By Nabil Derbel, Jawhar Ghommam, Quanmin Zhu
This booklet offers crucial reviews and purposes within the context of sliding mode regulate, highlighting the newest findings from interdisciplinary theoretical experiences, starting from computational set of rules improvement to consultant functions. Readers will simply tailor the recommendations to deal with their advert hoc functions.
To make the content material as obtainable as attainable, the booklet employs a transparent course in each one paper, relocating from history to motivation, to quantitative improvement (equations), and finally to case studies/illustrations/tutorials (simulations, reviews, curves, tables, etc.). although basically meant for graduate scholars, professors and researchers from similar fields, the e-book also will profit engineers and scientists from industry.
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3) mm sign(sm (k)) where Φ (Φ ∈ m×m ) is a diagonal matrix such 0 ≤ Φi, i < 1, ∀ i = 1 . . m and mi (mi ∈ ) is a positive gain. And sign is the signum function defined as: sign(si (k)) = −1 si si (k) < 0 ; 1 si si (k) > 0 i ∈ 1 ... m Using the considered reaching law, the sliding mode control law can be expressed as: ⎡ ⎤ m1 sign(s1 (k)) ⎢ ⎥ .. 4) ⎦ . mm sign(sm (k)) To study the robustness of the control law, we suppose that the system is subject to external disturbances as follows: x(k + 1) = Ax(k) + Bu(k) + f (k) where f (k) is the external disturbances vector.
Function S(t, x) and its derivative S(t, ˙ S(t, x) = 0 and S(t, x) = 0, a sliding mode control is applied to this new second order system. Therefore, we obtain the finite time convergence of S(t, x) and of its ˙ x) to zero. derivative S(t, Consider a dynamic system described by Eq. S. Nouri et al. 49) Using Eqs. 50) is a second order one. 51) The system whose input is u˙ (t) and whose output is σ(t, x) is of relative degree ‘one’, so a sliding mode can exist on σ(t, x) (Sira-Ramirez 1990). So the input u˙ (t) can be taken as: • u˙ (t) = −M sign (σ(t, x)).
Nouri, A. S. (2012b). New discrete sliding mode control for nonlinear multivariable systems: multi-periodic disturbances rejection and stability analysis. International Journal of Control Science and Engineering, 2(2), 7–15. R. (2006). Robust stability condition of repetitive control systems and analysis on steady-state tracking errors. Proceedings of the International Joint Conference on SICEICASE, pp. 5169–5174. Fateha, M. , Tehranib, H. , & Karbassic, S. M. (2013). Repetitive control of electrically driven robot manipulators.
Applications of Sliding Mode Control by Nabil Derbel, Jawhar Ghommam, Quanmin Zhu