Analysis of Sliding Mode Observers Using a Novel Time-Averaged Lyapunov Function

2017 ◽  
Author(s):  
Sagar Mehta ◽  
Krishna Vijayaraghavan
Keyword(s):  
Lyapunov Function ◽  
Gaussian Noise ◽  
Sliding Mode ◽  
Sliding Mode Observer ◽  
Sensor Noise ◽  
Model Uncertainties ◽  
Quadratic Lyapunov Function ◽  
Simulation Results ◽  
Sliding Mode Observers ◽  
The Stability

Sliding mode observers are known to be robust to model uncertainties. However, sliding mode observers have not been well analyzed in the presence of Gaussian disturbances and no previous results exist for a pure sliding mode observer in the presence of sensor noise. A traditional quadratic Lyapunov function that is used to determine the stability of sliding mode observers, fails for noisy systems. Hence this paper introduces a novel Lyapunov candidate function termed the time averaged Lyapunov (TAL) function to analyze the stability of noisy systems. The TAL specifically examines the effect of the Gaussian noise on a sliding mode observer. Using this TAL function, the paper demonstrates that Gaussian sensor noise does not affect the stability or chatter of the observer. Further, the covariance of the noise only affects the convergence rate of the observer. Simulation results are reported to demonstrate the effectiveness of the proposed approach on a Linear system.

Analysis of Sliding Mode Observers for Nonlinear Systems Using a Time-Averaged Lyapunov Function

2018 ◽  
Author(s):  
Sagar Mehta ◽  
Krishna Vijayaraghavan
Keyword(s):  
Steady State ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Convergence Rate ◽  
Sliding Mode ◽  
Sliding Mode Observer ◽  
Sensor Noise ◽  
Sliding Mode Observers

This paper is an extension of the authors’ previous paper on the analysis of sliding mode observers using a novel Time-Averaged Lyapunov function [1]. The paper presents the design of a sliding mode observer for a Lipschitz nonlinear system. The paper demonstrates that the external sensor noise (Gaussian) only affects the convergence rate of the observer without having any influence over its stability at steady state. Further, a condition for the existence of the observer is provided in the form of an LMI. The LMI can be solved offline using various commercial LMI solvers. An illustrative example is presented to demonstrate the effectiveness of this approach.

scholarly journals Robust RAM Control for WSR on the Water Surface

2018 ◽  
Vol 7 (3.7) ◽  
pp. 303
Author(s):  
K Chun ◽  
B Kim
Keyword(s):  
Lyapunov Function ◽  
Water Surface ◽  
Controller Design ◽  
Sliding Mode ◽  
Fast Response ◽  
Target Point ◽  
Nonlinear Controller ◽  
Sign Function ◽  
Simulation Results ◽  
The Stability

This paper discusses a robust rotate and move (RAM) controller by considering a water striding robot (WSR) with two wheels. The proposed controller commands the WSR to rotate and move straight toward the desired target by considering the two wheel WSR characteristics. Sliding mode control (SMC) is one of the solutions in nonlinear controller design and it has fast response and robustness. SMC is applied to the WSR RAM control. However, the sliding mode has a problem called chattering because of using sign function in controller design and this will cause the system unstable in WSR control because the chattering make the WSR sink into water easily. As a solution, sign function is replaced by saturation function. The proposed controller is noble and track the target point easily and also has robustness. The stability of the proposed controller is proved by Lyapunov function and the simulation results show the fast response and robustness.  

Sensorless FOC Strategy for the Salient-pole PMSM using Improved Fullorder Sliding Mode Observer

2019 ◽  
Vol 12 (4) ◽  
pp. 339-346
Author(s):  
Oussama Saadaoui ◽  
Imen Tlili ◽  
Amor Khlaief ◽  
Abdelkader Chaari
Keyword(s):  
Sliding Mode ◽  
Estimation Method ◽  
Sliding Mode Observer ◽  
Field Oriented Control ◽  
New Approach ◽  
High Speeds ◽  
Salient Pole ◽  
Simulation Results ◽  
The Stability ◽  
Mechanical Sensors

Background: This document presents a new approach to estimate speed and rotor position of the salient-pole Permament Magnet Synchronous Motor (PMSM). Methods: To eliminate the mechanical sensors, we apply a sensorless field oriented control (FOC) by using an improved full-order sliding mode observer (FO-SMO) at different speeds (low and high speeds). The stability of the Slide Mode Observer (SMO) was demonstrated with the Lyapunov function. Methods: The simulation results prove good properties of the proposed estimation method. Conclusion: The sensorless field oriented control strategy of the salient-pole PMSM has been proposed in this paper using an improved full-order SMO.

