Summary of Week 2
1. Linearization:
To provide a linear approximation of a process model that could predict local behavior around a chosen operating condition.
To obtain a linearized model of equation (1) with respect to the point: xo, uo and do, first obtain the following constants:

then the linearized model is given by

2. Linear Ordinary Differential Equations with constant coefficients.
  1. General Form:
  1. Solution:
x = xc+x p

where xc is the complementary solution and xp is the particular solution.
  1. In solving for the complementary solution, the procedure involves obtaining the characteristic equation:

whose n roots are the eigenvalues of the system described by (2).
  1. The eigenvalues determine the inherent behavior of the system: