PRE–ICTAL CHANGES AND EEG ANALYSES WITHIN THE FRAMEWORK OF LYAPUNOV THEORY

2000 ◽  
Author(s):  
H. R. MOSER ◽  
P. F. MEIER ◽  
H. G. WIESER ◽  
B. WEBER
Keyword(s):  
Lyapunov Theory

Control of Vibrations due to Moving Loads on Suspension Bridges

2006 ◽  
Vol 11 (3) ◽  
pp. 293-318 ◽  
Author(s):  
M. Zribi ◽  
N. B. Almutairi ◽  
M. Abdel-Rohman
Keyword(s):  
Bridge Deck ◽  
Suspension Bridge ◽  
Lyapunov Theory ◽  
Dynamic Responses ◽  
Suspension Bridges ◽  
Control Force ◽  
Moving Loads ◽  
Hydraulic Actuator ◽  
Long Span ◽  
Suspended Cables

The flexibility and low damping of the long span suspended cables in suspension bridges makes them prone to vibrations due to wind and moving loads which affect the dynamic responses of the suspended cables and the bridge deck. This paper investigates the control of vibrations of a suspension bridge due to a vertical load moving on the bridge deck with a constant speed. A vertical cable between the bridge deck and the suspended cables is used to install a hydraulic actuator able to generate an active control force on the bridge deck. Two control schemes are proposed to generate the control force needed to reduce the vertical vibrations in the suspended cables and in the bridge deck. The proposed controllers, whose design is based on Lyapunov theory, guarantee the asymptotic stability of the system. The MATLAB software is used to simulate the performance of the controlled system. The simulation results indicate that the proposed controllers work well. In addition, the performance of the system with the proposed controllers is compared to the performance of the system controlled with a velocity feedback controller.

scholarly journals Active Disturbance Rejection Control for Position Tracking of Electro-Hydraulic Servo Systems under Modeling Uncertainty and External Load

Actuators ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 20
Author(s):  
Manh Hung Nguyen ◽  
Hoang Vu Dao ◽  
Kyoung Kwan Ahn
Keyword(s):  
Angular Velocity ◽  
Disturbance Rejection ◽  
Lyapunov Theory ◽  
Tracking Performance ◽  
System Stability ◽  
Position Tracking ◽  
Parametric Uncertainties ◽  
Active Disturbance Rejection Control ◽  
Active Disturbance Rejection ◽  
Disturbance Rejection Control

In this paper, an active disturbance rejection control is designed to improve the position tracking performance of an electro-hydraulic actuation system in the presence of parametric uncertainties, non-parametric uncertainties, and external disturbances as well. The disturbance observers (Dos) are proposed to estimate not only the matched lumped uncertainties but also mismatched disturbance. Without the velocity measurement, the unmeasurable angular velocity is robustly calculated based on the high-order Levant’s exact differentiator. These disturbances and angular velocity are integrated into the control design system based on the backstepping framework which guarantees high-accuracy tracking performance. The system stability analysis is analyzed by using the Lyapunov theory. Simulations based on an electro-hydraulic rotary actuator are conducted to verify the effectiveness of the proposed control method.

scholarly journals Posture Dynamic Modeling and Stability Analysis of a Magnetic Driven Dual-Spin Spherical Capsule Robot

Micromachines ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 238
Author(s):  
Huiyuan Yang ◽  
Yongshun Zhang ◽  
Zhenhu Liu ◽  
Xu Liu ◽  
Guanxi Liu
Keyword(s):  
Angular Velocity ◽  
Magnetic Induction ◽  
Periodic Motion ◽  
Lyapunov Theory ◽  
Asymptotically Stable ◽  
Magnetic Torque ◽  
Stable Motion ◽  
Capsule Robot ◽  
Magnetic Induction Intensity ◽  
Spherical Capsule

In order to realize the intervention operation in the unstructured and ample environments such as stomach and colon, a dual-spin spherical capsule robot (DSCR) driven by pure magnetic torque generated by the universal rotating magnetic field (URMF) is proposed. The coupled magnetic torque, the viscoelastic friction torque, and the gravity torque were analyzed. Furthermore, the posture dynamic model describing the electric-magnetic-mechanical-liquid coupling dynamic behavior of the DSCR in the gastrointestinal (GI) tract was established. This model is a second-order periodic variable coefficient dynamics equation, which should be regarded as an extension of the Lagrange case for the dual-spin body system under the fixed-point motion, since the external torques were applied. Based on the Floquet–Lyapunov theory, the stability domain of the DSCR for the asymptotically stable motion and periodic motion were obtained by investigating the influence of the angular velocity of the URMF, the magnetic induction intensity, and the centroid deviation. Research results show that the DSCR can realize three kinds of motion, which are asymptotically stable motion, periodic motion, and chaotic motion, according to the distribution of the system characteristic multipliers. Moreover, the posture stability of the DSCR can be improved by increasing the angular velocity of the URMF and reducing the magnetic induction intensity.

