Convex Optimization
- Instructor: Amirhossein Nikoofard
Course outline
- Introduction
- Convex sets
- Convex functions
- Convex optimization problems
- Duality
- Approximation and fitting
- Statistical estimation
- Numerical linear algebra background
- Unconstrained minimization
- Equality constrained minimization
- Interior-point methods
- Advanced Topics on Convex optimization
Textbooks
- Boyd & L. Vandenberghe, “Convex Optimization ,” Cambridge Univ. Press, 2004 ( The most extensive text on convex optimization and one of the best written).
- Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization (SIAM).
- Bertsekas, A. Nedic, A.E. Ozdaglar, Convex Analysis and Optimization (Athena Scientific).
- Bertsekas, Convex Optimization Theory (Athena Scientific).
- M. Borwein and A. S. Lewis, Convex Analysis and Nonlinear Optimization (Springer).
- B. Hiriart-Urruty and C. Lemarechal, Convex Analysis and Minimization Algorithms (Springer).
- Luenberger and Y. Ye, Linear and Nonlinear Programming (Springer).
- Y. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course (Kluwer).
Game Theory
- Instructor: Amirhossein Nikoofard
Course outline
- Introduction and examples
- Elements of a game: players, objectives, information structure, actions and policies
- Classes of games: cooperative/non-cooperative, static/dynamic, zero/non-zero sum, open-/closed-loop, complete/incomplete information
- Zero-sum games
- Zero-sum matrix games
- Mixed policies
- Minimax theorem
- Extensive form of the game.
- Non-zero-sum games
- Two-player games
- Nash equilibria for bimatrix games
- N-player games
- Dynamic games
- Dynamic games
- One-player discrete- and continuous-time dynamic games
- State-feedback zero-sum dynamic games
- Bayesian games
- Bayesian Nash equilibrium
- Auctions
- Examples
- Stochastic games
- Market/electricity market
- Learning
Textbooks
- Fudenberge D., Birole J., Game Theory, MIT Press, Cambridge, Massachusetts, 1991.
- Basar, T., Olsder, G. J., Dynamic non-cooperative game theory, Second Edition, SIAM, 1999.
- Hespanha, Joao P,An introductory course in noncooperative game theory, 2011.
- P. Bertsekas, Dynamic Programming- Deterministic and Stochastic Models, Prentice-Hall, Inc., 1987.
- Han, D. Niyato, W. Saad, T. Basar, and A. Hjørungnes, Game Theory in Wireless and Communication Networks: Theory, Models, and Applications, Cambridge Press 2011.
- Fudenberg, D.Levine, The theory of learning in games, MIT Press, Cambridge, Massachusetts, 1998.
- Easley, J. Kleinberg, Networks, Crowds, and Markets: Reasoning about a Highly Connected World, Cambridge University Press, 2010.
Fuzzy Control Systems
Fuzzy logic is widely used in machine control. The term itself inspires a certain skepticism, sounding equivalent to “half-baked logic” or “bogus logic”, but the “fuzzy” part does not refer to a lack of rigour in the method, rather to the fact that the logic involved can deal with fuzzy concepts—concepts that cannot be expressed as “true” or “false” but rather as “partially true”. Although genetic algorithms and neural networks can perform just as well as fuzzy logic in many cases , fuzzy logic has the advantage that the solution to the problem can be cast in terms that human operators can understand, so that their experience can be used in the design of the controller. This makes it easier to mechanize tasks that are already successfully performed by humans.
- Instructor: Alireza Fatehi
Course outline
- Introduction and Basic Concepts
- Fuzzy Modeling
- Case Studies in Fuzzy Control
- T-S Fuzzy Model
- LMI-Based Design approach and Stable Controller Design
- Fuzzy Identification
- Fuzzy Clustering
- NeuroFuzzy
- Fuzzy Controller Design Using GA
- Fuzzy Supervisory Control
Textbooks
-
Passino K. M., Yurkovich S., Fuzzy Control, Addison-Wesley Longman, 1998
-
Wang L., A Course in Fuzzy Systems and Control, Prentice-Hall, 1997
-
لي وانگ، سيستمهاي فازي و كنترل فازي، ترجمه دكتر محمد تشنه لب، نيما صفارپور و داريوش افيوني، انتشارات دانشگاه صنعتي خواجه نصيرالدين طوسي، 1378
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Yen J., Langari R., Fuzzy Logic: Intelligence, Control & Information, Prentice Hall, 1998
-
Kazuo Tanaka, Huo Wang: Fuzzy Control Systems Design And Analysis, A Linear Matrix Inequality Approach, Wiley 2001
-
Cordon O., Herrera F., Hoffmann F., Magdalena L., Genetic Fuzzy Systems: Evolutionary Tuning and Learning of Fuzzy Knowledge Bases, World Scientific, 2001
-
Herrera F., Magdalena L., Genetic Fuzzy Systems: A Tutorial
-
مروری بر منطق فازی، برگرفته از: علیرضا فاتحی، “طراحی و تنظیم کنترل کننده های هوشمند برای فرایندهای صنعتی،” پایان نامه کارشناسی ارشد، دانشگاه تهران، 1373
-
مروری بر کنترل کننده های فازی، برگرفته از: علیرضا فاتحی، “طراحی و تنظیم کنترل کننده های هوشمند برای فرایندهای صنعتی،” پایان نامه کارشناسی ارشد، دانشگاه تهران، 1373
-
مروری بر الگوریتمهای ژنتیکی، برگرفته از: علیرضا فاتحی، “طراحی و تنظیم کنترل کننده های هوشمند برای فرایندهای صنعتی،” پایان نامه کارشناسی ارشد، دانشگاه تهران، 1373
Industrial Automation
- Instructor: Alireza Fatehi
Course outline
Textbooks
Soft Computing
- Instructor: Alireza Fatehi
Course outline
Textbooks
Advanced Process Control
- Instructor: Alireza Fatehi
Course outline
Textbooks
Linear Control Systems
Getting to know the methods of analysis and design of control systems, especially with linearity assumption in time and frequency domain. In this course, some simulation tools will be used for analysis and design. By means of doing final project, the students would implement the learned concepts on some control systems and study the results.
