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MSc in Electrical Engineering

## Course Information Package

Course Unit TitleLINEAR SYSTEMS ANALYSIS
Course Unit CodeAEEE542
Course Unit DetailsMSc Electrical Engineering (Required Courses) -
Number of ECTS credits allocated7
Learning Outcomes of the course unitBy the end of the course, the students should be able to:
1. Review eigenvalues, eigenvectors, Canonical coordinate systems and matrix functions. Classify Dynamic System, derive formulation of state models and time-domain solutions.
2. Identify the Relationship between State Variable and Transfer Function Description of Systems.
3. Use Liapunov stability analysis for the design of feedback control systems.
4. Apply Controllability and Observability conditions for Time Invariant Systems with Distinct and Arbitrary Eigenvalues.
5. Apply Controllability and Observability Conditions, such as Kalman Canonical Forms, Stabilizability and Detectability.
6. Apply pole assignment techniques using state feedback, observers. Implement experimentally, Successive Loop Closure/Pole Placement Design For 2 DOF Plant.
7. Evaluate the effect of state and output Feedback on System Properties.
Mode of DeliveryFace-to-face
PrerequisitesNONECo-requisitesNONE
Recommended optional program componentsNONE
Course Contents
• Review of Matrix algebra: Eigenvalues, eigenvectors, Canonical coordinate systems and matrix functions.
• Review of State Space Concepts: Dynamic System classifications,formulation of state models, Time-domain solutions, Extension of state space model to non-linear and time-varying systems
• The Relationship between State Variable and Transfer Function Description of Systems: Transfer Function Matrices from State Equations; State Equations from Transfer Matrices, Realizations; Definition and Implication of Irreducible Realizations; Determination of Irreducible Realizations; Minimal Realizations from Matrix Fraction description.
• Stability Analysis of Linear Systems: Equilibrium State; Stability Definitions; Linear System Stability; Direct Method of Lyapunov; Use of Lyapunov Methods in Feedback Design.
• Controllability and Observability for Linear Systems: Definitions and Concepts; Time Invariant Systems with Distinct and Arbitrary Eigenvalues; Other Controllability and Observability Conditions; Kalman Canonical Forms; Stabilizability and Detectability.
• Design of Linear Feedback Control Systems: State and Output feedbacks; Effect of Feedback on System Properties; Pole Assignment Using State feedback; Partial Pole Assignment Using Static Output Feedback; Observers; A Separation Principle for Feedback Controllers; Transfer Function Version of Pole Placement; Design of Decoupled or Non-interactive Systems.
Recommended and/or required reading:
Textbooks
• R.C. Dorf and R.H. Bishop, Modern Control Systems, Prentice Hall, 2004
• K. Ogata, Modern Control Engineering, Prentice Hall, 2002
References
• G.F. Franklin, J.P. Powell and Enami-Naeini, Feedback Control of Dynamic Systems, Prentice Hall, 2002.
• N.S. Nise, Control Systems Engineering, John Willey & Sons, 2000.
Planned learning activities and teaching methods

Students are taught the course through lectures (3 hours per week) in classrooms or lectures theatres, by means of traditional tools or using computer demonstration.

Auditory exercises, where examples regarding matter represented at the lectures, are solved and further, questions related to particular open-ended topic issues are compiled by the students and answered, during the lecture or assigned as homework.

Topic notes are compiled by students, during the lecture which serve to cover the main issues under consideration and can also be downloaded from the lecturer’s webpage. Students are also advised to use the subject’s textbook or reference books for further reading and practice in solving related exercises. Tutorial problems are also submitted as homework and these are solved during lectures or privately during lecturer’s office hours. Further literature search is encouraged by assigning students to identify a specific problem related to some issue, gather relevant scientific information about how others have addressed the problem and report this information in written or orally.

Students are assessed continuously and their knowledge is checked through tests with their assessment weight, date and time being set at the beginning of the semester via the course outline.

Students are prepared for final exam, by revision on the matter taught, problem solving and concept testing and are also trained to be able to deal with time constraints and revision timetable.

The final assessment of the students is formative and summative and is assured to comply with the subject’s expected learning outcomes and the quality of the course.
Assessment methods and criteria
 Assignments 10% Tests 30% Final Exam 60%
Language of instructionEnglish
Work placement(s)NO