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δω δω δω δω

The system performance specifications are represented by LTI transfer functions, and their corresponding Bode plots are shown in Fig. 2.10 by the upper and lower bounds BU and BL, respectively.

2-3.6 QFT DESIGN

The tracking design objective is to

(a) Synthesize a compensator G(s) of Fig. 2.9 that

results in satisfying the desired performance specifications of Fig. 2.8, results in the closed-loop frequency responses

ιLT shown in Fig. 2.12, and

results in the δL (jωi) of Fig. 2.12, of the compensated system, being equal to or smaller than δP(jωi) of Fig. 2.10 for the uncompensated system and that it is equal or less than δR(jωi), for each value of ωi of interest; that is:

2-4 INSIGHT TO THE QFT TECHNIQUE

2-4.1 OPEN-LOOP PLANT

a)s(s

K' a)s(s

Ka(s)P +

=

+ =ι (2.8)

2-4.2 CLOSED-LOOP FORMULATION

==

1 (2.10)

)(1

)()( )(

+ = (2.11)

2-4.3 RESULTS OF APPLYING THE QFT DESIGN TECHNIQUE

The proper application of the robust QFT design technique requires the utilization of the prescribed performance specifications from the onset of the design process, and the selection of a nominal plant Po from the J LTI plants. Once the proper loop shaping of Lo(s) = G(s)Po(s) is accomplished, a synthesized G(s) is achieved that satisfies the desired performance specifications. The last step of this design process is the synthesis of the pre-filter that ensures that the Bode plots of

ιRT all lie between the upper and lower bounds BU and BL.