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Goal
Design the pre-filter (W) and controller (K) on the basis of a nominal model LaTeX:  P_0 for the plant LaTeX:  P such that the feedback system exhibits the following properties:

  1. Stability: if the system is perturbed then the system will return to equilibrium
  2. Small tracking error
  • Good low frequency command following
  • Good low frequency disturbance attenuation
  • Good high frequency noise attenuation

Note
The stated goals must be achieved in the presence of the following sources of uncertainty

  • LaTeX: P_0 \ne P
  • LaTeX: H is not known exactly
  • LaTeX: d_i and LaTeX: d_o are not known exactly
  • LaTeX: n is not known exactly