical and functional, Taylor series. Theory of ordinary differential equations.
3. Fundamentals of Electrical Eng. (4+3) (4+4+1) 8
Electrostatics: the Coulomb's law and the electric field vector, potential, the Gauss's law, conductors and the dielectrics in electrostatic field, electric forces and energy, motion of a charged particle in electrostatic field. Time-constant electric current: basic concepts, First Kirchoff's law, conductivity and resistivity, resistors and the Ohm's law, the Jule's law, the electric generators and the second Kirchoff's law, the methods for solving the electric circuit problems - loop currents and node potentials, the theorems of electric circuits: superposition theorem, reciprocity theorem, the Thevenin's theorem, the compensation theorem, and the theorem of conserving of energy, the basic electrical measurments, electric circuits with capacitors. Time constant magnetic field: the Biot-Savart law, the magnetic forces and torques, the magnetic flux, motion of a charged particle in a magnetic field, the Ampere's law, the generalised Ampere's law, the magnetic properties of materials, the magnet ic circuits. Time-varying electric and magnetic fields: the Faraday's law, self inductance and mutual inductance, energy and forces in the magnetic field, the general electromagnetic field equations. Electric circuits with time-varying currents: the basic equations, circuits with time-harmonic currents, the Kirchoff's laws in complex form, three-phase systems, basic electrical measurments, basic concepts on transients.
4. Physics (3+2) (3+2+2) 7
Standards and elementary theories in phisics. Mechanics: Kinematics, Dynamics. Weight and acceleration due to gravity. Motion of inclined and declined plane. Impulse. Conservation of momentum. Mechanical work and power. Potential and kinetic energy. Non inertial coordinate systems and inertial forces. Special and general theory of relativity. Gravity: Newton's law, Gauss's law and Kepler's laws. Statics or equilibrium. Dynamics of rotation. Conservaton laws: angular momentum,energy, center of mass.Elements of collision theory. Elastic body mechanics. Fluid theory-elements. Heat propagation theory and thermodinamics. Molecular-kinetic theory of gases. Mechanical oscillations. Wawe propagation. Elements of geometrical and phsycal optics.
5. Fundamentals of Computer Eng. (2+2) (2+2) 9
Boolean algebra. Switching circuits. Minimization. Karnaugh maps. Combinational and sequential switching cicruits. Logic and memory elements. Analysis and synthesis of combinational and synchronous sequential circuits. Microoperations. Register interconections, busses. Decoders, multiplexers, ALU, Registers, shifters. RAM. Computer structure. Processor, memory, I/O devices. Instruction formats, data types, adressing modes, instruction set. Processor organization. Interrupt. I/O organization. DMA.
6. Sociology (2+1) (2+0) 9 
The concept and meaning of sociology as a social science. Problems of society and its structure (family, classes and social stratification, nations and national problems today, govering over society and the state, bureacuracy and technocracy). Human culture and civilisation (religion and spirutual human life, ethics and society, philosophy, science and ideology, social changes and development (scientific-techincal progres and social development). Goverment structure. Legislation. Economic politics.
Regulations.
7. National defence (3+0) (3+0) 9
Theory of warfare. Modern warfare. Strategic disposition of Yugoslavia. Guerrilla warfare. Conception of national defence. The structure of armed forces. National security. Civil defence.
II Year III IV
8. Mathematics III (4+4) (4+4) 9
Functions of several variables. Line and multiple integrals. Surface integrals. Field theory and vector calculus. Fourier's series and transform. Theory of partial differential equations. Introduction to mathematical physics. Laplace transform. Complex analysis. Theory of probability. Optimization techniques. Introduction to special functions. Galois fields and codes. Graphs and nets.
9. Technology of Electrical Materials (3+1+1) 6
Cristal structure of solid bodies. Materials division into conductors, semiconductors and dielectrics (clasification in respect of specific electrical resistivity and energy gap). Zonal model of solid bodies. Semiconductors: Si, GaAs and other semiconductor compounds and alloys, fabrication processes of thin monocrystal films. Planar techology of Si integrated circuits. Technology of thin film integrated circuits. Hybrid technologies. Isolaton techniques. Bipolar cicuits designing, MOS technologies, Further development prospects of microelectronics technologies and materials. Dielectric materials: paraelectrics, feroelectrics. Technical use of dielectrics. Piezoelectric effect. Dielectrics in time-varying electric fields. Magnetic materials: paramagnetics, diamagnetics and feromagnetics. Technical use of magnetics. Conductors and superconductors.