- Instructor(s): Ali Khaki-Sedigh, Amirhossein Nikoofard, Alireza Fatehi
Course outline
- Introduction
Getting to know the control systems,
Modeling some typical systems, state space model and transfer function,
Introducing different control structure (closed and open loop, forward and feedback)
Presentation a sample for modeling (for example dc motor)
- Displaying of linear control systems
Block diagram and the rules of their simplification
Signal flow-graph, Mason’s flow-graph loop rule and finding of flow graph from transfer function
- Time response of linear system
Impulse response, Step response, Ramp response, Acceleration input response and analysis of steady state error
Definition of system type and order of inputs and steady state error
Study of transient response of systems for the above mentioned inputs and specifications of time responses of first and second order circuits, rise time, settling time, steady state error, overshoot, damping ratio
- Stability analysis
Definition of BIBO stability
Characteristic equation, poles and conditions on stability
Routh-Hurwitz stability criterion
The above mentioned criterion in presence of delay time
- Root locus method
Root locus curves and the relation between the poles of closed loop and the loop gain
The laws of drawing of root locus
The drawing of root locus in presence of time delay and with positive feedback
Analysis of control systems by root locus, finding the gain, design of static gain, desired characteristics, the relation between time and frequency domain
Design by root locus method
Design of proportional gain, phase lead, phase lag, phase lead-phase lag, by means of root locus
Design of PID by means of root locus
- Frequency response methods
Reminder of the Bode diagram, the relation between amplitude and phase, definition of minimum phase and non-minimum phase systems and comparison of their Bode diagrams, draw of phase curve from amplitude for a minimum phase system
Reminder of Nyquist diagram, containing and the number of closed loop poles, regular and singular points, Nyquist stability criterion, stability characteristics, poles and zeroes on imaginary axis, the relation between Bode and Nyquist diagram
The relationship of loop gain L, sensitivity function S and closed loop transfer function T
Nichol’s chart, the M curves, sensitivity and definition of sensitivity for transfer functions, feedback characteristics and loop gain in Nichol’s chart
- Design in frequency domain
Definition of stability margins, gain and phase margins, band width, Failure frequencies, the relationship of time response and frequency response
The design of controller based on Nichol’s chart
The design of P controller based on stability margins
The design of PI controller based on the steady state characteristics or disturbance rejection in steady state
The design of lag controller, PD controller and band width of closed loop, lead controller, lag-lead controller and PID, with comprehensive example
Textbooks
- Ali khaki Seddigh, Linear Control Systems, PNUniversity, 2001.
- R.C. Dorf & R. H. Bishop, Modern Control Systems, 9/e., Prentice-Hall, 2001
- K. Ogata, Modern Control Engineering, Prentice Hall, 3rd ed., 1996.
- B.C. Kuo, Automatic Control Systems, Prentice Hall, 1991.
Engineering Economics
General Theory of Relativity or the theory of relativistic gravitation is the one which describes black holes, gravitational waves and expanding Universe. The goal of the course is to introduce you into this theory. The introduction is based on the consideration of many practical generic examples in various scopes of the General Relativity. After the completion of the course you will be able to solve basic standard problems of this theory.
- Instructor: Amirhossein Nikoofard
Course outline
- Introduction:
- Engineering Economic Decisions, Decision-Making Process, Fundamental Principles of Engineering Economics, Fixed, Variable, Marginal, and Average Costs, Incremental Costs, Cash Flow Diagram
- Engineering Economic Analysis:
- Internal Rate of Return(IRR), Present Worth Analysis, Time Value of Money, Simple Interest, Compound Interest, Repaying a Debt, Inflation, Future Worth Analysis, Benefit–Cost Ratio Analysis, Sensitivity and Breakeven Analysis, Payback Period, Annual Equivalence Analysis, Rate of Return Analysis, Depreciation and Income Taxes, Cash Flow Analysis, Effects of Inflation of Project Cash Flows
- Uncertainty and Risk Analysis:
- Origins of Project Risk
- Methods of Describing Project Risk: Sensitivity, Breakeven and Scenario Analysis
- Calculation of expected NPV and IRR
- Economic Decision Trees
- Determining the distribution of NPV and IRR
Textbooks
- G. Newnan, T. G .Eschenbach, J. P. Lavelle, Engineering economic analysis, Oxford University Press, 2012
- S .Park, Contemporary Engineering Economics, 6th Ed., Prentice Hall, 2016
- M. Oskounejad, Engineering Economy-Industrial projects economical assessment. Amirkabir university publishing: Tehran, 2011 (Persian).
- R. Soltani, Engineering Economics, 8th Ed, Shiraz university publishing, 2007 (Persian).
Modern Control
This course aims to introduce the state space methods in modeling and feedback control of linear time invariant systems. The concepts induced in this framework such as controllability, stabilzability, observability and detectability is defined and elaborated in this course. Next the system transformation, stability and realization and state controller and observer design will be discussed.
Due to the structure of this course, required linear system theories are developed, with an applied vision and the application of those theories in practice is emphasized. The expertise of the students are examined in a thorough and comprehensive design task as a term project.
- Instructor: Ali Khaki-Sedigh
Course outline
LTI System Representation: State space representation, modeling based on physical principles, electrical systems, electromechanical systems, mechanical systems, hydraulic systems, modeling based on Lagrange equation, mathematical linearization, modeling uncertainty.
Linear system theory: Linear system properties, solution to linear system D.E., zero-input solution, zero state solution, state transition matrix, state transition matrix derivation methods: Laplace, Dynamical modes, Caley-Hamilton, Silvester methods, similarity transformations, system poles and transmission zeros, diagonalization, Jordan forms, block-Jordan forms.
Controllability and Observability: Observability, observability matrix, eigenvector test, controllability, duality, Kalman canonical decomposition.
Realization: Controllable and Observable canonical form, realization of MISO systems, realization of SIMO systems, MIMO realizations.
Stability: Stability definitions, internal stability, BIBO stability, Lyapunov matrix equation.
State feedback: State feedback properties, tracking objective, pole placement methods, pole placement for MIMO systems, optimal state feedback LQR, applied gain selection, disturbance rejection, State integral feedback.
State Observer: State observer general idea, full state observer, Luengerger Observer, optimal state Observer LQE, Kalman Filter.
State feedback-Observer: Separation Theorem, state feedback with disturbance estimation, closed loop performance.
Textbooks
- An Introduction to modern control, Hamid D. Taghirad, 4th Edition, K.N. Toosi University of Technology, 2018.
- Control engineering: a modern approach, Pierre Bélanger, Saunders College Pub., 1995.
- Fundamentals of Modern Control, Ali K. Sedigh, Tehran University Publication, 2016.
- Linear systems, Thomas Kailath, Englewood Cliffs, N.J. Prentice-Hall, 1980.
- Modern control theory, William L. Brogan, 3rd ed., Englewood Cliffs, N.J., Prentice Hall, 1991.
- Modern control engineering, Katsuhiko Ogata, 4th ed., NJ, Prentice Hall, 2010.
Engineering Mathematics
In this course, those areas of applied mathematics that are most relevant for solving practical problems are thought to the student. However the basic prerequisites of this course are General Mathematics II and Differential Equations, at the beginning session, a concise introduction about vector spaces, the inner product spaces and the basis of a vector spaces especially the orthogonal basis are introduced to the students. A brief discussion about the mentioned concepts helps the students to perceive the concept of the Fourier series much better.
