240AR011 - Linear Multivariable Control Systems

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Marlene Barber
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1 Coordinating unit: Teaching unit: Academic year: Degree: ECTS credits: ETSEIB - Barcelona School of Industrial Engineering ESAII - Department of Automatic Control MASTER'S DEGREE IN AUTOMATIC CONTROL AND ROBOTICS (Syllabus 2012). (Teaching unit Compulsory) 6 Teaching languages: English Teaching staff Coordinator: Others: ROBERTO GRIÑO CUBERO Primer quadrimestre: YOLANDA BOLEA MONTE - 10 ROBERTO GRIÑO CUBERO - 10 MARIA SERRA PRAT - 10 Prior skills The student should have basic skills in mathematics (linear algebra, elementary calculus, complex variable and linear differential equations), in automatic control (continuous-time linear systems, in their time and frequency domain approach) and in signal analysis. Degree competences to which the subject contributes Specific: 2. The student will be able to use analysis tools and computer-aided design of control systems in the tasks usual analysis, simulation and controller design. 3. The student will be able to analyze and design linear systems (single and multiple variables, external and internal representation) and nonlinear systems. This includes their stability, controller design and evaluation of closed-loop response. Generical: 1. Have adequate mathematical skills, analytical, scientific, instrumental, technological, and management information. 4. Ability to reason and act based on the so-called culture of safety and sustainability Transversal: 5. FOREIGN LANGUAGE: Achieving a level of spoken and written proficiency in a foreign language, preferably English, that meets the needs of the profession and the labour market. Teaching methodology The teaching methodology will combine lectures together with supervised learning based on problems and autonomous learning. The classes will be organized in theoretical sessions and problems/practice sessions in the computer labs. The master classes will be focused in the explanation of theoretical concepts by the Professor, promoting an active participation of the students. In the problems/practices classes in the computer lab, different problems will be proposed requiring the use of Computer Aided Control Systems Design (CACSD) computer tools for their resolution. Learning objectives of the subject 1 / 5

2 The objective of this course is to introduce the students in the analysis and design techniques of feedback control for multivariable systems from an external description standpoint (input-output). A special emphasis will be put in the use of the feedback in order to modify the system dynamics and to reduce its sensitivity in front of perturbations and uncertainties of the plant's model. Learning Outcomes: Use the basics of linear classical control and linear multivariable control in continuous-time systems. Use essential software for control system analysis and design and dynamic system modeling. Analyse the benefits and limitations of control systems and their applications. Compulsory contents: Time and frequency analysis of linear dynamic systems and control design. External and internal representation of dynamic systems. Analysis and design of multivariable control systems. Stability of dynamic systems. Performance specifications and limitations in the design of feedback systems. Controllers' parametrization. Linear representations of dynamic systems. Study load Total learning time: 150h Hours large group: 0h 0.00% Hours medium group: 36h 24.00% Hours small group: 18h 12.00% Guided activities: 0h 0.00% Self study: 96h 64.00% 2 / 5

3 Content Elements of linear systems theory Learning time: 25h Theory classes: 9h Laboratory classes: 0h Self study : 16h Matrix theory, singular values decomposition (SVD), rules for vectors and matrixes, systems descriptions, stability, poles and zeros, controllability and observability, internal stability, controller parametrization and systems rules. Lectures Know basic results of mathematics useful for the subject. Know and handle basic concepts of linear systems theory. Advanced aspects in the analysis and design of monovariable control systems Learning time: 52h 47m Theory classes: 15h Laboratory classes: 4h Self study : 33h 47m Frequency domain, feedback control and stability, performance evaluation of closed-loop systems, controller design (using transfer functions in open and closed loop), design limitations, perfect control and plant inversion, uncertainty in the frequency domain, robust stability and robust performance. Lectures and problems/practices sessions. Widen knowledge of monovariable linear systems. Know and handle the implications in the design of limitations imposed by the plant characteristics. Know and use the frequency description of the uncertainty and the concepts of stability and robust performance. 3 / 5

4 Analysis and design of multivariable control systems Learning time: 72h 13m Theory classes: 18h Laboratory classes: 8h Self study : 46h 13m External description in multivariable systems, frequency response, relative gain array, control of multivariable plants, general control problem, design limitations, uncertainty representation, robust stability, structured singular value (mu), robust stability using mu, robust performance, introduction to mu-synthesis, controller design (LQG, H2 and Hinf), model reduction and controller's implementation. Lectures and problems/practices sessions. Know and handle external and internal descriptions of multivariable systems. Know and handle classical control and analysis techniques of multivariable systems. Know and use fluently the general control problem formulation with and without uncertainty and the concepts of robust stability and robust performance. Know and handle some well-known methods in controller design for multivariable systems. Know basic aspects of the methods for model reduction and for those problems which appear in controllers' implementations. Qualification system The acquired competences and abilities will be evaluated on the basis of three qualifications: the mark of a practical work exam solved in the computer room (30%), the mark of the discretional evaluation of the practical works sessions (10%) and the mark of the subject's final exam (60%). Revaluation (July): * Final exam consisting of problems over the entire course syllabus. The new final mark resulting from the revaluation is calculated by substituting in the previous formula the final exam by the reevaluation exam. Regulations for carrying out activities The exams can be done with all the written information (books and prepared notes) that students want to take with them to the exam. 4 / 5

5 Bibliography Basic: Skogestad, Sigurd; Postlethwaite, Ian. Multivariable feedback control : analysis and design. 2nd ed. Chichester: John Wiley & sons, cop ISBN Complementary: Zhou, Kemin; Doyle, John C. Essentials of robust control. Upper Saddle River: Prentice Hall International, cop ISBN Zhou, Kemin; Glover, Keith; Doyle, John C. Robust and optimal control. Upper Saddle River, NJ: Prentice Hall, cop ISBN Maciejowski, Jan Marian. Multivariable feedback design. Wokingham: Addison-Wesley, ISBN Chen, Chi-Tsong. Linear system theory and design. 3rd ed. New York ; Oxford: Oxford University Press, cop ISBN Kailath, Thomas. Linear systems. Englewood Cliffs, NJ: Prentice-Hall, cop ISBN Horn, Roger A; Johnson, Charles R. Matrix analysis. 2nd ed. Cambridge etc.: Cambridge University Press, ISBN Horn, Roger A; Johnson, Charles R. Topics in matrix analysis. Cambridge: Cambridge University Press, ISBN X. Marcus, Marvin; Minc, Henryk. A Survey of matrix theory and matrix inequalities. New York: Dover, ISBN X. Bernstein, Dennis S. Matrix mathematics : theory, facts, and formulas. 2nd ed. Princeton ; Oxford: Princeton University Press, ISBN / 5

SAM - Sensors, Actuators and Microcontrollers in Mobile Robots

SAM - Sensors, Actuators and Microcontrollers in Mobile Robots Coordinating unit: Teaching unit: Academic year: Degree: ECTS credits: 2017 230 - ETSETB - Barcelona School of Telecommunications Engineering 710 - EEL - Department of Electronic Engineering BACHELOR'S