Dynamic output feedback control for nonlinear large-scale interconnected systems

2020 ◽  
Vol 39 (4) ◽  
pp. 801-821
Author(s):  
Ezzeddine Touti ◽  
Ali Sghaier Tlili ◽  
Muhannad Almutiry
Keyword(s):  
Decentralized Control ◽  
Output Feedback ◽  
Large Scale ◽  
Optimization Problem ◽  
Lyapunov Theory ◽  
Interconnected Systems ◽  
Dynamic Output Feedback ◽  
Content Type ◽  
Dynamic Output ◽  
Control Scheme

Purpose This paper aims to focus on the design of a decentralized observation and control method for a class of large-scale systems characterized by nonlinear interconnected functions that are assumed to be uncertain but quadratically bounded. Design/methodology/approach Sufficient conditions, under which the designed control scheme can achieve the asymptotic stabilization of the augmented system, are developed within the Lyapunov theory in the framework of linear matrix inequalities (LMIs). Findings The derived LMIs are formulated under the form of an optimization problem whose resolution allows the concurrent computation of the decentralized control and observation gains and the maximization of the nonlinearity coverage tolerated by the system without becoming unstable. The reliable performances of the designed control scheme, compared to a distinguished decentralized guaranteed cost control strategy issued from the literature, are demonstrated by numerical simulations on an extensive application of a three-generator infinite bus power system. Originality/value The developed optimization problem subject to LMI constraints is efficiently solved by a one-step procedure to analyze the asymptotic stability and to synthesize all the control and observation parameters. Therefore, such a procedure enables to cope with the conservatism and suboptimal solutions procreated by optimization problems based on iterative algorithms with multi-step procedures usually used in the problem of dynamic output feedback decentralized control of nonlinear interconnected systems.

Sampled-data extended state observer-based backstepping control of two-link flexible manipulator

2019 ◽  
Vol 41 (13) ◽  
pp. 3581-3599 ◽  
Author(s):  
Umesh Kumar Sahu ◽  
Bidyadhar Subudhi ◽  
Dipti Patra
Keyword(s):  
Control Strategies ◽  
Estimation Error ◽  
Experimental Studies ◽  
State Observer ◽  
Lyapunov Theory ◽  
Extended State Observer ◽  
Flexible Manipulator ◽  
Sampled Data ◽  
Extended State ◽  
Model Uncertainties

Currently, space robots such as planetary robots and flexible-link manipulators (FLMs) are finding specific applications to reduce the cost of launching. However, the structural flexible nature of their arms and joints leads to errors in tip positioning owing to tip deflection. The internal model uncertainties and disturbance are the key challenges in the development of control strategies for tip-tracking of FLMs. To deal with these challenges, we design a tip-tracking controller for a two-link flexible manipulator (TLFM) by developing a sampled-data extended state observer (SD-ESO). It is designed to reconstruct uncertain parameters for accurate tip-tracking control of a TLFM. Finally, a backstepping (BS) controller is designed to attenuate the estimation error and other bounded disturbances. Convergence and stability of the proposed control system are investigated by using Lyapunov theory. The benefits (control performance and robustness) of the proposed SD-ESO-based BS controller are compared with other similar approaches by pursuing both simulation and experimental studies. It is observed from the results obtained that SD-ESO-based BS Controller effectively compensates the deviation in tip-tracking performance of TLFM due to non-minimum phase behavior and model uncertainties with an improved transient response.

A Unified Approach to the Design of Adaptive and Repetitive Controllers for Robotic Manipulators

1990 ◽  
Vol 112 (4) ◽  
pp. 618-629 ◽  
Author(s):  
Nader Sadegh ◽  
Roberto Horowitz ◽  
Wei-Wen Kao ◽  
Masayoshi Tomizuka
Keyword(s):  
Lyapunov Theory ◽  
Control Input ◽  
Robot Arm ◽  
Unified Approach ◽  
Parameter Adaptation ◽  
Control Laws ◽  
Position Errors ◽  
Adaptive Compensator ◽  
Mechanical Manipulators ◽  
Repetitive Controller

A unified approach, based on Lyapunov theory, for synthesis and stability analysis of adaptive and repetitive controllers for mechanical manipulators is presented. This approach utilizes the passivity properties of the manipulator dynamics to derive control laws which guarantee asymptotic trajectory following, without requiring exact knowledge of the manipulator dynamic parameters. The manipulator overall controller consists of a fixed PD action and an adaptive and/or repetitive action for feed-forward compensations. The nonlinear feedforward compensation is adjusted utilizing a linear combination of the tracking velocity and position errors. The repetitive compensator is recommended for tasks in which the desired trajectory is periodic. The repetitive control input is adjusted periodically without requiring knowledge of the explicit structure of the manipulator model. The adaptive compensator, on the other hand, may be used for more general trajectories. However, explicit information regarding the dynamic model structure is required in the parameter adaptation. For discrete time implementations, a hybrid version of the repetitive controller is derived and its global stability is proven. A simulation study is conducted to evaluate the performance of the repetitive controller, and its hybrid version. The hybrid repetitive controller is also implemented in the Berkeley/NSK SCARA type robot arm.