As the class projects, some of the CAS experiments presented at the first reference of the course are assigned to the students to make them familiar with the numeric and symbolic environments of the MATLAB and Maple softwares.
- Instructor: Ali Khaki-Sedigh
Course outline
Partial Differential Equations (PDEs): Basic Concepts of PDEs, Wave Equation, Solution of Wave Equation by Separating Variables and Use of Fourier Series, D’Alembert’s Solution of the Wave Equation, Heat Equation, Solution of Heat Equation by Separating Variables and Use of Fourier Series, Steady Two-Dimensional Heat Problems, Solution of Heat Equation for Very Long Bars by Use of Fourier Integrals, Two-Dimensional Wave Equation, Double Fourier Series, Laplacian in Cylindrical, Spherical and Polar Coordinates.
Complex Differentiation: Complex Numbers and Their Geometric Representation, Polar Form of Complex Numbers, Powers and Roots, Limit and Derivative of an Analytic Function, Cauchy–Riemann Conditions, Laplace’s Equation, Harmonic Functions, Harmonic Conjugate Function, Complex Exponential Function, Complex Trigonometric and Hyperbolic Functions, Complex Logarithm Function, General Complex Power Function.
Complex Integration: Line Integral in the Complex Plane, Indefinite Integration and Substitution of Limits, Use of a Representation of a Path, Cauchy’s Integral Theorem, Derivatives of an Analytic Functions.
Power Series and Taylor Series: Sequences, Series, Convergence Tests, Power Series, Operations on Power Series, Power Series Representation of an Analytic Function, Taylor and Maclaurin Series, Important Special Taylor Series.
Laurent Series and Residue Integration: Laurent Series, concepts of Singularities and Zeros, Residue Integration Method, Residue Integration of Real Integrals.
Conformal Mapping: Conformal Mapping, Linear Fractional Transformations (Möbius Transformations), Fixed Points, Special Linear Fractional Transformations, Conformal Mapping by Other Functions.
Textbooks
- Erwin Kreyszig, Advanced Engineering Mathematics, Tenth Edition, Wiley, 2010.
- Michael Greenberg, Advanced Engineering Mathematics, Second Edition, Pearson Education, 2013.
Industrial Control
In this course, students learn various industrial control loop structures, design procedure and implementation issues of them in industry. Although in this course the students are taught to solve the problems by benefiting from the analytical methods, the useful commands of the MATLAB software are also introduced to the students to be used for evaluating the obtained analytical results.
- Instructor: Alireza Fatehi
Course outline
- Introduction and general definitions:
An introduction to industrial processes, automation, modeling and control of a process, PID controller.
Industrial automation: Introduction and general structure of an industrial control systems. introducing DCS, FCS, and P&ID. Fundamental of PLC, hardware, programing, ladder program, some simple industrial PLC program example
- Process Modeling:
First principle modeling, extraction of state space model, extracting model of some processes like level, flow, air pressure, temperature and concentration control systems.
Introducing static model, dynamic model, extraction of time domain models like first order with/without delay, integrally processes, under-damped processes, introducing some parameters like controllability ratio and normalized ultimate gain
Frequency domain modeling like Ziegler-Nichols and feedback relay methods
System Identification: Least square method for discrete and higher order models
- Design, and implementation of PID controller
Design criteria of a controller: stability, setpoint tracking, disturbance reduction, noise attenuation and low sensibility to model
Introducing parts of a PID controller like integral anti-windup, setpoint weighted PID, PI+D
PID implementation by means of electrical, electronical, pneumatical & digital technologies.
PID controller design: time-domain Ziegler-Nichols, ISE and IAE criteria, frequency-domain Zigler-Nichols, introducing some other methods like Fertic and extended Z-N, PID pros and cons.
- Introducing industrial control loop structures:
On/off, feedforward, cascade, selector, override, ratio and split-range structures
Textbooks
- K.J. Astrom & T. Hagglund, PID Controller, The International Society of Measuremet and Control, 1995.
- A.J. Crispin, PLC and their engineering application, McGraw Hill, 1990.
- Hamid D. Taghirad, An Introduction to Industrial Automation and Process Control, with complete presentation of Siemens Step7 PLC, 2nd Edition, K.N. Toosi University Press, 2009.
- Alireza Fatehi, Process Control Systems, K.N. Toosi University Press, Tehran, Iran, 2008.
Digital Control
This course is a comprehensive introduction to control system synthesis in which the digital computer plays a major role, reinforced with hands-on homework assignments and simulation experiences. The course covers elements of real-time computer architecture; input-output interfaces and data converters; analysis and synthesis of sampled-data control systems using classical and modern (state-space) methods; analysis of trade-offs in control algorithms for computation speed and quantization effects. The purpose of the course is to present control theory that is relevant to the analysis and design of computer-controlled systems, with an emphasis on basic concepts and ideas. The control-system design is carried out up to the stage of implementation in the form of computer programs in a high-level language.
- Instructor: Alireza Fatehi
Course outline
PART I: Analysis
Introduction to digital control, fundamental concepts, principles and application of digital control system analysis and design. State Space Representation of Discrete-time Systems. Difference Equations, Properties and uses of the Z-transform, Region of Convergence, Inverse Z- transformation Methods, The Pulse Transform, Sampling and Reconstruction of Continuous- time Signals, Zero and First Order Holds, Step Responses of First and Second Discrete- time Systems, Discretization Methods, Z- mapping Properties, Steady State Errors, Stability Analysis, Jury Test, Nyquist Method, and Bilinear Transformation Method.
PART II: Controller Design
Sampling Period Selection Methods, Design of Digital Controllers using via Classical Techniques, such as Lead, Lag, Lag/Lead, Dead Beat and PID Controllers using Root Locus, Direct and Indirect Digital Design Techniques, W- plane Design Method, Modern Control Techniques Based on State Space Models, State Feedback Controller Design, Pole Placement, Ackermann’s Formula,
PART III: Observer Design
Discrete- time State Estimator, Open- loop Observer, Output- injection Observer, Prediction Estimators, Current Estimators, Full Order Estimator Design, Kalman Filter, Reduced Order Estimator Design, Observer-Based Control and the Separation Principle
Textbooks
- F. Franklin, J. D. Powell and M. L. Workman, Digital Control of Dynamic Systems, 3rd Edition, Ellis-Kagle Press, 2006.
- B. C. Kuo, Digital Control Systems, Oxford University Press, 2nd Edition, Indian Edition, 2007.
- K. Ogata, Discrete Time Control Systems, Prentice Hall, 2nd Edition, 1995.
