美国麻省理工大学：《航空系统的估计与控制》教学资源（讲义）Handout 14：Introduction to nonlinear systesm

Handout 14: Introduction to nonlinear systesm Eric feron Mar29,2004 Linear systems reminder: y(u)= main properties of linear dynamical systems

Handout 14:Introduction to nonlinear systesm Eric Feron Mar 29, 2004 Linear systems reminder: y(u) = main properties of linear dynamical systems 1Ma

rom transfer functions to ordinary differential equations: 2

From transfer functions to ordinary differential equations: 2

Differential equations and physical systems 3

Differential equations and physical systems 3

Nonlinear systems: Examples Nonlinear pendulum Chemical reactions kinetics: 4

Nonlinear systems: Examples Nonlinear Pendulum Chemical Reactions Kinetics: 4

very)nonlinear mechanical systems: Rollercoasters Case 1: Not linear at equilibrium Case II: High sensitivity to initial conditions(not like linea systems 5

(very) nonlinear mechanical systems: Rollercoasters Case 1: Not linear at equilibrium Case II: High sensitivity to initial conditions (not like linear systems) 5

hard” nonlinearities Dead zones Saturations

”hard” nonlinearities Dead zones Saturations 6

m BangBang acklash 7

”Bang Bang” Backlash 7

ress Dry Friction, Stiction, Stick-slip 8

Hysteresis Dry Friction, Stiction, Stick­slip 8