Robust control
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Faculteit  Science and Engineering 
Jaar  2018/19 
Vakcode  WIRC09 
Vaknaam  Robust control 
Niveau(s)  master 
Voertaal  Engels 
Periode  semester II a 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Robust control  
Leerdoelen  At the end of the course, the student is able to: 1. reproduce the geometric characterizations of the systems properties of controllability, stabilizability, observability and detectability. 2. state the problem of stabilization by dynamic output feedback, and reproduce its solution via the notion of separation principle. 3. state the formulation of the Hinfinity suboptimal control problem, both in the timedomain and in transfer function terms. 4. state the formulation of the bounded real lemma, and to reproduce its proof. 5. state the necessary and sufficient conditions for solvability of the Hinfinity control problem in terms of linear matrix inequalities (LMIs). 6. reproduce the formulation of the optimal robust stabilization problem for additive and multiplicative perturbations, and is able to outline the solutions to these problems using the solution of the Hinfinity control problem. 7. state the small gain theorem, and to outline its proof. 8. apply the material presented in the course to formulate and prove extensions of results from the course, and present these results written in a mathematically sound way. 

Omschrijving  The course Robust Control is an advanced course on control theory for linear systems. We start the course with a brief review of basic concepts from the theory of finite dimensional, linear, timeinvariant systems like controllability, observability, stabilizability and detectability, and the problem of internal stabilization by measurement feedback. The next subject is the design of feedback controllers that make the influence of unknown external disturbance inputs to the system on the to be controlled system outputs small. This influence is measured in terms of the Hinfinity norm of the associated closed loop transfer matrix. We give necessary and sufficient conditions for the existence of these controllers in terms of linear matrix inequalities (LMI’s). Subsequently, the results on the Hinfinity control problem is applied to compute feedback controllers that not only stabilize the nominal system model, but also all system models in a maximal neighbourhood of the nominal system model. The latter control problem is known as the problem of optimal robust stabilization. A controller is called 'robust' if it also works well for all system models in a neighbourhood of the nominal model. The notion of neighborhood depends on the nature of the perturbations that are considered. We distinguish between additive and multiplicative perturbations. A robust controller is expected to work well also for the actual physical system to which it is applied.  
Uren per week  
Onderwijsvorm 
Hoorcollege (LC), Opdracht (ASM)
(The course consists of eight weeks of lectures, 4 hours per week. After week 1 and 4, a set of homework assignments is handed out. The students work on these problems individually for three weeks and then hand in the workedout solutions. Each of the two homework assignments is graded.) 

Toetsvorm 
Opdracht (AST), Schriftelijk tentamen (WE)
(The final grade is determined as the weighted average of the two homework assignments (each counts for 30%) and the grade for the written exam (counting for 40%).) 

Vaksoort  master  
Coördinator  prof. dr. H.L. Trentelman  
Docent(en)  prof. dr. H.L. Trentelman  
Verplichte literatuur 


Entreevoorwaarden  The course builds on knowledge of systems and control, obtained in e.g. "Project Systems Theory” (BSc), “Advanced Systems Theory” (BSc), and "Calculus of Variations and Optimal Control" (BSc).  
Opmerkingen  
Opgenomen in 