- M. Gopal, Digital Control and State Variable Methods, Tata McGraw Hill, 2nd Edition, 2003.
- K. J. Astroms and B. Wittenmark, Computer Controlled Systems – Theory and Design, Prentice Hall, 3rd Edition, 1997.
Modeling and Simulation
The students should after the course be able to
- build mathematical models of technical systems from first principles
- use the most powerful tools (softwares) for modeling and simulation
- construct mathematical models from measured data
During the course the student should learn to apply the: MATLAB Toolbox for modeling like IDENT, SIMULINK Toolbox, Simulation parameters, Sim power, Sim Electronic, Sim mechanic, Solid Work, 20 Sim for Bond Graph, AMESim, …
- Instructor: Mahdi Aliyari Shoorehdeli
Course outline
Modeling: What is Modeling? What is simulation? System and simulation, error of modeling, evaluation index, uncertainty in modeling, types of modeling, Database modeling, physical modeling, Linear and nonlinear model, Discrete model, Continues model, ODE, DAE, PDE.
Modeling based on physical principles: electrical systems, Mechanical systems (rotation and translation), electromechanical/Mechatronic systems, hydraulic systems, modeling based on Lagrange equation, mathematical linearization, modeling uncertainty.
Bond Graph: Multiport Systems and Bond Graphs, Engineering Multiports, Ports, Bonds, and Power, Inputs, Outputs, and Signals, Basic Bond Graph Elements, Basic 1-Port Elements, Basic 2-Port Elements, The 3-Port Junction Elements, Causality Considerations for the Basic Elements, Causality and Block Diagrams, System Models: Electrical Systems,Electrical Circuits, Electrical Networks, Mechanical Systems, Mechanics of Translation, Fixed-Axis Rotation, Plane Motion, Hydraulic and Acoustic Circuits, Fluid Resistance, Fluid Capacitance,
Fluid Inertia, Fluid Circuit Construction, An Acoustic Circuit Example, Transducers and Multi-Energy-Domain Models, Transformer Transducers, Gyrator Transducers, Multi-Energy-Domain Models, State-Space Equations and Automated Simulation, Standard Form for System Equations, Algebraic Loops, Derivative Causality.
Modeling based on data: System identification, Black/grey/whit box model, linear and nonlinear model, parametric and non-parametric model, static linear models, least square, weighted least square, recursive least square, dynamic linear model, FIR, OE, ARX, ARMAX, ARARX, BJ.
Simulation: Numerical simulation, Numerical methods for solving ODEs, Numerical methods for DAEs, Objective oriented simulation and modeling
Textbooks
- Frank L. Severance, System Modeling and Simulation, 2001.
- L. Ljung and T. Glad, Modeling of Dynamic Systems, 1994. New edition 2004.
- D.C. Karnopp, D.L. Margolis & R.C. Rosenberg, System Dynamics. Modeling and Simulation of Mechatronic Systems 4th Edition, 2012.
- O. Nelles, Nonlinear System Identification: From Classical Approaches to Neural Networks and Fuzzy Models, 2001.
Signals & Systems
Signals & Systems is usually encountered between different engineering courses that require students to cope with work on different signals & systems. Therefore, this course aims to present the kinds of signals & systems, then survey analysis of continuous & discrete LTI systems versus time and frequency with applications.
Although in this course the students are taught to solve the problems by benefiting from the different transforms, the useful commands of the MATLAB software are also introduced to the students to be used for evaluating the obtained analytical results.
- Instructor: Mahdi Aliyari
Course outline
Continuous & Discrete Time Signals ans Systems: Mathematic representation of Continuous time signals and Discrete time signals, Power & Energy of signals, Property of signals, Impulse & Step & Complex Exponential signals, Continuous time & Discrete time systems and their properties.
LTI Systems and their properties: Impulse Response, Convolution concept, property of impulse response, Description of systems according to differential & diference equations, I & II Direct Realization based on differential & difference equations, FIR and IIR response.
The Fourier series of periodic continuous signals: The fourier series and it’s the convergence & properties, Importance of fourier series in calculation of response of the LTI continuous systems.
The Fourier Transform of continuous signals: The fourier transform and its properties, The convergence of fourier transform, Relation of between the fourier series & the fourier transform, Fourier transform of periodic signals, Analysis of the LTI continuous systems with the fourier transform, I & II Direct Realization based on the fourier transform.
The Laplace Transform: The Two-sided Laplace transform and its the convergence & properties, Inverse Laplace transform, Relation of between the two-sided laplace transform & the fourier transform, Unilateral Laplace Transform and it’s the convergence & properties, Analysis of the LTI continuous systems with the laplace transform, I & II Direct Realization based on the laplace transform, The stability concept with laplace transform.
Sampling: Sampling theorem, Ideal forms, aliasing phenomenon, Reconstruction.
The Fourier series of periodic discrete signals: The fourier series and it’s the convergence & properties, Importance of fourier series in calculation of response of the LTI discrete systems.
The Fourier Transform of discrete signals: The discrete time fourier transform (DTFT) and it’s the convergence & properties, Relation of between the fourier series and DTFT, DTFT for the periodic signals, Discrete Fourier Transform (DFT) and it’s the convergence & properties, FFT algorithms, Analysis of the LTI discrete systems with DTFT, I & II Direct Realization based on DTFT.
The z Transform: The Two-sided z transform and it’s the convergence & properties, Inverse z transform, Between the two-sided z transform & the DTFT, Unilateral z Transform and it’s the convergence & properties, Analysis of the LTI discrete systems with z transform , I & II Direct Realization based on z transform, Relation of between z transform and the laplace transform, Simulating continuous time systems with discrete time systems (Impulse Invariant response, Backward Difference Approximation, The Bilinear Transformation), The stability concept with z transform.
Some Applications: filtering and applications, Modulation (DSB & AM), Analysis of systems with state space.
Textbooks
- A.V. Oppenheim & A.S. Willsky & S.H. Nawab, Signas and Systems ,second edition ,Pearson., 2014.
- R.E. Ziemer & W.H. Tranter & D.R. Fannin, Signals and Systems Continuous and Discrete, 4th Edition, Pearson, 2014.
- S. Haykin & B. Van Veen, Signals and Systems, Second Edition, Wiley, 2003.
- M.J. Roberts, Signals and Systems Analysis Using Transform Methods and Matlabs, International Edition, McGraw-Hill , 2004.
- Graduate
-
Convex Optimization
- Instructor: Amirhossein Nikoofard
More About This CourseCourse outline
- Introduction
- Convex sets
- Convex functions
- Convex optimization problems
- Duality
- Approximation and fitting
- Statistical estimation
- Numerical linear algebra background
- Unconstrained minimization
- Equality constrained minimization
- Interior-point methods
- Advanced Topics on Convex optimization
Textbooks
- Boyd & L. Vandenberghe, “Convex Optimization ,” Cambridge Univ. Press, 2004 ( The most extensive text on convex optimization and one of the best written).
- Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization (SIAM).
- Bertsekas, A. Nedic, A.E. Ozdaglar, Convex Analysis and Optimization (Athena Scientific).
- Bertsekas, Convex Optimization Theory (Athena Scientific).
- M. Borwein and A. S. Lewis, Convex Analysis and Nonlinear Optimization (Springer).
- B. Hiriart-Urruty and C. Lemarechal, Convex Analysis and Minimization Algorithms (Springer).
- Luenberger and Y. Ye, Linear and Nonlinear Programming (Springer).
- Y. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course (Kluwer).
Game Theory
- Instructor: Amirhossein Nikoofard
More About This CourseCourse outline
- Introduction and examples
- Elements of a game: players, objectives, information structure, actions and policies
- Classes of games: cooperative/non-cooperative, static/dynamic, zero/non-zero sum, open-/closed-loop, complete/incomplete information
- Zero-sum games
- Zero-sum matrix games
- Mixed policies
- Minimax theorem
- Extensive form of the game.
- Non-zero-sum games
- Two-player games
- Nash equilibria for bimatrix games
- N-player games
- Dynamic games
- Dynamic games
- One-player discrete- and continuous-time dynamic games
- State-feedback zero-sum dynamic games
- Bayesian games
- Bayesian Nash equilibrium
- Auctions
- Examples
- Stochastic games
- Market/electricity market
- Learning
Textbooks
- Fudenberge D., Birole J., Game Theory, MIT Press, Cambridge, Massachusetts, 1991.
- Basar, T., Olsder, G. J., Dynamic non-cooperative game theory, Second Edition, SIAM, 1999.
- Hespanha, Joao P,An introductory course in noncooperative game theory, 2011.
- P. Bertsekas, Dynamic Programming- Deterministic and Stochastic Models, Prentice-Hall, Inc., 1987.
- Han, D. Niyato, W. Saad, T. Basar, and A. Hjørungnes, Game Theory in Wireless and Communication Networks: Theory, Models, and Applications, Cambridge Press 2011.
- Fudenberg, D.Levine, The theory of learning in games, MIT Press, Cambridge, Massachusetts, 1998.
- Easley, J. Kleinberg, Networks, Crowds, and Markets: Reasoning about a Highly Connected World, Cambridge University Press, 2010.
Fuzzy Control Systems
Fuzzy logic is widely used in machine control. The term itself inspires a certain skepticism, sounding equivalent to “half-baked logic” or “bogus logic”, but the “fuzzy” part does not refer to a lack of rigour in the method, rather to the fact that the logic involved can deal with fuzzy concepts—concepts that cannot be expressed as “true” or “false” but rather as “partially true”. Although genetic algorithms and neural networks can perform just as well as fuzzy logic in many cases , fuzzy logic has the advantage that the solution to the problem can be cast in terms that human operators can understand, so that their experience can be used in the design of the controller. This makes it easier to mechanize tasks that are already successfully performed by humans.
- Instructor: Alireza Fatehi
More About This CourseCourse outline
- Introduction and Basic Concepts
- Fuzzy Modeling
- Case Studies in Fuzzy Control
- T-S Fuzzy Model
- LMI-Based Design approach and Stable Controller Design
- Fuzzy Identification
- Fuzzy Clustering
- NeuroFuzzy
- Fuzzy Controller Design Using GA
- Fuzzy Supervisory Control
Textbooks
-
Passino K. M., Yurkovich S., Fuzzy Control, Addison-Wesley Longman, 1998
-
Wang L., A Course in Fuzzy Systems and Control, Prentice-Hall, 1997
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لي وانگ، سيستمهاي فازي و كنترل فازي، ترجمه دكتر محمد تشنه لب، نيما صفارپور و داريوش افيوني، انتشارات دانشگاه صنعتي خواجه نصيرالدين طوسي، 1378
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Yen J., Langari R., Fuzzy Logic: Intelligence, Control & Information, Prentice Hall, 1998
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Kazuo Tanaka, Huo Wang: Fuzzy Control Systems Design And Analysis, A Linear Matrix Inequality Approach, Wiley 2001
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Cordon O., Herrera F., Hoffmann F., Magdalena L., Genetic Fuzzy Systems: Evolutionary Tuning and Learning of Fuzzy Knowledge Bases, World Scientific, 2001
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Herrera F., Magdalena L., Genetic Fuzzy Systems: A Tutorial
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مروری بر منطق فازی، برگرفته از: علیرضا فاتحی، “طراحی و تنظیم کنترل کننده های هوشمند برای فرایندهای صنعتی،” پایان نامه کارشناسی ارشد، دانشگاه تهران، 1373
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مروری بر کنترل کننده های فازی، برگرفته از: علیرضا فاتحی، “طراحی و تنظیم کنترل کننده های هوشمند برای فرایندهای صنعتی،” پایان نامه کارشناسی ارشد، دانشگاه تهران، 1373
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مروری بر الگوریتمهای ژنتیکی، برگرفته از: علیرضا فاتحی، “طراحی و تنظیم کنترل کننده های هوشمند برای فرایندهای صنعتی،” پایان نامه کارشناسی ارشد، دانشگاه تهران، 1373
Industrial Automation
- Instructor: Alireza Fatehi
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Soft Computing
- Instructor: Alireza Fatehi
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Advanced Process Control
- Instructor: Alireza Fatehi
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- Undergraduate
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Linear Control Systems
Getting to know the methods of analysis and design of control systems, especially with linearity assumption in time and frequency domain. In this course, some simulation tools will be used for analysis and design. By means of doing final project, the students would implement the learned concepts on some control systems and study the results.
