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| ELKL7410 | Multivariable Control Systems | 3+0+0 | ECTS:7.5 | | Year / Semester | Fall Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of ELECTRICAL and ELECTRONICS ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face, Group study | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | -- | | Co-Lecturer | | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The objective of this course is to introduce the students to analysis and synthesis methods to design multivariable control systems. In addition, the course aims to provide solutions of H2 and H∞ optimal control problems and heuristic algorithms used in controller design. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | Have the background of multivariable control system design | 1,3,5 | 1,3,6 | | PO - 2 : | Calculate L2 , H2 , L∞ and H∞ norms and internal stability . | 1,3,5 | 1,3,6 | | PO - 3 : | Design H2 ve H∞ optimal controllers. | 1,3,5 | 1,3,6 | | PO - 4 : | Design PID and FOPID controllers using heuristic algorithms | 1,3,5,8 | 1,3,6 | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| Linear spaces, Invariant subspaces, Multivariable system poles and zeros, Hilbert spaces, H2 and H∞ spaces, Power and spectral norms, Computing L2 and H2 norms, Feedback structure, Well-posedness of feedback loop,? Internal stability, Model Reduction, Lyapunov equations and inequalities, Observability operator and grammian, Controllability operator and grammian, H2 optimal control motivation, Standard LQR problem, Extended LQR problem, H∞ control, Heuristic algorithms and cost functions used in controller design. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Motivation, Linear spaces, Eigenvalues and eigenvectors, Invariant subspaces, Vector and matrix norms | | | Week 2 | Linear dynamical systems, Controllability and observability, State space realization, Multivariable system poles and zeros | | | Week 3 | Hilbert spaces, H2 and H ∞ spaces, Power and spectral norms, Computing L2 and H2 norms | | | Week 4 | Computing L ∞ and H ∞ norms, Feedback structure, Well-posedness of feedback loop, Internal stability | | | Week 5 | Model Reduction, Lyapunov equations and inequalities, Observability operator and grammian, Controllability operator and grammian | | | Week 6 | Model uncertainty, Small gain theorem, Stability under unstructured uncertainty | | | Week 7 | Static state feedback stabilization via LMIs, An LMI characterization of the stabilization problem, Controller parametrization, Existence of stabilizing controllers | | | Week 8 | Parametrizing all stabilizing controller, H2 optimal control: motivation, Standard LQR problem, Extended LQR problem | | | Week 9 | Mid-term exam | | | Week 10 | H∞ optimal kontrol | | | Week 11 | Denetleyici tasarımında kullanılan sezgisel algoritmalar | | | Week 12 | Heuristic algorithms used in controller design, cost functions | | | Week 13 | PID and Fractional order PID (FOPID) controller design via particle swarm optimization algorithm | | | Week 14 | PID and Fractional order PID (FOPID) controller design via cuckoo search algorithm | | | Week 15 | PID and Fractional order PID (FOPID) controller design via flower pollination algorithm | | | Week 16 | End-of-term exam | | | |
| 1 | Zhou K.,1998; Essentials of Robust Control, Prentice-Hall | | | |
| 1 | Zhou, K. Doyle, J.C. and Glover, K.,1996; Robust and Optimal Control, Prentice Hall | | | 2 | Dullerud, G.E. Paganini F.G. 1999; A Course in Robust Control Theory: A convex Approach, Springer-Verlag | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | | 2 | 20 | | Project | 14 | | 10 | 30 | | End-of-term exam | 16 | | 2 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 2 | 10 | 20 | | Arasınav için hazırlık | 2 | 7 | 14 | | Arasınav | 2 | 1 | 2 | | Proje | 2 | 10 | 20 | | Dönem sonu sınavı için hazırlık | 1 | 5 | 5 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 105 |
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