Summary: Control Systems Design, SC4026
SC4026 Fall 2009, dr. A. Abate, DCSC, TU Delft
Lecture 2
· A few Examples (continued from previous lecture)
· Linearization: hints to nonlinear case
· First-order ordinary differential equations (ODE)
· Solution of a linear ODE
SC4026 Fall 2009, dr. A. Abate, DCSC, TU Delft 1
Linear Ordinary Differential Equations (Linear ODE)
· Recall dynamical model for spring-damper system:
¨q(t) =
1
m
(-c( q(t)) - kq(t) + u(t))
· It can be formulated as:
x1(t) = x2(t)
x2(t) = 1
m (-c(x2(t)) - kx1(t) + u(t))
· Introduce linear approximation of nonlinear term: c(x2(t)) c x2(t)
· Output equation: y(t) = x1(t)

Source: Abate, Alessandro - Faculty of Mechanical, Maritime and Materials Engineering, Technische Universiteit Delft

Collections: Engineering