- Instructor(s): Ali Khaki-Sedigh, Amirhossein Nikoofard, Alireza Fatehi
More About This CourseCourse outline
- Introduction
Getting to know the control systems,
Modeling some typical systems, state space model and transfer function,
Introducing different control structure (closed and open loop, forward and feedback)
Presentation a sample for modeling (for example dc motor)
- Displaying of linear control systems
Block diagram and the rules of their simplification
Signal flow-graph, Mason’s flow-graph loop rule and finding of flow graph from transfer function
- Time response of linear system
Impulse response, Step response, Ramp response, Acceleration input response and analysis of steady state error
Definition of system type and order of inputs and steady state error
Study of transient response of systems for the above mentioned inputs and specifications of time responses of first and second order circuits, rise time, settling time, steady state error, overshoot, damping ratio
- Stability analysis
Definition of BIBO stability
Characteristic equation, poles and conditions on stability
Routh-Hurwitz stability criterion
The above mentioned criterion in presence of delay time
- Root locus method
Root locus curves and the relation between the poles of closed loop and the loop gain
The laws of drawing of root locus
The drawing of root locus in presence of time delay and with positive feedback
Analysis of control systems by root locus, finding the gain, design of static gain, desired characteristics, the relation between time and frequency domain
Design by root locus method
Design of proportional gain, phase lead, phase lag, phase lead-phase lag, by means of root locus
Design of PID by means of root locus
- Frequency response methods
Reminder of the Bode diagram, the relation between amplitude and phase, definition of minimum phase and non-minimum phase systems and comparison of their Bode diagrams, draw of phase curve from amplitude for a minimum phase system
Reminder of Nyquist diagram, containing and the number of closed loop poles, regular and singular points, Nyquist stability criterion, stability characteristics, poles and zeroes on imaginary axis, the relation between Bode and Nyquist diagram
The relationship of loop gain L, sensitivity function S and closed loop transfer function T
Nichol’s chart, the M curves, sensitivity and definition of sensitivity for transfer functions, feedback characteristics and loop gain in Nichol’s chart
- Design in frequency domain
Definition of stability margins, gain and phase margins, band width, Failure frequencies, the relationship of time response and frequency response
The design of controller based on Nichol’s chart
The design of P controller based on stability margins
The design of PI controller based on the steady state characteristics or disturbance rejection in steady state
The design of lag controller, PD controller and band width of closed loop, lead controller, lag-lead controller and PID, with comprehensive example
Textbooks
- Ali khaki Seddigh, Linear Control Systems, PNUniversity, 2001.
- R.C. Dorf & R. H. Bishop, Modern Control Systems, 9/e., Prentice-Hall, 2001
- K. Ogata, Modern Control Engineering, Prentice Hall, 3rd ed., 1996.
- B.C. Kuo, Automatic Control Systems, Prentice Hall, 1991.
Engineering Economics
General Theory of Relativity or the theory of relativistic gravitation is the one which describes black holes, gravitational waves and expanding Universe. The goal of the course is to introduce you into this theory. The introduction is based on the consideration of many practical generic examples in various scopes of the General Relativity. After the completion of the course you will be able to solve basic standard problems of this theory.
- Instructor: Amirhossein Nikoofard
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- Introduction:
- Engineering Economic Decisions, Decision-Making Process, Fundamental Principles of Engineering Economics, Fixed, Variable, Marginal, and Average Costs, Incremental Costs, Cash Flow Diagram
- Engineering Economic Analysis:
- Internal Rate of Return(IRR), Present Worth Analysis, Time Value of Money, Simple Interest, Compound Interest, Repaying a Debt, Inflation, Future Worth Analysis, Benefit–Cost Ratio Analysis, Sensitivity and Breakeven Analysis, Payback Period, Annual Equivalence Analysis, Rate of Return Analysis, Depreciation and Income Taxes, Cash Flow Analysis, Effects of Inflation of Project Cash Flows
- Uncertainty and Risk Analysis:
- Origins of Project Risk
- Methods of Describing Project Risk: Sensitivity, Breakeven and Scenario Analysis
- Calculation of expected NPV and IRR
- Economic Decision Trees
- Determining the distribution of NPV and IRR
Textbooks
- G. Newnan, T. G .Eschenbach, J. P. Lavelle, Engineering economic analysis, Oxford University Press, 2012
- S .Park, Contemporary Engineering Economics, 6th Ed., Prentice Hall, 2016
- M. Oskounejad, Engineering Economy-Industrial projects economical assessment. Amirkabir university publishing: Tehran, 2011 (Persian).
- R. Soltani, Engineering Economics, 8th Ed, Shiraz university publishing, 2007 (Persian).
Modern Control
This course aims to introduce the state space methods in modeling and feedback control of linear time invariant systems. The concepts induced in this framework such as controllability, stabilzability, observability and detectability is defined and elaborated in this course. Next the system transformation, stability and realization and state controller and observer design will be discussed.
Due to the structure of this course, required linear system theories are developed, with an applied vision and the application of those theories in practice is emphasized. The expertise of the students are examined in a thorough and comprehensive design task as a term project.
- Instructor: Ali Khaki-Sedigh
More About This CourseCourse outline
Introduction: Why Feedback, Conceptual components of feedback systems, Physical components of Feedback systems, State definition, and state feedback.LTI System Representation: State space representation, modeling based on physical principles, electrical systems, electromechanical systems, mechanical systems, hydraulic systems, modeling based on Lagrange equation, mathematical linearization, modeling uncertainty.
Linear system theory: Linear system properties, solution to linear system D.E., zero-input solution, zero state solution, state transition matrix, state transition matrix derivation methods: Laplace, Dynamical modes, Caley-Hamilton, Silvester methods, similarity transformations, system poles and transmission zeros, diagonalization, Jordan forms, block-Jordan forms.
Controllability and Observability: Observability, observability matrix, eigenvector test, controllability, duality, Kalman canonical decomposition.
Realization: Controllable and Observable canonical form, realization of MISO systems, realization of SIMO systems, MIMO realizations.
Stability: Stability definitions, internal stability, BIBO stability, Lyapunov matrix equation.
State feedback: State feedback properties, tracking objective, pole placement methods, pole placement for MIMO systems, optimal state feedback LQR, applied gain selection, disturbance rejection, State integral feedback.
State Observer: State observer general idea, full state observer, Luengerger Observer, optimal state Observer LQE, Kalman Filter.
State feedback-Observer: Separation Theorem, state feedback with disturbance estimation, closed loop performance.
Textbooks
- An Introduction to modern control, Hamid D. Taghirad, 4th Edition, K.N. Toosi University of Technology, 2018.
- Control engineering: a modern approach, Pierre Bélanger, Saunders College Pub., 1995.
- Fundamentals of Modern Control, Ali K. Sedigh, Tehran University Publication, 2016.
- Linear systems, Thomas Kailath, Englewood Cliffs, N.J. Prentice-Hall, 1980.
- Modern control theory, William L. Brogan, 3rd ed., Englewood Cliffs, N.J., Prentice Hall, 1991.
- Modern control engineering, Katsuhiko Ogata, 4th ed., NJ, Prentice Hall, 2010.
Engineering Mathematics
In this course, those areas of applied mathematics that are most relevant for solving practical problems are thought to the student. However the basic prerequisites of this course are General Mathematics II and Differential Equations, at the beginning session, a concise introduction about vector spaces, the inner product spaces and the basis of a vector spaces especially the orthogonal basis are introduced to the students. A brief discussion about the mentioned concepts helps the students to perceive the concept of the Fourier series much better.
