By Khalid Abidi, Jian-Xin Xu
This ebook covers a large spectrum of structures similar to linear and nonlinear multivariable platforms in addition to keep watch over difficulties similar to disturbance, uncertainty and time-delays. the aim of this e-book is to supply researchers and practitioners a guide for the layout and alertness of complicated discrete-time controllers. The publication provides six various regulate ways looking on the kind of method and keep watch over challenge. the 1st and moment ways are in line with Sliding Mode keep watch over (SMC) conception and are meant for linear structures with exogenous disturbances. The 3rd and fourth ways are in accordance with adaptive keep watch over concept and are aimed toward linear/nonlinear platforms with periodically various parametric uncertainty or platforms with enter hold up. The 5th process relies on Iterative studying regulate (ILC) idea and is aimed toward doubtful linear/nonlinear structures with repeatable projects and the ultimate process relies on fuzzy good judgment keep watch over (FLC) and is meant for hugely doubtful platforms with heuristic regulate wisdom. precise numerical examples are supplied in each one bankruptcy to demonstrate the layout process for every keep watch over approach. a few sensible keep watch over purposes also are awarded to teach the matter fixing method and effectiveness with the complex discrete-time keep watch over methods brought during this book.
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Extra resources for Advanced Discrete-Time Control: Designs and Applications
08 Fig. 2 a System control input u 1 b System control input u 2 Fig. 3 Bode plot of some of the elements of the open-loop transfer matrix Magnitude 1010 GOL 11 GOL 12 GOL 13 GOL 11 GOL 12 GOL 13 105 ISM ISM ISM SM SM SM 100 10-2 Fig. 4 Sensitivity function of x1 with respect to f 1 and f2 100 ω [rad/s] 102 10-2 Magnitude 10-4 10-6 ISM x1 /d1 ISM x1 /d2 SM x1 /d1 SM x1 /d2 10-8 10-10 -2 10 100 ω [rad/s] 102 46 2 Discrete-Time Sliding Mode Control Fig. 2 & C= 1 0 . 0042 & C= 1 0 . 989 and, therefore, the system is minimum-phase.
15 that the disturbance estimate ηˆ k converges quickly to the disturbance. 4 t [sec] Fig. 05 Fig. 3 t [sec] Fig. 25 t [sec] Fig. 5 Discrete-Time Terminal Sliding Mode Control In this section we will discuss the design of the tracking controller for the system. The controller will be designed based on an appropriate sliding surface. Further, the stability conditions of the closed-loop system will be analyzed. The relation between TSM control properties and the closed-loop eigenvalue will be explored.
57) ζ k = dk − 2Γ (DΓ )−1 Ddk−1 + Γ (DΓ )−1 Ddk−2 . 58) where The magnitude of ζ k can be evaluated as below. 58) yield ζ k = (dk − 2dk−1 + dk−2 ) + I − Γ (DΓ )−1 D (2dk−1 − dk−2 ) . 1, it has been shown that (dk − 2dk−1 + dk−2 ) ∈ O T 3 . 4) we have I − Γ (DΓ )−1 D (2dk−1 − dk−2 ) = I − Γ (DΓ )−1 D Γ (2fk−1 − fk−2 ) + T Γ (2vk−1 − vk−2 ) + O T 3 2 Note that I − Γ (DΓ )−1 D Γ = 0, thus I − Γ (DΓ )−1 D Γ (2fk−1 − fk−2 ) + Furthermore, I − Γ (DΓ )−1 D O T 3 . This concludes that T Γ (2vk−1 − vk−2 ) = 0.