Modeling and Control of Complex Nonlinear Engineering System
Faculteit  Science and Engineering 
Jaar  2020/21 
Vakcode  WMMA02005 
Vaknaam  Modeling and Control of Complex Nonlinear Engineering System 
Niveau(s)  master 
Voertaal  Engels 
Periode  semester II a 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Modeling and Control of Complex Nonlinear Engineering Systems  
Leerdoelen  The student is able to: 1. mathematically model nonlinear system dynamics and consequences for qualitative dynamical behavior, and to evaluate its engineering relevance. 2. formulate relevant examples from the engineering and exact sciences into nonlinear systems descriptions. 3. analyze controllability and observability of nonlinear systems by performing Lie bracket tests. 4. apply Frobenius theorem for the solvability of nonlinear pde's to the problem of feedback linearization, and for determining uncontrollable dynamics. 5. perform asymptotic output tracking of nonlinear control systems by employing the notion of relative degree. 6. investigate stability of equilibria of nonlinear systems by the use of Lyapunov's first or second method, and is able to compare and combine these two methods. 7. apply dissipativity theory, and in particular the passivity and smallgain theorem, for robust control of nonlinear systems, and for setpoint regulation. 8. critically evaluate control aims and pertinent control strategies to achieve these aims. 

Omschrijving  In many areas of engineering and exact sciences one is confronted with systems which exhibit intrinsic nonlinearities. The course deals with the mathematical modeling, analysis and control of such complex dynamical systems, illustrated by a variety of examples from mechanical systems, electrical systems, mechatronics, power systems, as well as (bio)chemical systems. The first topic in the course is concerned with the extension of the fundamental concepts of controllability and observability from linear to nonlinear control systems. The key ingredient to analyze controllability of a nonlinear system turns out to be the geometric concept of (higherorder) Lie brackets of the associated system vector fields. Observability can be analyzed by considering the (repeated) Lie derivatives of the output mapping with respect to the system vector fields. The necessary mathematical preliminaries are introduced during the lectures, and the concepts are explained with engineering examples, where the relevance of the extension of the concepts to nonlinear engineering systems becomes apparent. With the same mathematical concepts and tools the problem of transforming a nonlinear control system into a linear control system by feedback transformations and the choice of state space coordinates is discussed. Applications with respect to key control problems such as tracking of desired output trajectories are provided. Another main topic concerns the study of the system's internal behavior via Lyapunov stability theory. The extension of Lyapunov stability theory to systems with inputs and outputs is accomplished by the introduction of the concept of dissipative systems. The two main examples of dissipative systems are passive systems and nonlinear control systems having finite inputoutput L2induced norm. Important results, such as the smallgain and passivity theorem, are highlighted and implications towards the analysis of complex interconnected systems are provided. 

Uren per week  
Onderwijsvorm  Hoorcollege (LC), Opdracht (ASM), Werkcollege (T)  
Toetsvorm 
Opdracht (AST), Schriftelijk tentamen (WE)
(There will be two Homework Assignments (with average grade HW). At the end of the course there will be a Written Exam (with grade WE). Final grade will be the weighted average of HW (40%) and WE (60%). The examinations will be differentiated into two tracks: one for students in Industrial Engineering and Management, and one for students in (Applied) Mathematics.) 

Vaksoort  master  
Coördinator  dr. ir. B. Besselink  
Docent(en)  dr. ir. B. Besselink ,prof. dr. ir. J.M.A. Scherpen  
Verplichte literatuur 


Entreevoorwaarden  Prior knowledge of Linear Algebra, Calculus, and Control Engineering or Systems Theory at bachelor level is expected.  
Opmerkingen  This course was registered last year with course code WIMCCNES12  
Opgenomen in 