10. Technical Mechanics and Hydraulics (3+2) 6
Kinematics: uniform and nonuniform motion of a particle, translator and rotational motion of a rigid body, planar motion of a rigid body, relative motion of a particle, relative motion of a rigid body. Dynamics of a heavy particle: introduction to dynamics, laws of Dynamics,differential equations of motion and theirs integration, laws of conservation in mechanics, forced motion of a partcle and D'Alembert's principle, oscillatiory motion of a particle, moving of a particle due to central force. Dynamics of a rigid body: introduction to system dynamics, laws of conservations in system dynamics, D'Alembert's principle for system, virtual movement principle, the general equation of dinamic. Collision theory.
11. English I . . 9
12. English II . . 9
13. Electrical Circuit Theory (2+2) (2+2) 6
Modelling of physical circuits. Basic concepts of the network topology. Applied gpaph theory. Kirchoff's laws. Circuit elements: two-, three-, and multiterminal elements. Energy and passivity. Basic exication functions. Time domain analysis: classical approach (using one differential equation: suorce free (zero - input), zero-state and complete response), state space approach and analysis using superposition and convolution integrals. Frequency domain analysis: steady state responces: sinusoidal, pseudo-sinusoidal and periodical - the analysis using complex representatives, complex network functions and their properties, resonant and antiresonant cicuits, circuit analysis using integral transforms: Fourier's and Laplace's, circuits with arbitrary order of complexity: the general circuit model (tableau model), loop and nodal analysis, analysis of degenerative circuits - the modified nodal analysis. Two port network analysis: network equations (basic and derived parameters), interconnections of networks, regularity of interconnections (Brune's test), equivalent networks, special networks : filters, equalisers and matching networks. Analysis of distributed parmeter networks: electrical trasmision lines - basic equations, basic and derived parameters, properties of progressive waves, transmision line terminated by arbitrary impedance, reflection, applications of transmision lines.
14. Programmning Languages and methods (2+2) (3+2) 9
Survey and classification of programming languages. Introduction to computer based problem solving. Data structures, operatores, objects. High level language constructions and cotrol structures. Input and output of data. Pseudolanguages. Program development methods. Programming language PASCAL. Syntaxes and semantics of programming languages. Complexity, correcness and performance of algorithms. Programming language BASIC and its use on personal computers. Programming language FORTRAN 77 and its application in engeneering problems solving.
15. Electronics (3+3+1) (3+2+1) 6
Semiconductor physics: electrons and holes in semiconductors, intrisic semiconductors, continuity equation, drift and diffusion of electrons and holes, the Einstein relation, carrier generation and recombination, minority carrier diffusion equations, the PN junction in equilibrium, the junction under reverse and forward bias, junction diode caracteristics, bipolar transistors operating modes and principles, Ebers-Moll 's statical model, operating bondaries, parasitic effects, BJT modelling, field effect transistors (JFET and MOSFET) physics and modelling.Transistors as amplifying elements: common emiter (source), common base (gate), common collector (drain), cascode and differential interconections. Transistor as current source and as a dinamic load in amplifiers. Feedback amplifiers (series and parallel feedback). Multistage amplifiers. Operational amplifiers: design and usage. Frequency caracteristics (Bode plots) of multistage amplifiers. Large signal amplifiers: class A, B, AB, C. Positive feedback and harmonic oscillators: Wien's bridge, Collpits's, Hartley's, Clapp's, Pierce's and Meacham's. DC sources: diode rectifiers (full and half wave), passive filters ( L and PI), and linear stabilizators, overload protection.
III Year V VI
16. Numerical Analysis (3+2) 9
Elements of error theory. Theory of iteration. Numerical methods in linear algebra (convergence of matrix sequences and series, direct methods of solving linear systems of equations, iterative methods, matrix inversion). Methods of solving nonlinear equations: linear iteration, Newton-Raphson's method, Regula falsi method, secant method. Methods of solving systems of nonlinar equations: gradient algorithm, Newton-Rapshon method. Methods of solving algebric equations. Approximation of functions: Lagrange and Hermite interpolation, finite difference calculus, mean quadratic approximation, minimax approximation. Numerical differentiation and integration: formulas for numerical differentiation, Newton-Cotes formulas, Gauss quadratic formulas, composite formulas, Monte Carlo methods. Numerical solving of ordinary differential equatios: Runge-Kutta methods, multiple steps methods, convergence and stability problems.