As the class projects, some of the CAS experiments presented at the first reference of the course are assigned to the students to make them familiar with the numeric and symbolic environments of the MATLAB and Maple softwares.
- Instructor: Ali Khaki-Sedigh
More About This CourseCourse outline
Fourier Analysis: Fourier Series, Arbitrary Period, Even and Odd Functions, Half-Range Expansions, Approximation by Trigonometric Polynomials, Sturm–Liouville Problems, Orthogonal Functions, Orthogonal Series, Fourier Integral.Partial Differential Equations (PDEs): Basic Concepts of PDEs, Wave Equation, Solution of Wave Equation by Separating Variables and Use of Fourier Series, D’Alembert’s Solution of the Wave Equation, Heat Equation, Solution of Heat Equation by Separating Variables and Use of Fourier Series, Steady Two-Dimensional Heat Problems, Solution of Heat Equation for Very Long Bars by Use of Fourier Integrals, Two-Dimensional Wave Equation, Double Fourier Series, Laplacian in Cylindrical, Spherical and Polar Coordinates.
Complex Differentiation: Complex Numbers and Their Geometric Representation, Polar Form of Complex Numbers, Powers and Roots, Limit and Derivative of an Analytic Function, Cauchy–Riemann Conditions, Laplace’s Equation, Harmonic Functions, Harmonic Conjugate Function, Complex Exponential Function, Complex Trigonometric and Hyperbolic Functions, Complex Logarithm Function, General Complex Power Function.
Complex Integration: Line Integral in the Complex Plane, Indefinite Integration and Substitution of Limits, Use of a Representation of a Path, Cauchy’s Integral Theorem, Derivatives of an Analytic Functions.
Power Series and Taylor Series: Sequences, Series, Convergence Tests, Power Series, Operations on Power Series, Power Series Representation of an Analytic Function, Taylor and Maclaurin Series, Important Special Taylor Series.
Laurent Series and Residue Integration: Laurent Series, concepts of Singularities and Zeros, Residue Integration Method, Residue Integration of Real Integrals.
Conformal Mapping: Conformal Mapping, Linear Fractional Transformations (Möbius Transformations), Fixed Points, Special Linear Fractional Transformations, Conformal Mapping by Other Functions.
Textbooks
- Erwin Kreyszig, Advanced Engineering Mathematics, Tenth Edition, Wiley, 2010.
- Michael Greenberg, Advanced Engineering Mathematics, Second Edition, Pearson Education, 2013.
Industrial Control
In this course, students learn various industrial control loop structures, design procedure and implementation issues of them in industry. Although in this course the students are taught to solve the problems by benefiting from the analytical methods, the useful commands of the MATLAB software are also introduced to the students to be used for evaluating the obtained analytical results.
- Instructor: Alireza Fatehi
More About This CourseCourse outline
- Introduction and general definitions:
An introduction to industrial processes, automation, modeling and control of a process, PID controller.
Industrial automation: Introduction and general structure of an industrial control systems. introducing DCS, FCS, and P&ID. Fundamental of PLC, hardware, programing, ladder program, some simple industrial PLC program example
- Process Modeling:
First principle modeling, extraction of state space model, extracting model of some processes like level, flow, air pressure, temperature and concentration control systems.
Introducing static model, dynamic model, extraction of time domain models like first order with/without delay, integrally processes, under-damped processes, introducing some parameters like controllability ratio and normalized ultimate gain
Frequency domain modeling like Ziegler-Nichols and feedback relay methods
System Identification: Least square method for discrete and higher order models
- Design, and implementation of PID controller
Design criteria of a controller: stability, setpoint tracking, disturbance reduction, noise attenuation and low sensibility to model
Introducing parts of a PID controller like integral anti-windup, setpoint weighted PID, PI+D
PID implementation by means of electrical, electronical, pneumatical & digital technologies.
PID controller design: time-domain Ziegler-Nichols, ISE and IAE criteria, frequency-domain Zigler-Nichols, introducing some other methods like Fertic and extended Z-N, PID pros and cons.
- Introducing industrial control loop structures:
On/off, feedforward, cascade, selector, override, ratio and split-range structures
Textbooks
- K.J. Astrom & T. Hagglund, PID Controller, The International Society of Measuremet and Control, 1995.
- A.J. Crispin, PLC and their engineering application, McGraw Hill, 1990.
- Hamid D. Taghirad, An Introduction to Industrial Automation and Process Control, with complete presentation of Siemens Step7 PLC, 2nd Edition, K.N. Toosi University Press, 2009.
- Alireza Fatehi, Process Control Systems, K.N. Toosi University Press, Tehran, Iran, 2008.
Digital Control
This course is a comprehensive introduction to control system synthesis in which the digital computer plays a major role, reinforced with hands-on homework assignments and simulation experiences. The course covers elements of real-time computer architecture; input-output interfaces and data converters; analysis and synthesis of sampled-data control systems using classical and modern (state-space) methods; analysis of trade-offs in control algorithms for computation speed and quantization effects. The purpose of the course is to present control theory that is relevant to the analysis and design of computer-controlled systems, with an emphasis on basic concepts and ideas. The control-system design is carried out up to the stage of implementation in the form of computer programs in a high-level language.
- Instructor: Alireza Fatehi
More About This CourseCourse outline
PART I: Analysis
Introduction to digital control, fundamental concepts, principles and application of digital control system analysis and design. State Space Representation of Discrete-time Systems. Difference Equations, Properties and uses of the Z-transform, Region of Convergence, Inverse Z- transformation Methods, The Pulse Transform, Sampling and Reconstruction of Continuous- time Signals, Zero and First Order Holds, Step Responses of First and Second Discrete- time Systems, Discretization Methods, Z- mapping Properties, Steady State Errors, Stability Analysis, Jury Test, Nyquist Method, and Bilinear Transformation Method.
PART II: Controller Design
Sampling Period Selection Methods, Design of Digital Controllers using via Classical Techniques, such as Lead, Lag, Lag/Lead, Dead Beat and PID Controllers using Root Locus, Direct and Indirect Digital Design Techniques, W- plane Design Method, Modern Control Techniques Based on State Space Models, State Feedback Controller Design, Pole Placement, Ackermann’s Formula,
PART III: Observer Design
Discrete- time State Estimator, Open- loop Observer, Output- injection Observer, Prediction Estimators, Current Estimators, Full Order Estimator Design, Kalman Filter, Reduced Order Estimator Design, Observer-Based Control and the Separation Principle
Textbooks
- F. Franklin, J. D. Powell and M. L. Workman, Digital Control of Dynamic Systems, 3rd Edition, Ellis-Kagle Press, 2006.
- B. C. Kuo, Digital Control Systems, Oxford University Press, 2nd Edition, Indian Edition, 2007.
