Robust Tracking of a Class of Perturbed Nonlinear Systems via Multivariable Nested Sliding Mode Control

Author(s):  
Aras Adhami-Mirhosseini ◽  
Mohammad J. Yazdanpanah ◽  
Ali Khaki-Sedigh

In this paper, a new methodology for robust controller design in nonlinear multivariable systems is suggested to guarantee asymptotic output tracking. The systems under consideration are perturbed by functionally bounded matched and unmatched uncertainties/perturbations and assumed to be described in the strict-feedback form. The main idea of the methodology is based on the combination of conventional sliding mode control and backstepping algorithm. The proposed controller called nested sliding mode controller that is obtained through a stepwise algorithm. It has the ability of rejecting nonvanishing perturbations by using dynamic switches, unlike conventional and other hierarchical sliding mode design methods. Performance is studied through theorems and verified by two numerical examples.

Author(s):  
Hao Li ◽  
Lihua Dou ◽  
Zhong Su

This paper focuses on an adaptive dynamic surface based nonsingular fast terminal sliding mode control (ADS-NFTSMC) for a class of nth-order uncertain nonlinear systems in semistrict feedback form. A simple and effective controller has been obtained by introducing dynamic surface control (DSC) technique on the basis of second-order filters that the “explosion of terms” problem caused by backstepping method can be avoided. The nonsingular fast terminal sliding mode control is adopted in the last step of the controller design, and the error convergence rate is improved. An composite adaptive law is used to gain fast and accurate parameter estimation. Finally, simulation results are presented to illustrate the effectiveness of the proposed method.


The objective of this paper is to design a robust controller for a system modeled as a two-mass system, with a flexible coupling. Here, the flexible Joint between two-mass systems is characterized by a spring. In fact, a two-mass system represents most of an industrial drive, like rolling mill drives, automated arms, conveyor belts, and so on, that has a flexible joint, for which oscillation suppression and robust control against model uncertainties and external disturbances are very important. The proposed controller is based on sliding mode control with a back-stepping approach. Two subsystems (upper and lower) strategies are proposed for two- mass systems. On this basis, the classical sliding mode controller for each subsystem based on Lyapunov stability theory and sliding mode control theory is addressed to eliminate the influences of the parametric uncertainties, nonlinearities, and external disturbance load with the aid of sliding mode perturbation observer. Finally, comprehensive simulations are conducted to demonstrate the excellent performance of the proposed method.


2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Jeang-Lin Chang

For a class of linear MIMO uncertain systems, a dynamic sliding mode control algorithm that avoids the chattering problem is proposed in this paper. Without using any differentiator, we develop a modified asymptotically stable second-order sliding mode control law in which the proposed controller can guarantee the finite time convergence to the sliding mode and can show that the system states asymptotically approach to zero. Finally, a numerical example is explained for demonstrating the applicability of the proposed scheme.


2002 ◽  
Vol 8 (2) ◽  
pp. 189-217 ◽  
Author(s):  
Feijun Song ◽  
Edgar An ◽  
Samuel M. Smith

Successful controller development involves three distinct stages, namely, control law design, code debugging and field test. For Autonomous Underwater Vehicle (AUV) applications, the first two stages require special strategies. Since the dynamics of an AUV is highly nonlinear, and the environment that an AUV operates in is noisy with external disturbance that cannot be neglected, a robust control law must be considered in the first stage. The control law design is even more difficult when optimal criteria are also involved. In the second stage, since the software architecture on an AUV is very complicated, debugging the controllers alone without all the software routines running together often can not reveal subtle faults in the controller code. Thorough debugging needs at-sea test, which is costly. Therefore, a platform that can help designers debug and evaluate controller performance before any at-sea experiment is highly desirable. Recently, a 6 Degree of Freedom (DOF) AUV simulation toolbox was developed for the Ocean Explorer (OEX) series AUVs developed at Florida Atlantic University. The simulation toolbox is an ideal platform for controller in-lab debugging and evaluation. This paper first presents a novel robust controller design methodology, named the Sliding Mode Fuzzy Controller (SMFC). It combines sliding mode control and fuzzy logic control to create a robust, easy on-line tunable controller structure. A formal proof of the robustness of the proposed nonlinear sliding mode control is also given. A pitch and a heading controller have been designed with the presented structure and the controller code was tested on the simulation software package as well as at sea. The simulated and at-sea test data are compared. The whole controller design procedure described in this paper clearly demonstrates the advantage of using the simulation toolbox to debug and test the controller in-lab. Moreover, the pitch and heading controller have been used in the real system for more than 2 years, and have also been successfully ported to other types of vehicles without any major modification on the controller parameters. The similarity of the controller performances on different vehicles further demonstrates the robustness of the proposed Sliding Mode Fuzzy Controller. The main contribution of this paper is to provide useful insights into the design and implementation of the proposed control architecture, and its application in AUV control.


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