Advanced Discrete-Time Control: Designs and Applications by Khalid Abidi, Jian-Xin Xu

By Khalid Abidi, Jian-Xin Xu

This ebook covers a large spectrum of structures comparable to linear and nonlinear multivariable platforms in addition to regulate difficulties akin to disturbance, uncertainty and time-delays. the aim of this ebook is to supply researchers and practitioners a handbook for the layout and alertness of complex discrete-time controllers. The booklet provides six varied keep watch over techniques looking on the kind of process and keep an eye on challenge. the 1st and moment ways are in keeping with Sliding Mode regulate (SMC) thought and are meant for linear structures with exogenous disturbances. The 3rd and fourth ways are in keeping with adaptive regulate concept and are aimed toward linear/nonlinear platforms with periodically various parametric uncertainty or structures with enter hold up. The 5th method is predicated on Iterative studying keep watch over (ILC) thought and is aimed toward doubtful linear/nonlinear structures with repeatable projects and the ultimate strategy relies on fuzzy common sense keep an eye on (FLC) and is meant for hugely doubtful platforms with heuristic keep an eye on wisdom. exact numerical examples are supplied in each one bankruptcy to demonstrate the layout technique for every keep an eye on procedure. a couple of useful regulate purposes also are provided to teach the matter fixing procedure and effectiveness with the complex discrete-time regulate methods brought during this book.

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Extra info for Advanced Discrete-Time Control: Designs and Applications

Example text

105) are the eigenvalues of Λd and the openloop zeros of the system (Φ, Γ, D). Thus, m poles of the closed-loop system can be selected by the proper choice of the matrix Λd while the remaining poles are stable only if the system (Φ, Γ, D) is minimum-phase. Note that both rk+1 and xm,k are reference signals and are bounded. Therefore we need only to show the boundedness of ζ k which is ζ k = I − Γ (DΓ )−1 D dk + Γ (DΓ )−1 D dk − dˆ k − Γ (DΓ )−1 D dk−1 − dˆ k−1 . 107) are O T 2 . 107) can be written as I − Γ (DΓ )−1 D dk = I − Γ (DΓ )−1 D Γ ηk + O T 3 = O T3 .

Thus, we have xk+1 = (Φ − Γ K ) xk + dk − Γ (DΓ )−1 Ddk−1 − Γ (DΓ )−1 D (dk−1 − dk−2 ) . 56), the disturbance estimate dˆ k has been replaced by dk−1 . 57) ζ k = dk − 2Γ (DΓ )−1 Ddk−1 + Γ (DΓ )−1 Ddk−2 . 58) where The magnitude of ζ k can be evaluated as below. 58) yield ζ k = (dk − 2dk−1 + dk−2 ) + I −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 .

2) dˆ k = dk−1 = xk − Φxk−1 − Γ uk−1 . 67) Note that dk−1 is the exogenous disturbance and bounded, therefore dˆ k is bounded for all k. 67), the actual ISM control law is given by uk = (CΓ )−1 ak − C dˆ k . 67) are used. 68) can be rewritten as uk = (CΓ )−1 rk+1 − Λek − CΦxk + σ k − C dˆ k = − (CΓ )−1 (CΦ − ΛC) xk − (CΓ )−1 C dˆ k + (CΓ )−1 (rk+1 − Λrk ) + (CΓ )−1 σ k . 2) yields the closed-loop state dynamics xk+1 = Φ − Γ (CΓ )−1 (CΦ − ΛC) xk + dk − Γ (CΓ )−1 C dˆ k + Γ (CΓ )−1 (rk+1 − Λrk ) + Γ (CΓ )−1 σ k .

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