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

By Khalid Abidi, Jian-Xin Xu

This e-book covers a large spectrum of platforms comparable to linear and nonlinear multivariable structures in addition to keep an eye on difficulties corresponding to disturbance, uncertainty and time-delays. the aim of this booklet is to supply researchers and practitioners a guide for the layout and alertness of complex discrete-time controllers. The ebook offers six varied keep an eye on methods 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) concept and are meant for linear structures with exogenous disturbances. The 3rd and fourth methods are in response to adaptive regulate idea and are aimed toward linear/nonlinear platforms with periodically various parametric uncertainty or structures with enter hold up. The 5th process is predicated on Iterative studying keep watch over (ILC) thought and is aimed toward doubtful linear/nonlinear platforms with repeatable initiatives and the ultimate process is predicated on fuzzy common sense keep an eye on (FLC) and is meant for hugely doubtful platforms with heuristic keep watch over wisdom. targeted numerical examples are supplied in every one bankruptcy to demonstrate the layout process for every keep an eye on strategy. a few functional keep an eye on purposes also are offered to teach the matter fixing strategy and effectiveness with the complex discrete-time regulate methods brought during this book.

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5. 1, the ultimate error bound on Δxk will be one order higher than the bound on ζ k . Thus, the ultimate bound on the output tracking error is ek ≤ C · Δxk = O (T ) . 5 Error Bound for a Minimum-Phase (Φ, Γ, D) In the case that it is only possible to satisfy (Φ, Γ, D) to be minimum-phase, a different reference model needs to be selected. For this new reference model, select the matrices K 1 = Γ (DΓ )−1 DΦ and K 2 = Γ (DΓ )−1 . 87) can be written as xm,k+1 = Φ − Γ (DΓ )−1 DΦ xm,k + Γ (DΓ )−1 rk+1 ym,k = Dxm,k = rk .

112) that the tracking error bound is only dependent on the disturbance estimation ζ k . On the other hand, the disturbance observer requires (Φ, Γ, C) to be minimumphase, hence is not implementable in this case. 106) becomes ζ k = dk − Γ (DΓ )−1 dk−1 = dk − dk−1 + I − Γ (DΓ )−1 D = O T2 + O T3 = O T2 . 113) 38 2 Discrete-Time Sliding Mode Control As a result, the closed-loop system is Δxk+1 = Φ − Γ (DΓ )−1 (DΦ − Λd D) Δxk + O T 2 . 1, the ultimate bound on Δxk = O (T ), and therefore, the ultimate bound on the tracking error is ek ≤ D · Δxk = O (T ) .

126) i=0 which can be simplified to x˜ k − x˜ k−1 = [(Φ − LC) − In ] (Φ − LC)k−1 x˜ 0 + dk − dˆ k . 128) and δ k can be expressed ultimately as δ k = C dˆ k − dk + dk−1 − dˆ k−1 − CΦ (˜xk − x˜ k−1 ) = C dˆ k − dk + dk−1 − dˆ k−1 − CΦ dk − dˆ k . 4, the disturbance estimation error dk − dˆ k is O T 2 . Therefore we have δk = C · O T 2 + O T 2 − CΦ · O T 2 = O T 2 . 122) the ultimate bound on ek is O (T ). 11 Note that the guaranteed tracking precision is O (T ) because the control problem becomes highly challenging in the presence of state estimation and disturbance estimation errors, and meanwhile aiming at arbitrary reference tracking.

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