# American Institute of Mathematical Sciences

May  2020, 3(2): 81-99. doi: 10.3934/mfc.2020007

## A triple mode robust sliding mode controller for a nonlinear system with measurement noise and uncertainty

 College of Engineering, Department of Electrical Engineering, TAIF University KSA, TAIF, KSA

* Corresponding author: NasimUllah

Received  December 2019 Revised  January 2020 Published  May 2020

This research work proposes a novel triple mode sliding mode controller for a nonlinear system with measurement noise and uncertainty. The proposed control has the following goals (1) it ensures the transient and steady state robustness of the system in closed loop (2) it reduces chattering in the control signal with measurement noise. Fuzzy system is used to tune the appropriate order of the fractional operators for the proposed control system. Depending on the tuned range of the fractional operators, the proposed controller can operate effectively in the following three modes (1) classical sliding mode (SMC) (2) fractional order sliding mode (FSMC) (3) Integral sliding mode control (ISMC). With the noisy feedback, the performance of the classical SMC and SMC with boundary layer degrades significantly while ISMC shows better performance. However ISMC exhibits large transient overshoots.The proposed control method optimally selects the appropriate mode of the controller to ensure performance(transient and steady state) and suppresses the effect of noisy feedback. The proposed scheme is derived for the permanent magnet synchronous motor, s (PMSM) speed regulation problem which is subject to uncertainties, measurement noise and un-modeled dynamics as a case study. The effectiveness of proposed scheme is verified using numerical simulations.

Citation: Nasim Ullah, Ahmad Aziz Al-Ahmadi. A triple mode robust sliding mode controller for a nonlinear system with measurement noise and uncertainty. Mathematical Foundations of Computing, 2020, 3 (2) : 81-99. doi: 10.3934/mfc.2020007
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##### References:
(a): variation of $\alpha$ with $|S_{3} |$ (b): Variation of $\beta$ with $|S_{3} |$
(a): Fuzzy sets of input variable $|S_{3} |$(b): Fuzzy sets of out variable $\alpha$(c): Fuzzy sets of out variable $\beta$(d): Variation of $\beta$ with $\alpha$
(a) speed regulation, (b) control signal, (c) sliding surface
Enlarged view of (a) speed regulation, (b) control signal, (c) sliding surface
(a) speed error, (b) control signal, (c) sliding surface with $D(X, u, t)$
Enlarged view of (a) speed error, (b) control signal, (c) sliding surface with $D(X, u, t)$
(a) speed error, (b) control signal, (c) sliding surface with $D(X, u, t)$ and measurement noise
Enlarged view of (a) speed error, (b) control signal, (c) sliding surface with $D(X, u, t)$ and measurement noise
Speed regulation (b) Speed error (c) Control signal (d) Sliding surface with with $D(X, u, t)$ and measurement noise
(a) Speed error (b) Control signal (c) Sliding surface with with $D(X, u, t)$ and measurement noise
(a) Adaptation of $\alpha$ (b) Adaptation of $\beta$
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