Course: Multivariable Control Systems

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Course title Multivariable Control Systems
Course code MTI/RVS
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Frequency of the course Every school year
Semester Summer
Number of ECTS credits 5
Language of instruction Czech
Status of course Compulsory-optional
Form of instruction Face-to-face
Work placements Course does not contain work placement
Recommended optional programme components None
  • Hubka Lukáš, Ing. Ph.D.
  • Školník Petr, Ing. Ph.D.
Course content
1. MIMO internal representation: state variable, disturbance model, reachability, observability, canonical decomposition, minimal realization, SVD factorization, model reduction. Input/output representation of MIMO systems, poles and zeros, gain matrix, directional gain, condition number. 2. The control design problem of MIMO systems, control structures, limitations on performance in MIMO systems, unstable zeros and poles of the transfer matrix, influence of time delay. Decentralized and centralized feedback control. 3. Decentralized control: Multi-loop control structure, control-loop interaction. 4. The Relative Gain Array (RGA) methology and the rules for the proper input-output pairing selection. 5. Decoupled feedback control: problem formulation, ideal, simplified and static decoupling. 6. Centralized feedback control: Internal model control (IMC) design for MIMO systems. 7. State control of MIMO systems: state estimation, separation theorem, Kalman filter. 8. Optimal states feedback LQG and LQR control for MIMO systems. 9. Fundamentals of robust control for MIMO systems. 10. Application of switching control design for MIMO systems.

Learning activities and teaching methods
Monological explanation (lecture, presentation,briefing), Project teaching
  • Semestral paper - 50 hours per semester
  • Preparation for credit - 20 hours per semester
  • Preparation for exam - 40 hours per semester
  • Class attendance - 40 hours per semester
Learning outcomes
This subject offers an overview of control methods of MIMO systems. The subject focuses on explaining decentralized and centralized control methods of MIMO systems. The accent is put on an appropriate balance between extensive theory and possibilities of engineering application. This rule is kept by exercises and lab work. There is used the MATLAB support by analysis and synthesis of MIMO systems. Laboratory with physical models serve for practical implementation of evaluated control algorithm.
"The students will acquire good knowledge of practical parameter estimation for determined MIMO model structure and method of order reduction, analysis of MIMO systems. They will become familiar with the control structure of MIMO systems and will acquire experience in decentralized and centralized control. They will gain the pairing method of measured and actuating variable and the decomposition method. By centralized control they will learn synthesis of internal model control for MIMO systems, synthesis of LQG and LQR state controller, basics of robust design control and basics of methodic of switching control design. Students will gain also the practical experiences in this given area."
The requirement is knowledge of RSS/ARI subject substance and recommended is also the absolving of MTI/CRI and MTI/STR.

Assessment methods and criteria
Combined examination, Oral exam, Written exam, Practical demonstration of acquired skills

Requirements for getting a credit are activity at the practicals /seminars and presentation of reports. Examination is of the written and oral forms.
Recommended literature
  • Albertos, P., Sala, A. Multivariable Control Systems. Springer Verlag,, 2004. ISBN 1852337389.
  • Bequette, B., W. Process Control. Modeling, Design and Simulation.. Prentice Hall, 2003. ISBN 133536408.
  • Goodwin, G., C., Graebe, S., F., Salgado, M., S. Control System Design. Prentice Hall, 2001. ISBN 139586539.
  • Marlin, T., E. Process control. Designing processes and control systems for dynamic performance.. McGraw Hill, 2000. ISBN 70404917.
  • Phillips, Ch., L., Harbor, R., D. Feedback Control Systems. Prentice Hall, 2000. ISBN 133736970.
  • Skogestad, S., & Poslethwaite, I. :. Multivariable Feedback Control. Analysis and Design.. John Wiley & Sons, 1996. ISBN 470011688.

Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Mechatronics, Informatics and Interdisciplinary Studies Study plan (Version): Automatic Control and Applied Computer Science (2016) Category: Special and interdisciplinary fields 2 Recommended year of study:2, Recommended semester: Summer