17. Elements of Electronic Devices (3+1+1) 8
Descrete resistors: linear (wire-, carbonpaste- and metalcoated resistors), nonlinear (thermistors (NTC and PTC), photo resistors, magnetic resistors, VDR), limitatios in usage, high power resistors, low noise resistors, high frequency modelling of varyious resistors. Descrete capacitors: electrolitic, ferodielectric, air, paper, liscun, ceramical.Varicap diodes. Advantages and disadvantages of varyious capacitors. High frequency modelling of a capacitor. Descrete coils: design of a short coils by Kammerloher and Nagaoka's methods, design of a long coils. Design of net transformers. Design of pulse transformers. Relay switches: characteristics, usage. Principles of high power protection with reley system. Reliability of electronic circuits. Redundant design, backup.
18. Measurements in Power Engineering (2+0) 6
Introduction to engeneering measurements. Basic statistics and error theory. Dynamical properties of measurment systems.Force and torsion measurments: measuring ribbon, magnetostrictional sensor. Displacement, velocity and acceleration measurments: potentiometric, cord, inductive and capacitive sensors, optical and inductive encoders, piezoelectric sensors, stroboscopic sensors, interferometric sensors. Pressure measurements: manometric sensors, Bourdone's pipe, film (capacitive, inductive and semiconductor) sensors, resistive sensors, vakuummeters (McLeod's, thermal and ionisational). Fluids speed and flow measurements: volumetric sensors, turbine sensors, rotametric sensors, vortex sensors, laser Doppler's sensors, anemometric sensors, thermal sensors, Pitoo's tube. Thermal measurements: themperature scales, thermodinamical thermometers, thermometers with liquids, manometric thermometers, restive thermometers: linear and thermistoric, thermopars (Peltie's effect). Level measurements: descr ete and continual.
19. Electromagnetics (2+2) 9
Maxwell equations: integral and differential form. Boundary conditions. Complex vectors. Lorentz potentials. Poynting's theorem. Image theorems. Electrostatical field. Poisson and Laplace equations. Point and line dipols. Potential coefficients and partial capacitances. Stationary current field. Grounding. Stationary magnetic field. Elementary current loop. Quasistationary electromagnetic field. Electromagnetic induction. Inductances. Skin, edge and proximity effects. Dynamic electromagnetic field. Uniform plane waves. Propagation through dielectric and conducting media. Reflection from conducting plane. Refraction and reflection at interface between two media. Transmission lines. Field distribution for lines with homogenous dielectric. Telegraph's equations. Transients on transmission lines. Basic properties of transmitting and receiving antennas. Design of fast digital interconections. Electromagnetic compatibility. Electromagnetic protection.
20. Fundamentals of Telecommunications (4+2+1) (4+3+1.5) 7
Communiacation principles. Spectral representation of deterministic signals. Principles of digital communications: Sampling theorem and time-multiplexed systems. Linear transimission systems and signal propagation. Linear and nonlinear distortion of signals. Stochastic signals: random noise, Wiener-Hintchins's theorem, power spectrum of random signals. Signal processing: analog modulations: KAM, AM-DSB, AM-SSB, AM-ASB, FM, PM. Pulse modulations: PAM, PWM, PPM, delta modulation, adaptive delta modulation. S/N ratio and minimal receiveing power. PCM as basic digital modulation. Baseband digital signal transmission. Error probability. Nyquist criterias for ISI. Matched, optimal, transversal and predictional filters for digital transmission. Digital modulatons: ASK, PSK, FSK, MSK, 4PSK, QAM, DPM. Basic telecommuicational services.
21. Automatic Control Systems (3+2+1) (2+2+0.5) 6
Mathematical models of linear dynamic systems (examples from several engeneering fields). Servo systems. Structural block diagrams. Signal flow graphs. Mason's rule for obtaining transfer functions. State space approach: representing of transfer functions as a state space models, controlability, observability. Stability: Lyapunov's and BIBO approach. Stability of stationary continual linear systems, algebraic criteria of stability: Routh's and Hurwitz's, frequency criteria of stability: Mikhailov's and Nyquist's, stability margins. Control performances and quality of a transient process of controlled systems. Frequency methods of analysis and synthesis of control systems: Nichols diagrams and series and parallel compensation with Bode plots. Root locus method of compensation. MIMO systems: treatment of disturbances, feedforward compensation, model of a multivariable system, state feedback and its influece to quality of a transient process, elements of optimal control: Kalman's regulator, designing of a opserver. Analog computer technology. PI and PID industrial regulators.
