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, Input-output 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, input-to-state stability
5 Input-Output Stability. Input output stability, L stability, L2 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, full-state linearization, state-feedback control, Sliding mode control, Lyapunov redesign, backstepping, passivity-based control
8. Examples. Design of feedback control system for medical robots.
|Students 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 materiaal-Aanbevolen materiaal|
|Nonlinear systems – 0-13-067389-7|
|Zelfstudie met begeleiding|