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 Lisans Öğrencileri Lisansüstü Adayları


Credits: 3


Catalog Description: Analysis of linear control systems by differential equations and transfer function methods using Laplace transforms. Stability of closed loop systems. Routh-Hurwitz criterion, root-locus diagrams. System analysis in frequency domain. Bode and polar plots. Nyquist stability criterion.

Prerequisites: MATH 202, EE 201.

Coordinators: Yağmur Denizhan, Associate Professor of Electrical Engineering


Goals: To teach to and to enable the students to apply basic mathematical concepts and methods for analysis, design and simulation of linear automatic control systems.


Learning Objectives:


At the end of this course, students will be able to:

1.     Find mathematical models of dynamic systems.

2.     Analyse linear dynamic systems using transient and steady-state response analysis

3.     Analyse dynamic systems using their frequency response.

4.     Apply root-locus analysis of control systems.

5.     Analyze stability of dynamic systems by using Routh-Hurwitz or Nyquist stability criteria.

6.     Understand the fundamental concepts of linear control systems.


Textbook: K. Ogata, Modern Control Engineering, Fourth Edition, Prentice-Hall, 2002.

Reference Texts:


1.     G.F. Franklin, J.D. Powell, A. Emami-Naeini, Feedback Control of Dynamic Systems, Prentice-Hall, 2002.

2.     P.J. Dorf, Modern Control Systems,  Addison-Wesley, 1989.

3.     J. Golten and A. Verwer, Control System Design and Simulation, McGraw-Hill, 1991.


Prerequisites by Topic:

·         Ordinary differential equations

·         Vector-matrix analysis

·         Circuit analysis

·         Mechanics




1.     An introduction to control systems. (1 week)

2.     Modelling of dynamic systems. (3 weeks)

3.     Basic linear control actions (1 week)

4.     System time response. (1 weeks)

5.     Stability and Routh-Hurwitz criterion (1 week)

6.     Root-locus analysis of control systems. (2 weeks)

7.     Frequency response analysis. (1 weeks)

8.     Bode and polar plots. (2 weeks)

9.     Nyquist stability criterion. (1 week)


Course Structure: The class meets for three lectures a week, each consisting of 50-minute sessions, and one problem session consisting of a 50-minute session. Problem sessions are sometimes used to solve some example problems, for quizzes and one computer session per semester.  There are two in-class mid-term exams and a final exam.

Computer Resources: Students are encouraged to use MATLAB to understand the effects of different control actions and visualize the frequency domain plots.

Laboratory Resources: Computer lab.



·          Quizzes and lab    15 %

mid-terms              25 % each
Final                      35 %

Outcome Coverage:


·         Apply math, science and engineering knowledge. The course is about control systems modeling, design and simulation.  It makes use of different tools from mathematics (ordinary differential equations, linear algebra, complex variables, vector-matrix analysis) as well as from sciences (physics) and engineering (mechanics, circuit analysis).

·         Design a system, component or process to meet desired needs. Students are introduced to the fundamental concepts of control systems design. In particular, design of PID controllers with the root-locus method and frequency-response methods are covered.

·         Use of modern engineering tools. Students use MATLAB and a number of MATLAB packages (like Control Toolbox, Simulink) in the computer lab.


Prepared By: Yagmur Denizhan




Boğaziçi Üniversitesi - Elektrik ve Elektronik Mühendisliği Bölümü

34342 - Bebek / İSTANBUL

Tel: +90 212 359 64 14
Fax: +90 212 287 24 65







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