Control Theory Tutorial by Steven A. Frank

Author:Steven A. Frank
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

Figure 6.4 shows the regulation feedback system of Fig. 6.1 with additional weightings for the disturbance and noise inputs. The weightings modify the four system transfer functions and associated sensitivities in Eq. 6.2 to be , , , and . The cost function in Eq. 6.5 becomes

(6.9)

Consider an example in which we begin with the process, P, in Eq. 6.8. To emphasize low-frequency load disturbances, set to be a low-pass filter. That weighting filters out disturbances that are significantly greater than . To emphasize high-frequency sensor noise, set . That weighting filters out noise that is significantly less than . By using these two filters, the optimization method puts very low weight on any disturbances in midrange frequencies of .

By minimizing the weighted cost in Eq. 6.9, we obtain the optimal controller

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