By Khalid Abidi, Jian-Xin Xu
This e-book covers a large spectrum of structures equivalent to linear and nonlinear multivariable platforms in addition to keep watch over difficulties corresponding 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 ebook offers six diverse regulate techniques looking on the kind of process and keep an eye on challenge. the 1st and moment methods are in keeping with Sliding Mode keep an eye on (SMC) concept and are meant for linear structures with exogenous disturbances. The 3rd and fourth techniques are in line 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 procedure is predicated on Iterative studying regulate (ILC) thought and is geared toward doubtful linear/nonlinear platforms with repeatable projects and the ultimate method is predicated on fuzzy good judgment keep an eye on (FLC) and is meant for hugely doubtful platforms with heuristic keep watch over wisdom. specific numerical examples are supplied in each one bankruptcy to demonstrate the layout method for every keep an eye on approach. a few functional keep watch over purposes also are awarded to teach the matter fixing strategy and effectiveness with the complicated discrete-time keep watch over techniques brought during this book.
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Extra info for Advanced Discrete-Time Control: Designs and Applications
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.
To show the boundedness and facilitate later analysis on the tracking performance, we derive the relationship between the switching surface and the disturbance estimate, as well as the relationship between the output tracking error and the disturbance estimate. 2) is minimum-phase and the eigenvalues of the matrix Λ are within the unit circle. 84) and the error dynamics where δ k = C dˆ k − dk + dk−1 − dˆ k−1 . 65) as eq eq σ k+1 = ak − CΓ uk − Cdk = ak − CΓ uk − Cdk + CΓ uk − uk eq = CΓ uk − uk , eq where we use the property of equivalent control σ k+1 = ak − CΓ uk − Cdk = 0.
32) where Do is a constant matrix of rank m and rk ∈ m . The objective is to force the output yk to track the reference rk . 3 Classical Discrete-Time Sliding Mode Control Revisited 19 the closed-loop system has the following properties σ k+1 ∈ O T 2 rk+1 − yk+1 ∈ O T 2 Proof Similar to the regulation problem the discrete-time equivalent control is defined by solving σ k+1 = 0, . 33) with Do selected such that Do CΓ is invertible. 33) because of the lack of knowledge of dk which requires a priori knowledge of the disturbance f(t).