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Challenges and Paradigms in Applied Robust Control Part 14

Tham khảo tài liệu 'challenges and paradigms in applied robust control part 14', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | An Application of Robust Control for Force Communication Systems over Inferior Quality Network 379 time-delay L 0 exists between master and slave controllers symmetrically. The evaluated deviations 9 10 at each controller might be computed as follows. emL t xm t - Xs t - L 11 esL t Xs t - Xm t - L 12 In the rest of the chapter em0 es0 emL esL are called as errors in ideal computed deviation. The Laplace transform of computed deviation emL 11 is written as EmL s Xm s - e LsXs s Xm s - Xs s Xs s - e LSXs s Em0 s 1 - e L Xs s . 13 In the same way the Laplace transform of esL can be written as EsL s Es0 s 1 - e-Ls Xm s . 14 This means that the minimization of computed deviations EmL s EsL s is acomplished by the simultaneous minimization of Em0 s -Es0 s 1 - e-Ls Xs s and 1 - e-Ls Xm s from the inequality as EmL jw Em0 jw 1 - e w Xs jw Em0 jw WD jw L Xs jw . Em0 jw Wd jw Lmax Xs jw . 15 EsL jw Es0 jw Wd jw Lmax Xm jw . 16 As mensioned in previous section the time delay L includes uncertainty. But if the upper bound of L is obtained as Lmax according to 4and 5 the minimization problem can be acomplished by the minimization of Em0 s Wd s Lmax Xs s and Wd s Lmax Xm s . H theory gives a design method to obtain an appropriate feedback gain to keep stability and robustness against the type of model uncertainty. 4.3 Plant model Let us consider the two joystick mechanisms as a system with two inputs and two outputs plant Xm s Pm s 0 Um s Xs s 0 Ps s _ -Us 17 where PmW s Km . . s Jms Dm The purpose is the design of a controller Ps s s Iss Ds . 18 Um s Cmm s Cms s Xm s . Us s _Csm s Css s Xs s 19 380 Challenges and Paradigms in Applied Robust Control which satisfies the requirements specified as follows. The schematic diagram is depicted in Fig-6 a b Fig. 6. scheme of PE type master-slave system a ideal non time-delay scheme b practical implementable scheme tracking performance The closed loop system is a kind of regulator which makes the deviation e Xm Xs 0 as time goes. For the