scholarly journals Design of LPV-Based Sliding Mode Controller with Finite Time Convergence for a Morphing Aircraft

2017 ◽  
Vol 2017 ◽  
pp. 1-20 ◽  
Author(s):  
Nuan Wen ◽  
Zhenghua Liu ◽  
Yang Sun ◽  
Lingpu Zhu
Keyword(s):  
Finite Time ◽  
Sliding Mode ◽  
Linear Time ◽  
Stability Control ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Morphing Aircraft ◽  
Finite Time Convergence ◽  
Lpv System ◽  
Parameter Dependent

This paper proposes a finite time convergence sliding mode control (FSMC) strategy based on linear parameter-varying (LPV) methodology for the stability control of a morphing aircraft subject to parameter uncertainties and external disturbances. Based on the Kane method, a longitudinal dynamic model of the morphing aircraft is built. Furthermore, the linearized LPV model of the aircraft in the wing transition process is obtained, whose scheduling parameters are wing sweep angle and wingspan. The FSMC scheme is developed into LPV systems by applying the previous results for linear time-invariant (LTI) systems. The sufficient condition in form of linear matrix inequality (LMI) constraints is derived for the existence of a reduced-order sliding mode, in which the dynamics can be ensured to keep robust stability and L2 gain performance. The tensor-product (TP) model transformation approach can be directly applied to solve infinite LMIs belonging to the polynomial parameter-dependent LPV system. Then, by the parameter-dependent Lyapunov function stability analysis, the synthesized FSMC is proved to drive the LPV system trajectories toward the predefined switching surface with a finite time arrival. Comparative simulation results in the nonlinear model demonstrate the robustness and effectiveness of this approach.

scholarly journals A New Control Method for Second-Order Multiple Models Control System Based on Global Sliding Mode

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Dan-xu Zhang ◽  
Yang-wang Fang ◽  
Peng-fei Yang ◽  
You-li Wu ◽  
Tong-xin Liu
Keyword(s):  
Control System ◽  
Sliding Mode Control ◽  
Finite Time ◽  
Sliding Mode ◽  
Second Order ◽  
Multiple Models ◽  
Finite Time Convergence ◽  
Mode Control ◽  
Global Sliding Mode Control ◽  
Control Scheme

This paper proposed a finite time convergence global sliding mode control scheme for the second-order multiple models control system. Firstly, the global sliding surface without reaching law for a single model control system is designed and the tracking error finite time convergence and global stability are proved. Secondly, we generalize the above scheme to the second-order multimodel control system and obtain the global sliding mode control law. Then, the convergent and stable performances of the closed-loop control system with multimodel controllers are proved. Finally, a simulation example shows that the proposed control scheme is more effective and useful compared with the traditional sliding mode control scheme.

Time-varying sliding-mode control for finite-time convergence

2010 ◽  
Vol 92 (7-8) ◽  
pp. 257-268 ◽  
Author(s):  
Yu-Sheng Lu ◽  
Chien-Wei Chiu ◽  
Jian-Shiang Chen
Keyword(s):  
Sliding Mode Control ◽  
Finite Time ◽  
Sliding Mode ◽  
Time Varying ◽  
Finite Time Convergence ◽  
Mode Control

Parameter-Dependent Feedback Compensator Design for a Time-Fractional Reaction-Diffusion Equation

2021 ◽  
Author(s):  
Jun-Wei Wang ◽  
Hua-Cheng Zhou
Keyword(s):  
Linear Time ◽  
Design Method ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Linear Matrix ◽  
Parametric Form ◽  
Coupled Equations ◽  
Reaction Coefficient ◽  
Standard Linear ◽  
Parameter Dependent

Abstract This paper presents a parameter-dependent design of feedback compensator with space-varying gains for Mittag-Leffler stabilization of linear time fractional parabolic MIMO partial differential equations subject to space-varying diffusion and reaction coefficients. In the proposed design method, under a boundedness assumption, the reaction coefficient is written in a parametric form. By using the parametric form for the reaction coefficient and multiple non-collocated observation outputs, an observer-based state feedback compensator with space-varying gains is then constructed such that the resulting closed-loop coupled equations are Mittag-Leffler stable. By applying the Lyapunov technique with Caputo fractional derivative and variants of Poincaré–Wirtinger’s inequality, a sufficient condition for the existence of such feedback compensator is presented in terms of standard linear matrix inequalities. Finally, simulation results are presented to support the proposed design method.

Time Delay-Free Nonlinear Bilateral Teleoperation With Model-Based Predictive Display

2001 ◽  
Author(s):  
Vicente Parra-Vega
Keyword(s):  
Nonlinear Dynamics ◽  
Time Delay ◽  
Finite Time ◽  
Linear Models ◽  
Sliding Mode ◽  
Linear Time ◽  
Contact Forces ◽  
Rigorous Result ◽  
Model Based ◽  
Predictive Display

