 MECHATRONICS ENGINEERING (ENGLISH, NONTHESIS) Master TR-NQF-HE: Level 7 QF-EHEA: Second Cycle EQF-LLL: Level 7

# Course Introduction and Application Information

 Course Code Course Name Semester Theoretical Practical Credit ECTS MCH5001 Linear System Theory Fall 3 0 3 8

### Basic information

 Language of instruction: English Type of course: Must Course Course Level: Mode of Delivery: Face to face Course Coordinator : Dr. Öğr. Üyesi MUSTAFA EREN YILDIRIM Recommended Optional Program Components: None Course Objectives: To provide advanced system theoretic concepts with emphasis on linear systems.

### Learning Outcomes

 The students who have succeeded in this course; Students will be able - to define a dynamical system as a mathematical object - to comprehend linearity and time-invariance - to relate time- and frequency-domain representations of linear time-invariant (LTI) systems - to determine response of LTI systems to specific inputs - to understand the concept of controllability and to relate it to such problems as setting up the initial conditions, eigenvalue placement by state feedback, stabilization by optimal feedback control - to understand the concept of observability and to relate it to such problems as calculation of the initial conditions and observer design

### Course Content

 Dynamical system representation. State-space representation of continuous-time (CT) systems: Solution of CT state equations, impulse response, convolution integral. State-space representation of discrete-time (DT) systems: solution of DT state equations, pulse response, convolution sum. Modes of unforced solutions. Transfer function. Controllability and state feedback. Observability and observer design. Dynamic output feedback

### Weekly Detailed Course Contents

 Week Subject Related Preparation 1) Dynamical system representation. Concept of state. Causality. 2) Finite state, finite dimensional and infinite dimensional systems. Lineariy and time-invariance. 3) State space representation of continuous-time (CT) linear systems. State transition matrix. 4) State-space representation of CT linear, time-invariant (LTI) systems. Impulse response and transfer function matrices. 5) Modes of CT LTI systems. Modal decomposition of solutions. 6) Discrete-time (DT) LTI systems. 7) Sampled-data systems. 8) Review and midterm exam 9) Controllability of LTI systems. Setting up the initial conditions. 10) Observability of LTI systems. Calculation of the initial state. 11) Canonical decomposition. Separation of controllable and unobservable subspaces. 12) Eigenvalue assignment by state-feedback. 13) Observer design. 14) Pole placement by dynamic output feedback.

### Sources

 Course Notes / Textbooks: - W.L. Brogan, Modern Control Theory, Prentice Hall References: - C-T. Chen, Linear System Theory and Design, HRW

### Evaluation System

 Semester Requirements Number of Activities Level of Contribution Homework Assignments 5 % 25 Midterms 1 % 25 Final 1 % 50 Total % 100 PERCENTAGE OF SEMESTER WORK % 50 PERCENTAGE OF FINAL WORK % 50 Total % 100