Lecture #12: Gain scheduling

Date: Wednesday, 10 May 96

Outline:

A. Introduction to nonlinear control
   1. xdot = f(x, y), u = alpha(x, r) -> xdot = f(x,alpha(x,r)) = ftilde(x)
   2. Thm: if linearization around equilibrium point is stable then
      nonlinear system is locally stable
   3. Nonlinearities in the ducted fan
      a. geometric nonlinearities due to SE(2)
      b. mechanical nonlinearities due to stand mechanics
      c. actuator nonlinearities (saturation)

B. Gain scheduling
   1. Basic idea: allow different operating points (diagram showing
      construction of gain scheduling between two operating points)
   2. Example: ducted fan
   3. Properties:
      a. works when lambdadot << 1, but often works okay even if it isn't 
      b. conservative analysis tools are starting to emerge
      c. tweaks allow the addition of integrators

Next time: feedback linearization