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 corresponding to linear and nonlinear multivariable structures in addition to regulate difficulties akin to disturbance, uncertainty and time-delays. the aim of this ebook is to supply researchers and practitioners a guide for the layout and alertness of complex discrete-time controllers. The publication offers six assorted keep an eye on techniques reckoning on the kind of process and keep an eye on challenge. the 1st and moment techniques are in keeping with Sliding Mode keep an eye on (SMC) concept and are meant for linear platforms with exogenous disturbances. The 3rd and fourth methods are in line with adaptive keep an eye on conception and are geared toward linear/nonlinear structures with periodically various parametric uncertainty or structures with enter hold up. The 5th process relies on Iterative studying regulate (ILC) conception and is geared toward doubtful linear/nonlinear platforms with repeatable initiatives and the ultimate procedure relies on fuzzy common sense regulate (FLC) and is meant for hugely doubtful platforms with heuristic keep an eye on wisdom. specified numerical examples are supplied in every one bankruptcy to demonstrate the layout technique for every keep an eye on technique. a couple of functional keep an eye on purposes also are offered to teach the matter fixing approach and effectiveness with the complicated discrete-time keep watch over ways brought during this book.

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4 that ISM control greatly reduces the effect of the disturbance as compared to SM control. Moreover ISM presents a larger open-loop gain at the lower frequency band by virtue of the integral action in the sliding manifold, which ensures a more accurate closed-loop response to possible reference inputs. 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.

However, the stability of the whole system is guaranteed only if the transmission zeros are stable. 37), it is very simple to show that Φ − Γ (CΓ )−1 CΦ has m eigenvalues in the origin. Note, that those m deadbeat eigenvalues correspond to the output deadbeat response. If the matrices are partitioned as shown Φ= Γ1 Φ11 Φ12 , Γ = Φ21 Φ22 Γ2 & C = C1 C2 where (Φ11 , C1 , Γ1 ) ∈ m×m , (Φ12 , C2 ) ∈ m×n−m , (Φ21 , Γ2 ) ∈ n−m×m and Φ22 ∈ n−m×n−m . 41) The above result shows that there are m eigenvalues at the origin.

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 . Therefore ζ k = O T 2 which is bounded. We have established the stability condition for the closed-loop system, but, have yet to establish the ultimate tracking error bound. 105) it can be seen that the tracking error bound is dependent on the disturbance estimate dˆ k as well as the selection of K 1 and K 2 .

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