30 CHAPTER 2. OVERVIEWOF THE UNDERLYING THEORY
Figure 2.7: LFT configuration for controller synthesis, G(s)=F
l
[P(s),K(s)]
Note that the interconnection structure, P(s), given here, differs from that discussed in
the previous section. Here we set up P(s) so that the input, w, is the unknown signals
entering our system. Typical examples would be sensor noise, plant disturbances or
tracking commands. The output, e, represent signals that we would like to make small.
In an engineering application these could include actuator signals and tracking errors.
The signal yis the measurement available to the controller,K(s). Inany realistic
problem, some weighted component of wwould be added to yto model sensor noise.
The output of the controller, u, is our actuation input to the system. Again, a
reasonable engineering problem would include a weighted usignalas acomponent of the
penalty output, e.
The interconnection structure, P(s), also contains any frequency weightings on the
signals eand w. Weightings on components of eare used to determine the relative
importance of the various error signals. Weightfunctions on windicate the relative
expected size of the unknown inputs.
Xµprovides functions to calculate the controllers minimizing either the H2or H∞norm
of G(s). We will coverb othof these approaches in the context of the design problem
illustrated in Figure 2.7.
Note that neither of these design approaches takesadvantage of any information about
structured perturbations occuring within the model. Thefollowing discussion can be
considered as applying to a nominal design problem. Section 2.5 uses D-Kiteration to