- K. Ogata, Discrete Time Control Systems, Prentice Hall, 2nd Edition, 1995.
- M. Gopal, Digital Control and State Variable Methods, Tata McGraw Hill, 2nd Edition, 2003.
- K. J. Astroms and B. Wittenmark, Computer Controlled Systems – Theory and Design, Prentice Hall, 3rd Edition, 1997.
Modeling and Simulation
The goal of this course is teach systematic methods for building mathematical models of dynamical systems based on physical principles and measured dataThe students should after the course be able to
- build mathematical models of technical systems from first principles
- use the most powerful tools (softwares) for modeling and simulation
- construct mathematical models from measured data
During the course the student should learn to apply the: MATLAB Toolbox for modeling like IDENT, SIMULINK Toolbox, Simulation parameters, Sim power, Sim Electronic, Sim mechanic, Solid Work, 20 Sim for Bond Graph, AMESim, …
- Instructor: Mahdi Aliyari Shoorehdeli
More About This CourseCourse outline
Introduction: Why modeling, Why simulation applications in control engineering and other fields.Modeling: What is Modeling? What is simulation? System and simulation, error of modeling, evaluation index, uncertainty in modeling, types of modeling, Database modeling, physical modeling, Linear and nonlinear model, Discrete model, Continues model, ODE, DAE, PDE.
Modeling based on physical principles: electrical systems, Mechanical systems (rotation and translation), electromechanical/Mechatronic systems, hydraulic systems, modeling based on Lagrange equation, mathematical linearization, modeling uncertainty.
Bond Graph: Multiport Systems and Bond Graphs, Engineering Multiports, Ports, Bonds, and Power, Inputs, Outputs, and Signals, Basic Bond Graph Elements, Basic 1-Port Elements, Basic 2-Port Elements, The 3-Port Junction Elements, Causality Considerations for the Basic Elements, Causality and Block Diagrams, System Models: Electrical Systems,Electrical Circuits, Electrical Networks, Mechanical Systems, Mechanics of Translation, Fixed-Axis Rotation, Plane Motion, Hydraulic and Acoustic Circuits, Fluid Resistance, Fluid Capacitance,
Fluid Inertia, Fluid Circuit Construction, An Acoustic Circuit Example, Transducers and Multi-Energy-Domain Models, Transformer Transducers, Gyrator Transducers, Multi-Energy-Domain Models, State-Space Equations and Automated Simulation, Standard Form for System Equations, Algebraic Loops, Derivative Causality.
Modeling based on data: System identification, Black/grey/whit box model, linear and nonlinear model, parametric and non-parametric model, static linear models, least square, weighted least square, recursive least square, dynamic linear model, FIR, OE, ARX, ARMAX, ARARX, BJ.
Simulation: Numerical simulation, Numerical methods for solving ODEs, Numerical methods for DAEs, Objective oriented simulation and modeling
Textbooks
- Frank L. Severance, System Modeling and Simulation, 2001.
- L. Ljung and T. Glad, Modeling of Dynamic Systems, 1994. New edition 2004.
- D.C. Karnopp, D.L. Margolis & R.C. Rosenberg, System Dynamics. Modeling and Simulation of Mechatronic Systems 4th Edition, 2012.
- O. Nelles, Nonlinear System Identification: From Classical Approaches to Neural Networks and Fuzzy Models, 2001.
Signals & Systems
Signals & Systems is usually encountered between different engineering courses that require students to cope with work on different signals & systems. Therefore, this course aims to present the kinds of signals & systems, then survey analysis of continuous & discrete LTI systems versus time and frequency with applications.
Although in this course the students are taught to solve the problems by benefiting from the different transforms, the useful commands of the MATLAB software are also introduced to the students to be used for evaluating the obtained analytical results.
- Instructor: Mahdi Aliyari
More About This CourseCourse outline
Introduction: concepts of mathematics for signal processing & system analysis,Continuous & Discrete Time Signals ans Systems: Mathematic representation of Continuous time signals and Discrete time signals, Power & Energy of signals, Property of signals, Impulse & Step & Complex Exponential signals, Continuous time & Discrete time systems and their properties.
LTI Systems and their properties: Impulse Response, Convolution concept, property of impulse response, Description of systems according to differential & diference equations, I & II Direct Realization based on differential & difference equations, FIR and IIR response.
The Fourier series of periodic continuous signals: The fourier series and it’s the convergence & properties, Importance of fourier series in calculation of response of the LTI continuous systems.
The Fourier Transform of continuous signals: The fourier transform and its properties, The convergence of fourier transform, Relation of between the fourier series & the fourier transform, Fourier transform of periodic signals, Analysis of the LTI continuous systems with the fourier transform, I & II Direct Realization based on the fourier transform.
The Laplace Transform: The Two-sided Laplace transform and its the convergence & properties, Inverse Laplace transform, Relation of between the two-sided laplace transform & the fourier transform, Unilateral Laplace Transform and it’s the convergence & properties, Analysis of the LTI continuous systems with the laplace transform, I & II Direct Realization based on the laplace transform, The stability concept with laplace transform.
Sampling: Sampling theorem, Ideal forms, aliasing phenomenon, Reconstruction.
The Fourier series of periodic discrete signals: The fourier series and it’s the convergence & properties, Importance of fourier series in calculation of response of the LTI discrete systems.
The Fourier Transform of discrete signals: The discrete time fourier transform (DTFT) and it’s the convergence & properties, Relation of between the fourier series and DTFT, DTFT for the periodic signals, Discrete Fourier Transform (DFT) and it’s the convergence & properties, FFT algorithms, Analysis of the LTI discrete systems with DTFT, I & II Direct Realization based on DTFT.
The z Transform: The Two-sided z transform and it’s the convergence & properties, Inverse z transform, Between the two-sided z transform & the DTFT, Unilateral z Transform and it’s the convergence & properties, Analysis of the LTI discrete systems with z transform , I & II Direct Realization based on z transform, Relation of between z transform and the laplace transform, Simulating continuous time systems with discrete time systems (Impulse Invariant response, Backward Difference Approximation, The Bilinear Transformation), The stability concept with z transform.
Some Applications: filtering and applications, Modulation (DSB & AM), Analysis of systems with state space.
Textbooks
- A.V. Oppenheim & A.S. Willsky & S.H. Nawab, Signas and Systems ,second edition ,Pearson., 2014.
- R.E. Ziemer & W.H. Tranter & D.R. Fannin, Signals and Systems Continuous and Discrete, 4th Edition, Pearson, 2014.
- S. Haykin & B. Van Veen, Signals and Systems, Second Edition, Wiley, 2003.
- M.J. Roberts, Signals and Systems Analysis Using Transform Methods and Matlabs, International Edition, McGraw-Hill , 2004.