152 CHAPTER 4. DEMONSTRATION EXAMPLES
The loopshaping controller had good nominal performance and very poor robust
performance. This was illustrated with a relatively small perturbation. Thedifference
between the µand H∞controllers was small in both the nominal and perturbed cases.
This may not alwaysbe the case for several reasons.
Only a single D-Kiteration was performed here. Further iterations would further
improvethe performanceof the µcontroller.
The perturbation chosenfor the above simulation was not the worst case one. Note that
here, each of the three closed loop systems will have a different worst case perturbation.
Tofind these, p erform a µcalculation on eachclosed lo op system and use mkpertto
construct the appropriate perturbations.
The theoretical measure of performanceis theH∞norm of the closed loop transfer
function. When assessing different controllers by simulation we are applying additional,
unformalized performance measures.
In this case, the performance and perturbation channelswere about equally scaled. The
resulting D-scales were within an order of magnitude of unity. Choosing a different set
of units for αand/or θwould changethe H∞normof the result without changing µ.A
poor choice of engineering units could therefore lead to a larger difference between the
H∞controller and the µcontroller.