A loop shaping design procedure
In this chapter we have incorporated the normalized LCF robust stabilization problem into a loop shaping based design technique. This enables both performance and robust stability objectives to be traded-off, and preserves the exact solution associated with this particular H∞ problem. The design method is straightforward and systematic, incorporating only the simpler aspects of ‘classical’ loop shaping. The normalized LCF robust stabilization problem has been shown to be particularly well suited for this approach because the H∞ controller synthesized causes only a limited deterioration of the specified loop shape. Coprime factor model reduction techniques can be simply incorporated into this framework.
An interesting problem is the question of how the design indicator, εmax, in the Loop Shaping Design Procedure, varies with changes in the selected shaping function. A promising approach seems to be to investigate the asymptotic behaviour of εmax as either W1 or W2 become very large or small.
As a final comment, it should be noted that the Loop Shaping Design Procedure is restricted to a particular set of H∞ objectives. However, we will shown in the next chapter that the design technique yields simple and effective controllers.
KeywordsShaping Function Stability Margin Loop Gain Loop Shaping Plant Input
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