Robust sliding mode observer design for simultaneous fault reconstruction in perturbed Takagi-Sugeno fuzzy systems using non-quadratic stability analysis

2020 ◽  
Vol 26 (11-12) ◽  
pp. 1092-1105
Author(s):  
Samira Asadi ◽  
Alireza Khayatian ◽  
Maryam Dehghani ◽  
Navid Vafamand ◽  
Mohammad Hassan Khooban
Keyword(s):  
Lyapunov Function ◽  
Fault Detection ◽  
Sliding Mode ◽  
Sliding Mode Observer ◽  
Observer Design ◽  
Performance Criteria ◽  
Linear Matrix ◽  
Quadratic Lyapunov Function ◽  
Fault Reconstruction ◽  
Takagi Sugeno

Appearing faults in a practical system is dispensable, and if it is not compensated, it results in poor system performance or even dysfunction of the system. The fault detection has become a promising challenging issue to guarantee the safety and reliability of systems. In this paper, a novel fuzzy-based sliding mode observer for the simultaneous actuator and sensor fault reconstruction of nonlinear systems subjected to external disturbance is proposed. The proposed approach employs the Takagi-Sugeno fuzzy model, sliding mode observer and non-quadratic Lyapunov function. First, by filtering the system output, a fictitious system whose actuator faults are the original actuator and sensor faults is constructed. Then, by considering the [Formula: see text] performance criteria, the effect of disturbance on the state estimations is minimized. It is proved that the estimations asymptotically converge to their actual values for non-perturbed systems. In the process of designing the observer gains, some transformation matrices are obtained by solving linear matrix inequalities. The proposed approach has some superiority over the existing methods. First, considering the non-quadratic Lyapunov function leads to relaxed results and good estimation performance. Second, using the sliding mode observer makes the proposed approach insensitive to the uncertainties and unknown inputs and determines the shape and size of the fault. Third, assuming the premise variables are immeasurable makes the presented approach more applicable. In conclusion, two practical systems are considered and simulation results illustrate the merits of the proposed approach in comparison with the recent methods from the fast and precise fault detection performance viewpoints.

scholarly journals Multisensor Fault Identification Scheme Based on Decentralized Sliding Mode Observers Applied to Reconfigurable Manipulators

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Bo Zhao ◽  
Yuanchun Li
Keyword(s):  
Sliding Mode ◽  
Sliding Mode Observer ◽  
Fault Identification ◽  
Stable Theory ◽  
Sensor Fault ◽  
Identification Scheme ◽  
Neural Network Controller ◽  
Network Controller ◽  
Sliding Mode Observers ◽  
Reconfigurable Manipulators

This paper concerns with a fault identification scheme in a class of nonlinear interconnected systems. The decentralized sliding mode observer is recruited for the investigation of position sensor fault or velocity sensor fault. First, a decentralized neural network controller is proposed for the system under fault-free state. The diffeomorphism theory is utilized to construct a nonlinear transformation for subsystem structure. A simple filter is implemented to convert the sensor fault into pseudo-actuator fault scenario. The decentralized sliding mode observer is then presented for multisensor fault identification of reconfigurable manipulators based on Lyapunov stable theory. Finally, two 2-DOF reconfigurable manipulators with different configurations are employed to verify the effectiveness of the proposed scheme in numerical simulation. The results demonstrate that one joint’s fault does not affect other joints and the sensor fault can be identified precisely by the proposed decentralized sliding mode observer.

scholarly journals Active Sliding Mode for Synchronization of a Wide Class of Four-Dimensional Fractional-Order Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Bin Wang ◽  
Yuangui Zhou ◽  
Jianyi Xue ◽  
Delan Zhu
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Wide Class ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Order System ◽  
Fractional Order Calculus ◽  
Simulation Results ◽  
The Stability

We focus on the synchronization of a wide class of four-dimensional (4-D) chaotic systems. Firstly, based on the stability theory in fractional-order calculus and sliding mode control, a new method is derived to make the synchronization of a wide class of fractional-order chaotic systems. Furthermore, the method guarantees the synchronization between an integer-order system and a fraction-order system and the synchronization between two fractional-order chaotic systems with different orders. Finally, three examples are presented to illustrate the effectiveness of the proposed scheme and simulation results are given to demonstrate the effectiveness of the proposed method.

scholarly journals Sliding Mode Observer-based Control of Teleoperation System With Uncertain Dynamics and Kinematics

2021 ◽  
Author(s):  
Jianing Zhang ◽  
Fujie Wang ◽  
Guilin Wen
Keyword(s):  
Sliding Mode ◽  
Time Estimation ◽  
Joint Space ◽  
Estimation Errors ◽  
Uncertain Dynamics ◽  
Control Framework ◽  
End Effectors ◽  
Sliding Mode Observers ◽  
The Stability ◽  
Velocity Tracking

Abstract This paper concentrates on the control issue of nonlinear teleoperators in the presence of uncertain dynamics and kinematics. An observer-based control framework is introduced to compensate for the unfavorable effects arising from the uncertainties. The employment of the proposed sliding mode observers provide control system with the ability of finite-time estimation errors convergence, upon which, it is demonstrated that the bilateral teleoperators are stable and both of position and velocity tracking can be achieved with uncertain dynamics in joint space. Due to the practical requirement of driving the end-effectors to perform specific tasks, the control law which can ensure position coordination with uncertain dynamics and kinematics in task space is subsequently developed. The Lyapunov method is applied to demonstrate the stability of the closed-loop system. Simulation results are provided to testify the performance of the suggested algorithm.

Active Fault Tolerant Control Based on Fault Estimation

2014 ◽  
Vol 635-637 ◽  
pp. 1199-1202 ◽  
Author(s):  
Zheng Gao Hu ◽  
Guo Rong Zhao ◽  
Da Wang Zhou
Keyword(s):  
Active Fault ◽  
Fault Tolerant ◽  
Sliding Mode ◽  
Fault Tolerant Control ◽  
Sliding Mode Observer ◽  
Fault Estimation ◽  
Control Law ◽  
Active Fault Tolerant Control ◽  
The Stability ◽  
Twisting Algorithm

For the chattering problem in the traditional sliding mode observer-based fault estimation, a second order sliding mode observer based on the Super-twisting algorithm was proposed. In order to avoid the cumbersome process of proving the stability of the Super-twisting algorithm, a Lyapunov function was adopted. An active fault tolerant control law was designed based on the fault estimation. Finally, simulation show the effectiveness of the proposed approach.

Sliding Mode Observer and Controller Design for Nonlinear Supersonic Missile

2013 ◽  
Vol 718-720 ◽  
pp. 1228-1233
Author(s):  
Hong Chao Zhao ◽  
Xian Jun Shi ◽  
Ting Wang
Keyword(s):  
Lyapunov Stability ◽  
Controller Design ◽  
Sliding Mode ◽  
Equations Of Motion ◽  
Lyapunov Stability Theory ◽  
Sliding Mode Observer ◽  
Sliding Mode Controller ◽  
Output Redefinition ◽  
Simulation Results ◽  
Nonlinear Equations Of Motion

The nonlinear equations of motion were constructed for a supersonic anti-warship missile. In order to estimate the unknown angle-of-attack, a sliding mode observer was designed. The convergence capability of the sliding mode observer was analyzed according to the Lyapunov stability theory. A sliding mode controller was designed to drive the missile normal overload output to track its command, based on the output-redefinition approach. In order to confirm the performance of the designed sliding mode observer and controller, a simulation example was carried out for nonlinear missile model. The simulation results show the fast convergence capability of the designed sliding mode observer and controller.

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