# Modern Control Theory

 Title ΜΟΝΤΕΡΝΑ ΘΕΩΡΙΑ ΕΛΕΓΧΟΥ / Modern Control Theory Code 0462 Faculty Sciences School Mathematics Cycle / Level 1st / Undergraduate Teaching Period Spring Coordinator Nikolaos Karampetakis Common No Status Active Course ID 40000486

### Programme of Study: UPS of School of Mathematics (2014-today)

Registered students: 1
OrientationAttendance TypeSemesterYearECTS
CoreElective Courses845

 Academic Year 2015 – 2016 Class Period Spring Faculty Instructors Weekly Hours 3 Class ID 600004812
Type of the Course
• Scientific Area
• Skills Development
Course Category
Specific Foundation / Core
Mode of Delivery
• Face to face
Language of Instruction
• Greek (Instruction, Examination)
Learning Outcomes
Upon the successful completion of this course a student will be able to: a) transform the description of a linear, time-invariant, multivariable system to all possible descriptions (transfer function matrix, state space description etc. b) calculate and plot the time response of a state space system, c) transform of a given state space system to various canonical forms, d) design the block diagram and signal flow of a system described by state space equations, e) check system properties such as controllability , stabilizability, observability, and detectability, f) calculate and design a compensator capable to place the poles of the system to a specific region, g) calculate and design an optimal controller, h) calculate and design a system observer, i) create a controller that will use an oberver for the estimation of the states, j) to apply the separation principle.
General Competences
• Apply knowledge in practice
• Retrieve, analyse and synthesise data and information, with the use of necessary technologies
• Make decisions
• Work in teams
Course Content (Syllabus)
State space models of LTI continuous time systems. Single input – single output systems. Multivariable systems. Block diagrams and realizations of state space models. Examples. System equivalence and state space coordinate transformations. Examples. Eigenvalues and eigenvectors. Diagolalization of matrices and diagonalization of state space models by coordinate transformations. State space realizations of transfer functions. State space system responses. Unit impulse and unit step response of state space models. LTI systems. Free and forced response of state space models. Canonical forms of state space models. Controllability. Observaability. Controllability and Obserability criteria. Stabilization of state space models and decoupling zeros. Stability of state space models. Eigenvalue criteria for stability. Asymptotic and BIO stability. State feedback. Eigenvalue assignment by state feedback. Constant output feedback. State Observers and state reconstruction. Stabilization by state observers and state feedback. The separation principle.
Keywords
state space systems, modern control theory, controllability, observability, pole placement, observers, stability
Educational Material Types
• Notes
• Slide presentations
• Book
Use of Information and Communication Technologies
Use of ICT
• Use of ICT in Course Teaching
• Use of ICT in Laboratory Teaching
• Use of ICT in Communication with Students
Course Organization
Lectures391.3
Laboratory Work130.4
Total521.7
Student Assessment
Description
- Written exams at the end of the semester. - Optional monitoring a laboratory course where the result of the examination will count 30% of the final score. The remaining 70% of the score will come from the final exams.
Student Assessment methods
• Written Assignment (Summative)
• Written Exam with Problem Solving (Formative, Summative)
• Labortatory Assignment (Formative)
Bibliography
Course Bibliography (Eudoxus)
- Εισαγωγή στην Μαθηματική Θεωρία Σημάτων, Συστημάτων και Ελέγχου, Τόμος Β. Μοντέρνα Θεωρία Ελέγχου του Α. Βαρδουλάκη. - Γραμμικά συστήματα αυτομάτου ελέγχου των E. Charles, G. Donald, L. James, J. Melsa, C. Rohrs, D. Schultz. - Linear Systems [electronic resource] των P. J. Antsaklis, A. N. Michel.