Abstract Robotic teleoperation is a difficult task because of the inherent difficulty to model and control time-delay nonlinear models. In order to handle tractable models, typically there have been two ways to tackle this problem: i) The first approach is to assume that the system is fast enough and thus the time delay can be neglected, in this way time-delay-free differential equations are obtained such that the controller is time-delay-free. This approach needs further formal study to validate this assumption, and so far there is neither strict nor rigorous result that support this claim, when considering the full nonlinear telerobotic dyanmics. ii) In the second approach, the time delay is considered explicitly, however typically nonlinear dynamics is neglected and then linear models are used to derive time-delay-based control systems. The second approach ignores that the robots are nonlinear systems with strong nonlinear inertial couplings, and therefore controllers based on linear time-delay models render low performance. In this paper, the teleoperation of robots is modeled, including nonlinear dynamics in the continuous domain, without any time delay, and model-based nonlinear continuous second order sliding mode controllers are proposed which guarantee finite-time convergence. Thus, this approach attempts to propose a scheme for the second approach outlined above. The teleoperation system provides force reflection to the human operator, and a kinematic-based predictive display yields visual stimuli while the master robot yields kinesthetic feedback to the operator to allow planning better desired trajectories, including contact forces, in contrast to other predictive displays that have been proposed in the literature. Therefore, the theoretical foundations of finite-time convergent telecontrol system and its advantages are discussed.

A New Finite Time Control Solution for Robotic Manipulators Based on Nonsingular Fast Terminal Sliding Variables and the Adaptive Super-Twisting Scheme

2019 ◽  
Vol 14 (3) ◽  
Author(s):  
Vo Anh Tuan ◽  
Hee-Jun Kang
Keyword(s):  
Finite Time ◽  
Control Method ◽  
Sliding Mode ◽  
Robotic Manipulators ◽  
Control Law ◽  
Continuous Control ◽  
Terminal Sliding Mode ◽  
Finite Time Convergence ◽  
Position Errors ◽  
Time Control

In this study, a new finite time control method is suggested for robotic manipulators based on nonsingular fast terminal sliding variables and the adaptive super-twisting method. First, to avoid the singularity drawback and achieve the finite time convergence of positional errors with a fast transient response rate, nonsingular fast terminal sliding variables are constructed in the position errors' state space. Next, adaptive tuning laws based on the super-twisting scheme are presented for the switching control law of terminal sliding mode control (TSMC) so that a continuous control law is extended to reject the effects of chattering behavior. Finally, a new finite time control method ensures that sliding motion will take place, regardless of the effects of the perturbations and uncertainties on the robot system. Accordingly, the stabilization and robustness of the suggested control system can be guaranteed with high-precision performance. The robustness issue and the finite time convergence of the suggested system are totally confirmed by the Lyapunov stability principle. In simulation studies, the experimental results exhibit the effectiveness and viability of our proposed scheme for joint position tracking control of a 3DOF PUMA560 robot.

Parameter-dependent robust H∞ filtering for uncertain two-dimensional discrete systems in the FM second model

2020 ◽  
Vol 37 (4) ◽  
pp. 1114-1132
Author(s):  
Khalid Badie ◽  
Mohammed Alfidi ◽  
Mohamed Oubaidi ◽  
Zakaria Chalh
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Discrete Systems ◽  
Performance Criterion ◽  
Linear Matrix ◽  
Two Dimensional ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Error System ◽  
Parameter Dependent

Abstract This paper deals with the problem of robust $H_{\infty }$ filtering for uncertain two-dimensional discrete systems in the Fornasini–Marchesini second model with polytopic parameter uncertainties. Firstly, a new $H_{\infty }$ performance criterion is derived by exploiting a new structure of the parameter-dependent Lyapunov function. Secondly, based on the criterion obtained, a new condition for the existence of a robust $H_{\infty }$ filter that ensures asymptotic stability, and a prescribed $H_{\infty }$ performance level of the filtering error system, for all admissible uncertainties is established in terms of linear matrix inequalities. Finally, two examples are given to illustrate the effectiveness and advantage of the proposed method.

scholarly journals Finite-Time Output Feedback Controller Based on Observer for the Time-Varying Delayed Systems: A Moore-Penrose Inverse Approach

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Cong-Trang Nguyen ◽  
Yao-Wen Tsai
Keyword(s):  
Asymptotic Stability ◽  
Output Feedback ◽  
Finite Time ◽  
Sliding Mode ◽  
Feedback Controller ◽  
Delay Systems ◽  
Linear Matrix ◽  
Invariance Property ◽  
Time Varying ◽  
Output Feedback Controller

This study proposes a novel variable structure control (VSC) for the mismatched uncertain systems with unknown time-varying delay. The novel VSC includes the finite-time convergence sliding mode, invariance property, asymptotic stability, and measured output only. A necessary and sufficient condition guaranteeing the existence of sliding surface is given. A novel lemma is established to deal with the control design problem for a wider class of time-delay systems. A suitable reduced-order observer (ROO) is constructed to estimate unmeasured state variables of the systems. A novel finite-time output feedback controller (FTOFC) is investigated, which is based on the ROO tool and the Moore-Penrose inverse technique. Moreover, with the help of this lemma and the proposed FTOFC, restrictions on most existing works are also eliminated. In addition, an asymptotic stability analysis is implemented by means of the feasibility of the linear matrix inequalities (LMIs) and given desirable sliding mode dynamics. Finally, a MATLAB simulation result on a numerical example is performed to show the effectiveness and advantage of the proposed method.

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