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

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4 Fig. 11 Disturbance η and estimate ηˆ and deviating only when the discontinuities occur but attenuates very quickly. The disturbance estimation is seen in Fig. 11 and the estimation converges quickly to the actual disturbance. From Fig. 12 we can see the tracking error performance. The tracking error is about 6 × 10−6 which matches the theoretical results of O T 2 bound. Again like the previous two approaches, the control signal of the ISM control is smaller than that of the PI controller at the initial phase (Fig.

8, the performance is quite good and better than that of a PI controller. The tracking error for the ISM control is about 17 × 10−6 which corresponds to O T 2 at steady state. Note that even though the worst case scenario of O (T ) was predicted for this approach it was possible to achieve O T 2 at steady state. Also, similar to the state feedback approach the control signal of the ISM control controller is much smaller than that of the PI controller at the onset of motion (Fig. 9). 123). 4 allowing a fast enough convergence.

141) therefore, the final controller structure is given by u k = (sγ )−1 srk+1 − sΦrk + sΦek + βek − (sγ )−1 sdˆ k . 7 with regard to the closed-loop stability, first derive the closed-loop error dynamics. 139), we obtain ek+1 = Φ − γ (sγ )−1 sΦ ek − β (sγ )−1 ek − dk p + γ (sγ )−1 sdˆ k + I − γ (sγ )−1 s (rk+1 − Φrk ) . 143), we note that since the objective is to have xk → rk then there must exist a control input u m,k such that rk+1 = Φrk + γ u m,k . Thus, I − γ (sγ )−1 s (rk+1 − Φrk ) = I − γ (sγ )−1 s γ u m,k = 0.

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