Open loop configurations d y n d p s u ym cs e r y p

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Unformatted text preview: tracking of r when I Closed-loop vs. open-loop configurations (contd) d y n d P .s/ u ym C.s/ e r y P .s/ u C.s/ r In other words, I the main reason for using feedback is uncertainties whether they modeled as disturbances or as modeling mismatches. At the same time, I command following can be successfully done by open-loop control. So we may ask the following question: I why to waste feedback on command following ? 2-degrees-of-freedom (2DOF) control A solution is to combine open- and closed-loop schemes to take the best of two worlds. An example of such approach is d y P .s/ ym u Cf .s/ Cb .s/ F .s/ r n where C.s/ D Cf .s/Cb .s/ is any split3 of C.s/. The idea here is to design I I feedback part C.s/ to take care of uncertainties feedforward filter F .s/ to take care of command following Remark: Under any Cf .s/ and Cb .s/ such that C.s/ D Cf .s/Cb .s/, filter F .s/ I I doesn't affect feedback properties of C.s/ doesn't increase control efforts needed for good command following choice is Cf .s/ D C.s/ and Cb .s/ D 1. 3 Popular 2DOF control: design steps 1. design (stabilizing) C.s/ as if no command following is required: d y P .s/ ym u Cf .s/ Cb .s/ C.s/ F .s/ r n 2. Choose split C.s/ D Cf .s/Cb .s/ for which (stable) Ta .s/ P .s/Cf .s/ 1 C P .s/C.s/ has "favorable" properties (e.g., easy to invert) and Cf .s/ and Cb .s/ are implementable (proper) and have no unstable pole/zero cancellations. 3. design F .s/ for given C.s/ accounting only for r : y Ta .s/ F .s/ r 2DOF control: design of F .s/ y Ta .s/ F .s/ r The only limitation on F .s/ is that it must be stable (and, therefore, proper). Conceptually, the simplest approach based on plant inversion: 1. choose suitable reference model Tref .s/ 2. take F .s/ D Tref...
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This note was uploaded on 06/30/2011 for the course MECHANICAL 034406 taught by Professor Leonidmirkin during the Spring '10 term at Technion.

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