Course syllabus adopted 2021-02-26 by Head of Programme (or corresponding).
Overview
- Swedish nameRobust och olinjär reglering
- CodeEEN050
- Credits7.5 Credits
- OwnerMPSYS
- Education cycleSecond-cycle
- Main field of studyAutomation and Mechatronics Engineering, Electrical Engineering
- DepartmentELECTRICAL ENGINEERING
- GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Course round 1
- Teaching language English
- Application code 35120
- Block schedule
- Open for exchange studentsYes
Credit distribution
Module | Sp1 | Sp2 | Sp3 | Sp4 | Summer | Not Sp | Examination dates |
|---|---|---|---|---|---|---|---|
| 0119 Examination 4 c Grading: TH | 4 c |
| |||||
| 0219 Design exercise + laboratory 3.5 c Grading: UG | 3.5 c |
In programmes
- MPAUT - AUTOMOTIVE ENGINEERING, MSC PROGR, Year 2 (elective)
- MPEPO - SUSTAINABLE ELECTRIC POWER ENGINEERING AND ELECTROMOBILITY, MSC PROGR, Year 2 (elective)
- MPSYS - SYSTEMS, CONTROL AND MECHATRONICS, MSC PROGR, Year 1 (compulsory elective)
- MPSYS - SYSTEMS, CONTROL AND MECHATRONICS, MSC PROGR, Year 2 (elective)
Examiner
Balázs Adam Kulcsár- Professor, Systems and Control, Electrical Engineering
Eligibility
General entry requirements for Master's level (second cycle)Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Specific entry requirements
English 6 (or by other approved means with the equivalent proficiency level)Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Course specific prerequisites
A basic course in automatic control and familiarity with state space techniques (as taught in e.g. the course Linear control system design)
Aim
In this course we first purport to develop controllers that explicitly deals with uncertainty and disturbance. We start with linear time invariant and parameter dependent models and aim at designing robust controllers. Second, we introduce nonlinear dynamics and related controller design methods that covers a wide range and practically important class of systems. Application oriented methods are focused.
Learning outcomes (after completion of the course the student should be able to)
- Understand signals and systems sizes and explain the limitations of nominal Linear Time Invariant (LTI) control methods.
- Identify and describe the most important uncertainty phenomena for SISO and MIMO LTI dynamical systems;
- Formulate robust control objectives and understand methods for calculating them.
- Apply the theory of gain scheduled control to reach robust objectives.
- Understand the limitations of uncertain linear or parameter scheduled control systems. Analyse the stability properties of nonlinear systems;
- Apply a few methods for nonlinear control system design and to assess the performance of the resulting design;
- Use software tools for analysis and synthesis of nonlinear control systems, and to present and motivate their solution
Content
The course consists of two main parts.- Goals with robust control design, examples. Linear Time Invariant zeros-poles. Vector and system norms. IO (SGT) and internal stability, SISO vs MIMO.
- Uncertainty and robustness for SISO and MIMO system models. Nominal and robust stability and performance. Design trade-offs.
- Robust controller design; H2, H∞. From full information to central H∞. Lyapunov stability. Linear Parametrically Varying (LPV) Control System design.
- From LPV to nonlinear control design, examples
- Common nonlinearities, stationary points and limit cycles, stability, Lyapunov's method, input/output stability, passivity; phase plane analysis. Nonlinear controllability, observability.
- Relative degree, zero dynamics. Exact (Feedback) linearization. Back-stepping, passivation
Organisation
The course is organised as a number of lectures and problem sessions, and a mandatory project module, including analysis and design assignments and lab.Literature
(1) S Skogestad, I Postlethwaite: Multivariable Feedback Control: Analysis and Design
(2) HK Khalil: Nonlinear systems.
Examination including compulsory elements
Written exam with TH grading; project with assignments and laboratory sessions (pass/fail).The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.