Course detail
Robust and algebraic control
FEKT-MPA-RALAcad. year: 2022/2023
The course is focused on application of algebraic theory for control circuit’s synthesis. It consists of algebraic theory, the controller designs using polynomial methods, structured and unstructured uncertainties of dynamic systems and introduction into robust control.
Language of instruction
English
Number of ECTS credits
5
Mode of study
Not applicable.
Guarantor
Offered to foreign students
Of all faculties
Learning outcomes of the course unit
After passing the course, student should be able to
- solve algebraic equations and understand algebraic theory
- utilize basic algebraic methods for controller designs
- explain the relationship between sensitivity function and modulus stability margin
- describe the possibilities of sensitivity function shaping and use them for robust controller design
- determine stability of interval polynomials
- utilize parametric and non-parametric uncertainties in the environment of MATLAB Simulink
- design the controller using H infinity mixed sensitivity method
- solve algebraic equations and understand algebraic theory
- utilize basic algebraic methods for controller designs
- explain the relationship between sensitivity function and modulus stability margin
- describe the possibilities of sensitivity function shaping and use them for robust controller design
- determine stability of interval polynomials
- utilize parametric and non-parametric uncertainties in the environment of MATLAB Simulink
- design the controller using H infinity mixed sensitivity method
Prerequisites
The subject knowledge on the Bachelor´s degree level is requested.
Co-requisites
Not applicable.
Planned learning activities and teaching methods
Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations. Materials for lectures and exercises are available for students from web pages of the course. Students have to write a single project/assignment during the course.
Assesment methods and criteria linked to learning outcomes
Exercises. Individual project. Max. 30 points.
Exam. Max 70 points.
Exam. Max 70 points.
Course curriculum
1. Introduction into problematic.
2. Algebraic theory. Solution of polynomial equation, general solution, special solutions, solvability condition.
3. Application of algebraic methods to simple controller designs. Pole placement method, exact model matching problem, the group of stabilizing controllers.
4. Sensitivity function shaping design. Sensitivity function and modulus margin, sensitivity function template, additional polynomials in controller and in its design.
5. Time optimal discrete control. Feedforward control,
6. Quadraticaly optimal discrete control, 1DOF, 2DOF, finite and stable time optimum control with nonzero initial conditions.
7. Stochastic control. Minimum variance control, the evaluation of MVC controllers, generalized minimum variance control.
8. Interval polynomials. Zero exclusion principle, value sets, Mikhailov-Leonard stability criteria, Kharitonov polynomials.
9. Introduction to robust control. Robustness, signal and system norms.
10. H infinity control. Linear fractional transformation, mixed sensitivity design, gamma iteration.
11. H2 control, comparison with LQ control, H2 optimal state controller design, H2 optimal state observer design, duality of both approaches.
12. Uncertainties description. Classification of uncertainties, affine/polytopic uncertainties, gain scheduling controller design. Additive, multiplicative and feedback uncertainties. Small gain theorem, D-K iteration.
13. Linear Matrix Inequalities (LMI), quadratic form LJ and its conversion to LMI, LQG using LMI, H infinity using LMI
2. Algebraic theory. Solution of polynomial equation, general solution, special solutions, solvability condition.
3. Application of algebraic methods to simple controller designs. Pole placement method, exact model matching problem, the group of stabilizing controllers.
4. Sensitivity function shaping design. Sensitivity function and modulus margin, sensitivity function template, additional polynomials in controller and in its design.
5. Time optimal discrete control. Feedforward control,
6. Quadraticaly optimal discrete control, 1DOF, 2DOF, finite and stable time optimum control with nonzero initial conditions.
7. Stochastic control. Minimum variance control, the evaluation of MVC controllers, generalized minimum variance control.
8. Interval polynomials. Zero exclusion principle, value sets, Mikhailov-Leonard stability criteria, Kharitonov polynomials.
9. Introduction to robust control. Robustness, signal and system norms.
10. H infinity control. Linear fractional transformation, mixed sensitivity design, gamma iteration.
11. H2 control, comparison with LQ control, H2 optimal state controller design, H2 optimal state observer design, duality of both approaches.
12. Uncertainties description. Classification of uncertainties, affine/polytopic uncertainties, gain scheduling controller design. Additive, multiplicative and feedback uncertainties. Small gain theorem, D-K iteration.
13. Linear Matrix Inequalities (LMI), quadratic form LJ and its conversion to LMI, LQG using LMI, H infinity using LMI
Work placements
Not applicable.
Aims
To introduce to the students universal tool for solving tasks of automatic control and to became familiar with robust control.
Specification of controlled education, way of implementation and compensation for absences
The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.
Recommended optional programme components
Not applicable.
Prerequisites and corequisites
Not applicable.
