2.3. H∞AND H2DESIGN METHODOLOGIES 29
An area of work, knownas identificationin H∞, looks at experimental identification
techniques which minimize the worstca se H∞errorb etweenthe physical system and
the model. The following works address this issue: [27, 28, 29, 30, 31, 32, 33, 34, 35].
Applying the more standard, probabilistically based, identification techniques to
uncertain systems is also receiving attention. Relevant workin this area is described
in: [36, 37, 38, 39]
Model validation is the experimental testing of a given robust control model. This can
be useful is assessing model quality. This work is covered in the
following: [4,40, 41, 42, 43, 44, 45, 46]. An experimental example isdescribed by
Smith [47].
The problems of identifyingmodel parameters in an uncertain model is discussed further
in [48, 49, 50]. A nonlinear ad-hoc approach for obtaining suitable multiplicative
perturbation models for certain classes of systems is given in [51].
Several researchers are also formalizing the interplay between identificationa nd design
in iterative approaches. In practical situationsthe designer usually ends up with ad-hoc
identification/design iterations. The work in this area is described in [52, 53, 54, 55, 56].
On reading the above works, one will getthe impressio nthat this a reais the most
poorly developed of the current robust control theory. In obtaining these models
engineering judgementis of paramount importance. The users of this software are
encouraged to document their experiences and bringthis work to the authors’ attention.
2.3 H∞and H2Design Methodologies
The generic synthesis configuration is illustrated in LFT form in Figure 2.7. Here P(s)
is referred to as the interconnection structure. The ob jectiveis to design K(s) such that
the closed loop interconnection is stable and the resulting transfer function from wto e
(denoted by G(s)),
e=Fl[P(s),K(s)]w,
=G(s)w,
satisfies a norm objective.