Modeling and Control of Complex Nonlinear Engineering System

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 small-gain theorem, for robust control of nonlinear systems, and for set-point 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 (higher-order) 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 input-output L2-induced norm. Important results, such as the small-gain 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	Titel Auteur ISBN Prijs Lecture Notes 'Modelling and Control of Complex Nonlinear Engineering Sytems' A.J. van der Schaft, J.M.A. Scherpen Background material (optional reading): Nonlinear Dynamical Control Systems, Springer, 1990. H. Nijmeijer, A.J. van der Schaft Background material (optional reading): L2-Gain and Passivity Techniques in Nonlinear Control, Springer. 2017 A.J. van der Schaft Background material (optional reading): Nonlinear Systems, IAM, Springer, 1999. S. S. Sastry
Entreevoorwaarden	Prior knowledge of Linear Algebra, Calculus, and Control Engineering or Systems Theory at bachelor level is expected.
Opmerkingen
Opgenomen in	Opleiding Jaar Periode Type MSc Applied Mathematics: Systems and Control  (MSc Applied Mathematics: Systems and Control) - semester II a keuzegroep MSc Courses for Exchange Students: AI - Computing Science - Mathematics - semester II a MSc Industrial Engineering and Management: Production Technology and Logistics  (Optional technical PTL modules) - semester II a Elective SSCA MSc Mathematics: Statistics and Big Data  (Statistics and Big Data: Guided Choice) - semester II a guided choice MSc Mechanical Engineering: Advanced Instrumentation  (Electives ) 1 semester II a keuze MSc Mechanical Engineering: Smart Factories  (Electives ) 1 semester II a keuzegroep