Basic literature
Doyle, Francis, Tannenbaum: Feedback Control Theory, Macmillan Publishing (EN)
Havlena, V., Štecha, J.: Moderní teorie řízení, Skriptum ČVUT, Praha 2000 (EN)
Scherer, Weiland: Linear matrix inequalities in control. DISC, 2000 (EN)
Havlena, V., Štecha, J.: Moderní teorie řízení, Skriptum ČVUT, Praha 2000 (EN)
Scherer, Weiland: Linear matrix inequalities in control. DISC, 2000 (EN)
Recommended reading
Not applicable.
Elearning
eLearning: currently opened course
Classification of course in study plans
Type of course unit
Lecture
26 hod., optionally
Teacher / Lecturer
Syllabus
1. Introduction into problematic.
2. Algebraic theory. Solution of polynomial equation, general solution, special solutions, solvability condition.
3. Application of algebraic methods to simple controller designs. Pole placement method, exact model matching problem, the group of stabilizing controllers.
4. Sensitivity function shaping design. Sensitivity function and modulus margin, sensitivity function template, additional polynomials in controller and in its design.
5. Time optimal discrete control. Feedforward control,
6. Quadratically optimal discrete control, 1DOF, 2DOF, finite and stable time optimum control with nonzero initial conditions.
7. Stochastic control. Minimum variance control, the evaluation of MVC controllers, generalized minimum variance control.
8. Interval polynomials. Zero exclusion principle, value sets, Mikhailov-Leonard stability criteria, Kharitonov polynomials.
9. Introduction to robust control. Robustness, signal and system norms.
10. H infinity control. Linear fractional transformation, mixed sensitivity design, gamma iteration.
11. H2 control, comparison with LQ control, H2 optimal state controller design, H2 optimal state observer design, duality of both approaches.
12. Uncertainties description. Classification of uncertainties, affine/polytopic uncertainties, gain scheduling controller design. Additive, multiplicative and feedback uncertainties. Small gain theorem, D-K iteration.
13. Linear Matrix Inequalities (LMI), quadratic form LJ and its conversion to LMI, LQG using LMI, H infinity using LMI
2. Algebraic theory. Solution of polynomial equation, general solution, special solutions, solvability condition.
3. Application of algebraic methods to simple controller designs. Pole placement method, exact model matching problem, the group of stabilizing controllers.
4. Sensitivity function shaping design. Sensitivity function and modulus margin, sensitivity function template, additional polynomials in controller and in its design.
5. Time optimal discrete control. Feedforward control,
6. Quadratically optimal discrete control, 1DOF, 2DOF, finite and stable time optimum control with nonzero initial conditions.
7. Stochastic control. Minimum variance control, the evaluation of MVC controllers, generalized minimum variance control.
8. Interval polynomials. Zero exclusion principle, value sets, Mikhailov-Leonard stability criteria, Kharitonov polynomials.
9. Introduction to robust control. Robustness, signal and system norms.
10. H infinity control. Linear fractional transformation, mixed sensitivity design, gamma iteration.
11. H2 control, comparison with LQ control, H2 optimal state controller design, H2 optimal state observer design, duality of both approaches.
12. Uncertainties description. Classification of uncertainties, affine/polytopic uncertainties, gain scheduling controller design. Additive, multiplicative and feedback uncertainties. Small gain theorem, D-K iteration.
13. Linear Matrix Inequalities (LMI), quadratic form LJ and its conversion to LMI, LQG using LMI, H infinity using LMI
Fundamentals seminar
14 hod., compulsory
Teacher / Lecturer
Syllabus
7. The work on the project. Design of the controller using sensitivity function shaping.
8. Computation with parametric uncertainties. Interval uncertainties. Conversion to structured uncertainties.
9. H infinity controller design. Loop shaping design method.
10. H infinity controller design. Mixed sensitivity design.
11. H infinity controller design , inverted pendulum example.
12. Robust controller design for MIMO systems.
13. Reserve, conclusions.
8. Computation with parametric uncertainties. Interval uncertainties. Conversion to structured uncertainties.
9. H infinity controller design. Loop shaping design method.
10. H infinity controller design. Mixed sensitivity design.
11. H infinity controller design , inverted pendulum example.
12. Robust controller design for MIMO systems.
13. Reserve, conclusions.
Exercise in computer lab
12 hod., compulsory
Teacher / Lecturer
Syllabus
1. Becoming familiar with functions from Symbolic Math Toolbox in MATLAB.
2. Basic notations in algebraic methods.
3. Preparation of function for the computation of the general and particular solution of polynomial equation.
4. Stabilizing controller design, modal controller, EMMP problem solution.
5. Design of time optimal controllers for one degree of freedom control structure.
6. Design of time optimal controllers for two degrees of freedom control structure.
2. Basic notations in algebraic methods.
3. Preparation of function for the computation of the general and particular solution of polynomial equation.
4. Stabilizing controller design, modal controller, EMMP problem solution.
5. Design of time optimal controllers for one degree of freedom control structure.
6. Design of time optimal controllers for two degrees of freedom control structure.
Elearning
eLearning: currently opened course