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Open AccessArticle

Design of Robust Trackers and Unknown Nonlinear Perturbation Estimators for a Class of Nonlinear Systems: HTRDNA Algorithm for Tracker Optimization

1
Department of Electrical Engineering, National Cheng-Kung University, Tainan 701, Taiwan
2
Department of Electronic Engineering, National Chin-Yi University of Technology, Taichung 41107, Taiwan
3
Department of Computer Science and Information Engineering, National Cheng-Kung University, Tainan 701, Taiwan
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1141; https://doi.org/10.3390/math7121141
Received: 21 September 2019 / Revised: 17 November 2019 / Accepted: 20 November 2019 / Published: 22 November 2019
(This article belongs to the Special Issue Nonlinear Functional Analysis and Its Applications)
A robust linear quadratic analog tracker (LQAT) consisting of proportional-integral-derivative (PID) controller, sliding mode control (SMC), and perturbation estimator is proposed for a class of nonlinear systems with unknown nonlinear perturbation and direct feed-through term. Since the derivative type (D-type) controller is very sensitive to the state varying, a new D-type controller design algorithm is developed to avoid an unreasonable large value of the controller gain. Moreover, the boundary of D-type controller is discussed. To cope with the unknown perturbation effect, SMC is utilized. Based on the fast response of SMC controlled systems, the proposed perturbation estimator can estimate unknown nonlinear perturbation and improve the tracking performance. Furthermore, in order to tune the PID controller gains in the designed tracker, the nonlinear perturbation is eliminated by the SMC-based perturbation estimator first, then a hybrid Taguchi real coded DNA (HTRDNA) algorithm is newly proposed for the PID controller optimization. Compared with traditional DNA, a new HTRDNA is developed to improve the convergence performance and effectiveness. Numerical simulations are given to demonstrate the performance of the proposed method. View Full-Text
Keywords: PID controller; sliding mode control; hybrid Taguchi real coded DNA algorithm; perturbation estimator PID controller; sliding mode control; hybrid Taguchi real coded DNA algorithm; perturbation estimator
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MDPI and ACS Style

Fang, J.-S.; Tsai, J. .-H.; Yan, J.-J.; Tzou, C.-H.; Guo, S.-M. Design of Robust Trackers and Unknown Nonlinear Perturbation Estimators for a Class of Nonlinear Systems: HTRDNA Algorithm for Tracker Optimization. Mathematics 2019, 7, 1141.

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