22. Pulse and Digital Electronic (3+2+2) (3+2+1) 6
Introduction to pulse and digital electronics: analog and digital circuits and signals, number systems and codes. Logical circuits: logical functions and Boolean algebra, minimisation of logical functions, logic elemetns characteristics: ideal logic elements, noise margins, fan out, dynamic characteristics, dissipation and PDP. Switchig characteristics of bipolar elements: junction diodes, Schottky diodes, BJT. Statical and dynamical characteristics. Logical circuits with BJTs: RTL, DTL, TTL, STTL, LSTTL, ASTTL, ALSTTL, FTTL, ECL. Switchig characteristics of MOS transistors. Statical and dynamical characteristics. Logical circuits with MOS transistors: NMOS logical circuits, CMOS logical circuits: 74C, 74HC, 74HCT, 74AC, 74ACT. Interconnection of MOS and TTL logical circuits. Bistable circuits: latch circuits and synchronous flipflops. Comparators: differential and Schmitt's. Monostable and astable pulse generators with CMOS, TTL and ECL logic circuits. Pulse generators with comparators. Integrated timers: NE555 and ICM7555. Saw-tooth generators: Miller's and bootstrap. Combinational circuits: design of complex combinational networks, three state circuits, decoders, encoders, priority circuits, multiplexors (digital and analog). Sequetial circuits: synchronous and asynchronous networks, registers, shift registers, counters. Synchronisation of asynchronous signals, glitch elimination. Programmable logical networks: ROM, PROM, EPROM, EEPROM, PLA, PAL. Computer aided programming of programmable logical networks. Memories: SRAM, DRAM, VDRAM, NVRAM. Aritmetical circuits: adders, subtractors, multipliers, dividers, comparators, ALU. D/A conversion: basic characteristics, D/A converters with coded resistive network, D/A converters with ladder resistive network, capacitive D/A converters. D/A multipliers. A/D conversion: Flash A/D, A/D converters with succesive approximations, following A/D converters, single slope A/D converter s, dual slope A/D converters.
23. Linear Electronics (3+2+1) 7
Characteristics of bipolar and FET transistors at high frequencies: HF small signal models, approximations and restrictions. Analysis of multistage integrated amplifiers: zero time constans method, analysis of differential, cascode and Darlington amplifiers, Butterworth, Chebyshev and Bessel approximation of ideal frequency characteristics. Feedback amplifiers: stability root locus, Routh and Hurwitz criteria, Nyquist method, phase and amplitude margins, Compensation of operational amplifiers (compensation in feedback path, feedforward compensation and active compensation, local feedback compensation). Filters: approximation functions (Butterworth, Chebyshev, Besell, Elyptic), active and passive filters design. Inroduction to SC filters. PLL circuits: analog and digital. Noise in electronic circuits.
IV Year VII VIII
24. Sensors and Actuators (3+0+1) 10
Themal measurements: elements of heat radiation physics, radiometric sensors in different spectral areas. Fiberoptical sensors: principles, displacement sensors interferometric sensors, application in transmission of control signals. Elements of analog signal procession: principles and realisation. Medical sensors: elemets of biophysics, biocompatibility, artifical organs, ECG, computer tomography, NMR, pacemakers. Electrical actuators and its properties: DC, step and AC (synchronous and induction) motors.
25. Microprocessor Electronics (3+2) 8
Organisation of 8-bit and 32-bit microprocessors. Local and system bus: electrical properties and matching impedancees. Interconnection of memory and peripheral units. Assembler language for 80X86 CPU. Mascable and nonmascable interrupts. DMA controler. Interrupt controler. Time synchronisation. EPROM emulator. Software development tools for microprocessor systems.
