By Khalid Abidi, Jian-Xin Xu
This publication covers a large spectrum of platforms comparable to linear and nonlinear multivariable platforms in addition to keep watch over difficulties similar to disturbance, uncertainty and time-delays. the aim of this booklet is to supply researchers and practitioners a handbook for the layout and alertness of complex discrete-time controllers. The ebook provides six assorted keep watch over techniques looking on the kind of approach and keep watch over challenge. the 1st and moment ways are in line with Sliding Mode keep watch over (SMC) thought and are meant for linear platforms with exogenous disturbances. The 3rd and fourth methods are in keeping with adaptive keep an eye on concept and are geared toward linear/nonlinear structures with periodically various parametric uncertainty or platforms with enter hold up. The 5th method relies on Iterative studying regulate (ILC) idea and is aimed toward doubtful linear/nonlinear platforms with repeatable projects and the ultimate strategy is predicated on fuzzy common sense regulate (FLC) and is meant for hugely doubtful platforms with heuristic keep an eye on wisdom. unique numerical examples are supplied in each one bankruptcy to demonstrate the layout approach for every keep watch over strategy. a couple of useful keep watch over functions also are offered to teach the matter fixing procedure and effectiveness with the complex discrete-time regulate methods brought during this book.
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Additional info for Advanced Discrete-Time Control: Designs and Applications
5 Systems with a Piece-Wise Smooth Disturbance In practice, the disturbance of a motion system, f (x, t), may become discontinuous at certain circumstances. For example, due to the static friction force, a discontinuity occurs when the motion speed drops to zero. It is thus vital to examine the system performance around the time the discontinuity occurs. Suppose the the discontinuity of f (x, t) occurs at the jth sampling instant. The immediate consequence of the discontinuity in f (x, t) is the loss of the property d j − d j−1 = O (T ) instead of O T 2 , and the loss of the property d j − 2d j−1 + d j−2 = O (T ) instead of O T 3 .
It is necessary to investigate the effect of the disturbance estimation on the state estimation. 2) we get x˜ k+1 = [Φ − LC] x˜ k + dk − dˆ k . 124) It can be seen that the state estimation is independent of the control inputs. Under the assumption that (Φ, Γ, C) is controllable and observable, we can choose L such that Φ − LC is asymptotically stable. 1 the ultimate bound of x˜ k is O (T ). Later we will show that, for systems of relative degree greater than 1, by virtue of the integral action in the ISM control, the state estimation error will be reduced to O T 2 in the closed-loop system.
89) where Λ = I − E. 90) where ak = − (DΦ − ΛD) xk + Dxm,k+1 − ΛDxm,k + σ k . 91) = − (DΓ )−1 (DΦ − ΛD) xk + (DΓ )−1 Dxm,k+1 − ΛDxm,k − (DΓ )−1 Ddk . 91) is not implementable as it requires a priori knowledge of the disturbance. 92) where dˆ k is the disturbance estimation. However, note that the disturbance estimate used in the state feedback controller designed in Sect. 2 requires full state information which is not available in this case. Therefore, an observer that is based on output feedback is proposed and will be detailed in Sect.
Advanced Discrete-Time Control: Designs and Applications by Khalid Abidi, Jian-Xin Xu