By Khalid Abidi, Jian-Xin Xu
This publication covers a large spectrum of structures comparable to linear and nonlinear multivariable structures in addition to keep an eye on difficulties equivalent 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 complicated discrete-time controllers. The ebook offers six assorted regulate techniques reckoning on the kind of procedure and keep watch over challenge. the 1st and moment ways are in line with Sliding Mode keep an eye on (SMC) concept and are meant for linear platforms with exogenous disturbances. The 3rd and fourth techniques are in response to adaptive keep an eye on conception and are geared toward linear/nonlinear platforms with periodically various parametric uncertainty or platforms with enter hold up. The 5th procedure is predicated on Iterative studying regulate (ILC) thought and is geared toward doubtful linear/nonlinear platforms with repeatable initiatives and the ultimate method relies on fuzzy good judgment regulate (FLC) and is meant for hugely doubtful structures with heuristic regulate wisdom. targeted numerical examples are supplied in each one bankruptcy to demonstrate the layout method for every keep watch over process. a few sensible regulate purposes also are offered to teach the matter fixing strategy and effectiveness with the complex discrete-time keep an eye on ways brought during this book.
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Extra resources for Advanced Discrete-Time Control: Designs and Applications
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. 5 The conventional method guarantees that the sliding surface is of order O T 2 and deadbeat tracking error of order O T 2 . However, deadbeat response is not practical as it requires large control effort and the addition of input saturation would sacrifice global stability.
In practice, the quantity yk+1 is not available at the time instant k when computing ηˆ k . 92) we use the delayed estimate dˆ k = Γ ηˆ k−1 . 4 The observer output yd,k converges asymptotically to the true outputs yk , and the disturbance estimate dˆ k converges to the actual disturbance dk−1 with the precision order O T 2 . 94), and using ed,k−1 = C yk−1 − yd,k−1 , it is obtained that xd,k = Φ − Γ (CΓ )−1 (CΦ − Λd C) xd,k−1 + Γ (CΓ )−1 yk − Λd yk−1 + Γ (CΓ )−1 σ d,k−1 . 97) renders to xd,k = Φ − Γ (CΓ )−1 (CΦ − Λd C) xd,k−1 + Γ (CΓ )−1 yk − Λd yk−1 .
68), we obtain σ k+1 = C dˆ k − dk . Note that the switching surface σ k+1 is no longer zero as desired but a function of the difference dk − dˆ k . 1 the difference is O T 2 which is quite small in practical applications. 83), lead to ek+1 = Λek + C dˆ k − dk − C dˆ k−1 − dk−1 = Λek + C dˆ k − dk + dk−1 − dˆ k−1 = Λek + δ k . 1 we can conclude the boundedness of ek . 84). 67), the ultimate tracking error bound with ISM control is given by ek = O T 2 where · represents the Euclidean norm. 30 2 Discrete-Time Sliding Mode Control Proof In order to calculate the tracking error bound we must find the bound of δ k .
Advanced Discrete-Time Control: Designs and Applications by Khalid Abidi, Jian-Xin Xu