26. Electrical Machines and Devices (3+1+1) 6
Power plants: thermo, hydro and nuclear power plants. Power distribution. Principles of electromechanical conversion of energy: energy equations and flow charts. Torque and EMF equations. Rewiew of electrical machines. Thermal properties of electrical machines. DC machines: principles, windings, equations. DC generators: characteristics. DC motors: characteristics, ignition, speed regulation, breaking, regenerative breaking, losses, parasitic effects in DC machines. Technical use: advantages and disadvantages of DC machines. High power transformers: construction, protection, modelling. Power losses. Irregular work. Three-phase transformers: coupling and parallel work. Special types of transformers. Induction motors: construction and properties. Magnetic flux waves. Modelling. Torque and current equations. Ignition. Speed control. Special types of induction motors. Power losses. Synchronous machines: construction and properties. Rotating magnetic fields. Torque equation. Modelling. Synchronous generators: paralel work. Power factor correction with synchronous machines. Servomotors. Basic principles of power electronic.
27. Digital Control Systems (3+2) 9
Structure of digital control systems. Sampling: frequency and s-domain characteristics of sampled signals. Hold circuits. Z and modified z transform: properties and usage. Transfer functions algebra (z-domain). Realisation of digital transfer functions: recursive algorithm, DFT algorithm. State space description of digital systems: controlability and observability. Numerical approximations in digital control systems: Euler's and Tustin's approximation. Stability: Jury's test and Nyquist method. Lyapunov's method. Design of digital controllers: control performances and quality of a transient process criteria. Root-loci method. Types of digital compensation: direct, parallel, feedforward. Design of digital PID controllers: Ziegler-Nichols and Takahashi alogithm. Dahlin's algorithm. MIMO digital systems: optimal control and design of optimal controllers. State feedback: properties. Digital observers. Deadbeat controllers.
28. Stochastic Systems and Estimation (3+2) 9
Classical theory of estimation: parametric and space approach. Bayes's method of minimal risk. Minimal variation and maximum aposterior probability estimators. Maximum likehood estimators. Recursive estimators. Stochastic processes and signals: basic properties. Gauss-Markov's chains. Frequency modelling of stochastic signals. Spectral representation and decomposition. ARMAX modells. Stochastic differential and difference equations. State-space representation of stochastic systems. Design of estimators: frequency and time-domain approach. Wiener's filter: analog and digital. Properties and restrictions. Kalman's filter: analog and digital. Properties and usage. Connection between optimal regulator and Kalman's filter.
29. Nonlinear Control Systems (2+2+1) 8
Nonlinear dynamical systems with changing parameters - mathematical modelling - problems. Model structure. Control inputs. Initial conditions. Disturbance vector. Local character of linear model of control system. Regulators nNonlinear elements. Structural nonlinearities. Autonomous and non autonomous working regime. Various oscillations. Hold circuits. Input spectar transformation. Second order systems and phase plane method. Harmonic linearisation and equivalent transfer function. Stability of nonlinear dynamical stability. Asymptotic stability. Global asymptotic stability. Movement stability. Lyapunov direct method. Apsolute stability. Popov frequency criteria. Hyperstability. Nonlinear regulation problems. Asymptotic stability in tracking system. Design of tracking feedforward+feedback controller. Feedback linearisation. Monovariable system input-state and input-output linearisation. Application on multivariable systems. Regulators. Adaptive control and conditions for robust adaptive nonlinear systems control. Systems with divided parameters. Transform to nonlinear system in order to design nonlinear regulator. Examples. Multivariable system with constant and/or non constant parameters in continual/discrete linear/nonlinear regime, with deterministic/stohastic inputs and or disturbances - simulation.
30. Power Electronics (3+2) 6
Semiconductor switching devices: diodes, BJT's, MOSFET's, thyristors, GTO thyristors, IGBT transistors. Controlled and uncontrolled AC/DC converters: fullbridge and halfbridge converters. Three-phase converters. Principles of phase control. DC/DC converters: buck, boost, buck-boost, cuk, fullbridge. DC/DC converters control: PWM control, current control. Drive circuits and snubbers. Commutation methods in thyristor circuits. DC/AC converters: fast and slow switching topologies. Resonant converters. DC power suorces: flyback, forward, push-pull, halfbridge and fullbridge topologies. UPS. Motor drives: DC servosystems, V/f and vector control of induction motors, control of brushless motors. Step motor drives.
