
The goal of this course is to allow students to design control systems for systems with nonlinear dynamics. These control systems should meet certain stability specifications and provide reasonable robustness. By the end of the course, each student should be able to do the following:
 Analyze the qualitative behavior near equilibrium points of nonlinear systems and robots.
 Understand the fundamental properties of nonlinear systems (existence and uniqueness, differentiability of solutions and sensitivity, dependence on initial conditions and parameters), and implement these techniques on robotic systems.
 Analyze the controllability and observability of nonlinear systems and robotic systems.
 Analyze the stability of nonlinear systems.
 Design of feedback control systems for nonlinear systems and robots.


1 Introduction. Similarity transformations, diagonal form and Jordan form, functions of a square matrix, Lyapunov equation, quadratic form and positive/negative definiteness Singular value decomposition, norms of matrices, solution of LTI state equations, Inputoutput stability of LTI systems, internal stability, Lyapunov theorem, Controllability, observability, canonical decomposition, minimal realizations and coprime fractions, state feedback and state estimators
2 Nonlinear Systems. Multi equilibria, qualitative behavior near equilibrium points, limit cycles numerical construction of phase portraits. bifurcation analysis
3 Fundamental properties. Existence and uniqueness, continuous dependence on initial conditions and parameters, differentiability of solutions and sensitivity equations, comparison principle
4 Lyapunov Stability. The invariance principle, comparison functions, inputtostate stability
5 InputOutput Stability. Inputoutput stability, L stability, L_{2} gain Feedback system: The small gain theorem
6 Passivity. Passivity, memoryless functions, state models, feedback systems: passivity theorem, absolute stability, circle criterion, Popov criterion
7 Feedback Control. Feedback control: Stabilization via linearization, integral control, integral control via linearization, fullstate linearization, statefeedback control, Sliding mode control, Lyapunov redesign, backstepping, passivitybased control
8. Examples. Design of feedback control system for medical robots.




 VoorkennisStudents are expected to have background knowledge of differential equations, linear systems, linear control theory and modeling.
Familiarity with programming, mechanical system design and finite element analysis is recommended. 
Master Systems and Control 
Master Mechanical Engineering 
Master Electrical Engineering 
  Verplicht materiaalAanbevolen materiaalBookHassan K. Khalil, Nonlinear Systems, Third Edition, Prentice Hall, 2002, ISBN 9780130673893 

 WerkvormenAssessmentAanwezigheidsplicht   Ja 
 Colloquium
 Colstructie
 Eindproject
 Excursie
 HoorcollegeAanwezigheidsplicht   Ja 
 Ontwerp
 OpdrachtAanwezigheidsplicht   Ja 
 Overig onderwijs
 PracticumAanwezigheidsplicht   Ja 
 Project begeleidAanwezigheidsplicht   Ja 
 Stage
 Veldwerk
 Vragenuur
 Zelfstudie met begeleidingAanwezigheidsplicht   Ja 

 ToetsenAssignment


 