31. Computer Systems in Control (3+2) 6
Properties of computer controlled systems. Computer in feedback path. Interconnection of a computer and a controlled process. Types of interconnection. Data exchange through paralell data adapters. Synchronisation. Standard ports (8255). Parallel bus: synchronisation, standards, trancievers. Handshake principles. Programmed I/O and interrupted I/O. Serial busses: synchronous and asynchronous, standards. Timers and RTCs: programmed, hardware and programmable, watch-dog timer. Programmable controllers. Typical I/O modules and interconnection: D/A, A/D, registers, counters, encoders, step motors. Interrupt controllers. Data aquisition. I/O subsystems. Design of high quality servo systems.
32. Process Identification (2+2) 6
Introduction to system identification: problems and properties. Modelling problems and criterias. Measurable and unmeasureble disturbances. Least squares (LS) method. Gradient method, Gauss-Newton's method. Marquardt's algorithm. Linear dynamical SISO systems modelling: digital and analog models. Maximum likehood and twostage method. Recursive algorithms: gradient and LS. Identification of MIMO systems. Rafined Ziegler-Nichols method (RZN). Automatic tuning of digital PID controllers.
33. Real Time Process Control (3+2) 6
Introduction to real time systems control. Computers in Systems control. Information functions: gathering information, displaying information and alarms. Control functions control in closed loop, sequential control, supervision, planing, hierarchical and distributed control. Elements for interconnection between computer and controlled system. Sensors, and actuators. Sensors Characteristics: precision, resolution, repeatedness, stability, range, linearity. Adaptation of signals from sensors. Relay and continual actuators. Interconnection between computer and actuator and technics of checking actuator’s accuracy. Continual regulator programming. Continual Transfer functions discretisation. Structure of digital regulators. Self tuning regulators. Programming direct digital control. Types of algorithms. Changing of woking regime. Actuator’s saturation. Input signal filtering. Transport delay due to calculation. Finite word effects. Sampling time period. Sequential control realisation. PLC Organisation and protramming. Real time OS elements. Software design. Tasks organisation. Time sync. Distributed computer systems for Real time control. Computer interconnection and standards. Local area network. Distributed OS. Response time. Distributed systems design methodology. Real time systems reliability. Error detection and diagnostics. System failure prevention and system recovery. Configuration reliability and redundant systems. Real time system design examples. Closed loop control. Sequential control. Information system.
34. Digital Signal Processing (3+2) 10
Discrete Fourier series and DFT: properties, circular convolution, evaluation of linear convolution with DFT. FFT algorithms. Overlap-save and overlap-add algorithms. Design of digital filters: IIR (connection with analog filters: impulse invariant response and bilinear transform), FIR: properties and window functions: Bartlett, von Hann, Hamming, Blackman, Kaiser. CAD of digital filters: MATLAB. Spectral estimation of random signals: classical approach: peridogram, Bartlett's method, Blackman-Tukey method, Weltch's method. Properties of classical estimators: displacement and variation. Parametric modelling of random signals: Yulle-Walker's equations, properties of AR, MA and ARMA modells. AR modells: linear prediction, Levinson's algorithm, ladder representation, maximum likehood method, autocorelation and covariant methods, Burg's method. MA modells: Durbin's method. ARMA modells: maximum likehood methods, modified Yulle-Walker's equation s, two and three step methods. Introduction to adaptive filters: recursive methods. Adaptive FIR filters.
35. Robotics and Automatisation (3+2) 8
Introduction. Automatisation and flexible automatisation. Robots in industry. CIM. CAD/CAM. Production systems elements. Handling methods cutting, deformation... CNC plane, picker, handling cetnre...Quality control. Transport. Installing problems. Storing. Integration. Flexible automatisation. Flexible manufacturing sell, line and system. Hierarchical control organization. Robots systems - introduction. History and divisions. Non industrial division (medicine, transport,...). Configuration and robot movements. Kinematics and dinamics. Power systems. “hands”. Sensors in robotics. Control. Computer system hierarchical structure. Control types point to point and contour. Robots in industry. Applications. Material transfer and machine supply. Operations. Installing. Quality control. Modelling, simulation and programming in robotics. Expert systems in robotics. Examples. CNC robots and flexible cell programming.
V Year IX X
36. Process Control (3+2) 9
Introduction, problems and properties. Working regime. Design requirements technical, technological and economical. Goal function and limits. Program control and closed loop control. Systems control structure. Operator’s role. Optimal control. Use of nonlinear model. Required conditions for goal function minimum without limits. Systems with optimal speed and maximum principle. Principle. Dinamical programming, reccurent relations. Optimal control realisation in closed loop. Analysis of optimal control use on nonlinear and nonstabile electro mechanical system. Multivariable optimal linear regulator. Use of linear model and LQG. Various types of regulations (Optimal trajectory regulation...) P, and PI continual and discrete regulator with state feedback. Physical interpretation of state space. Use of observer in optimal regulator realisation. Design procedure. Analog and digital optimal regulator with state feedback for stabilization of nonlinear and nonstabile electromechanical system - analysis. Multivariable predictive linear regulator. Multivariable output regulator. Interaction, choices procedures. Predictive regulators. Smith predictor. Use of various responses in regulator realisation. Prediction horison. Reference model. Predictive regulator based on use multidimensional diferential equation. Compensation of measurable disturbances and local regulators. Design with control signal limits. Tuning and adaptation. Use of observer and state space discrete model in predictive regulator design. Use in digital control of real termical process - analysis.
37. Real time programming (3+1+1) 9
C++ programming language. Basic elements. Data types. Control structures. Input/output and system lybrary. Structural types. Access to hardware. Special (nonstandard) extensions. OS. OS Basics. OS components. Concurent and parallel execution. Communication and sync. “Real time” applications programming. Input/output and interrupt routines.APLI. Automation applications.
38. Artificial Inteligence and Neural Networks (3+1+1) 10
Introduction. Ideas in AI. Historical review. Radical thesis and Denial of AI. Basic Concepts. Production Systems. Definition. Examples. Divisions. Control strategies. Different search methods. A algorithm & A* algorithm. Heuristics and their restauraitons. Predicate calculus and types in AI systems. Unification. Rezolution. Implementation. Fuzzy sets and Fuzzy Logic basic and examples. Neural Networks. Divisions. Multilayer perceptron. Back propaagation algrithm. Generalisation. Metodhs for improving. Applications.
39. Biomedical Instrumentation (3+1+1) 10
Electrical activity of excitable cells. Biopotential electricity. Electrical behaviour and circuit models. Biopotential amplifier. Analog processing of biopotentials. Sensors in biomedical measurements. EMG, ENG, ECG, EEG recordings. Ultrasound in medicine. Ultrasound tomography, cardiosongraphy, measurements of the blood flow using Dopler ultrasound. Chemical biosensors. blood-gas and acid base physiology. Clinical lab instrumentation, spectrophotometry, chromatology, electrophoresis, hematology. Therapeutic and prosthetic devices. Cardiac pacemaker defibrilators, lithotripsy, laser surgery.
40. Pattern recognition (3+1+1) 10
Introduction to linear algebra, random variables and stochastic processes. Hypothesis Tests (Bayes test, Test of miniminal cost, Neyman-Pearson test, Min-max test, Test of one hypothesis, Sequential test, Wald's test). Operational characteristics; Burdick's chart; Upper boundaries of error probability; Bhattacharya distance. Parametric classifiers: Linear classifiers; Piece-wise linear classifiers; Quadratic classifiers. Nonparametric classifiers Pearson's estimators; Hystogram methods; k Nearest Neighbour method. Dimension reduction: Karhunen-Loeve expansion; Scatter matrix and dimension reduction based on them. Clustering: Branch and bound method; c-mean clustering; Normal decomposition; Maximum-likelihood approach. Introduction to soft-computing (neural networks and fuzzy systems) and its application in pattern recogniton problems. Textbook: Keinosuke Fukunaga: Introduction to Statistical Pattern Recognition.
41. Production Process Organization (3+1) 8
Basis mathematical techniques in economics. Supply, demand, pricing, cost of production. Elasticity. Optimisation. Linear programming. PERT graphs, etc. Prediction and planning. Shopfloor planning. Investment analysis. Discussion of human goals and incentives.
42. Diploma Thesis (from the course Stochastic Systems and Estimation) (18) 10 
Linearisation of 6 DOF Missile Model
Abstract. 
My diploma thesis was part of a problem nonlinear system is considered. The system was described by 6 DOF model and it was represented by 12 nonlinear differential equations. In order to apply the standard LQG control strategy, my task was to linearise the model concerned in the surrounding of properly chosen operating points. It has been done by using velocity linearisation. All results were verified by detailed computer simulations using Matlab program package.