Chaos Anti-Synchronization between Chen System and Lu System

2014 ◽  
Vol 631-632 ◽  
pp. 710-713 ◽  
Author(s):  
Xian Yong Wu ◽  
Hao Wu ◽  
Hao Gong
Keyword(s):  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Lyapunov Theory ◽  
State Variables ◽  
Chen System ◽  
System Parameters ◽  
Control Scheme ◽  
Error Dynamics ◽  
The Stability ◽  
Different Chaotic Systems

Anti-synchronization of two different chaotic systems is investigated. On the basis of Lyapunov theory, adaptive control scheme is proposed when system parameters are unknown, sufficient conditions for the stability of the error dynamics are derived, where the controllers are designed using the sum of the state variables in chaotic systems. Numerical simulations are performed for the Chen and Lu systems to demonstrate the effectiveness of the proposed control strategy.

3D Nonlinear Guidance Law for Bank-to-Turn Missile

2011 ◽  
Vol 317-319 ◽  
pp. 727-733
Author(s):  
Shuang Chun Peng ◽  
Liang Pan ◽  
Tian Jiang Hu ◽  
Lin Cheng Shen
Keyword(s):  
Three Dimensional ◽  
Lyapunov Theory ◽  
Line Of Sight ◽  
Rate Model ◽  
Guidance Law ◽  
Terminal Constraints ◽  
Guidance Laws ◽  
3D Guidance ◽  
Guidance Model ◽  
Vector Description

A new three-dimensional (3D) nonlinear guidance law is proposed and developed for bank-to-turn (BTT) with motion coupling. First of all, the 3D guidance model is established. In detail, the line-of-sight (LOS) rate model is established with the vector description method, and the kinematics model is divided into three terms of pitching, swerving and coupling, then by using the twist-based method, the LOS direction changing model is built for designing the guidance law with terminal angular constraints. Secondly, the 3D guidance laws are designed with Lyapunov theory, corresponding to no terminal constraints and terminal constraints, respectively. And finally, the simulation results show that the proposed guidance law can effectively satisfy the guidance precision requirements of BTT missile.

A fault-tolerant control scheme within adaptive disturbance observer for hypersonic vehicle

2017 ◽  
Vol 233 (3) ◽  
pp. 1071-1088 ◽  
Author(s):  
Jun Zhou ◽  
Jing Chang ◽  
Zongyi Guo
Keyword(s):  
Disturbance Observer ◽  
Fault Tolerant ◽  
Sliding Mode ◽  
Fault Tolerant Control ◽  
Lyapunov Theory ◽  
Sliding Mode Controller ◽  
Performance Guarantees ◽  
Uncertain Model ◽  
Control Scheme ◽  
And Performance

The paper describes the design of a fault-tolerant control scheme for an uncertain model of a hypersonic reentry vehicle subject to actuator faults. In order to improve superior transient performances for state tracking, the proposed method relies on a back-stepping sliding mode controller combined with an adaptive disturbance observer and a reference vector generator. This structure allows for a faster response and reduces the overshoots compared to linear conventional disturbance observers based sliding mode controller. Robust stability and performance guarantees of the overall closed-loop system are obtained using Lyapunov theory. Finally, numerical simulations results illustrate the effectiveness of the proposed technique.

scholarly journals Robust nonsingular sliding mode control of the maglev train system: case study

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
Kammogne Soup Tewa Alain ◽  
Kenmogne Fabien ◽  
Siewe Siewe Martin ◽  
Fotsin Hilaire Bertrand
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Lyapunov Theory ◽  
Magnetic Suspension ◽  
Added Value ◽  
Vertical Position ◽  
Maglev Train ◽  
Maglev System ◽  
Mode Control ◽  
Train System

AbstractThis paper deals with a new approach to explore the precise dynamic response of the maglev system train and its control. Magnetic-suspension systems are characterized by high nonlinearity and open-loop instability which are the core components of maglev vehicles. Firstly, we use the electromagnetics and mechanics laws to derive the mathematical expressions of the proposed maglev system. Analytical investigation and theoretical calculation show that for the specific values of the control system parameters, the maglev system train can be significantly improved. It points out that the inherent nonlinearity, the inner coupling, misalignments between the sensors and actuators, and external disturbances are the main issues that should be considered for maglev engineering. Secondly, a control strategy based on the precise model of a nonsing ular robust sliding mode control is designed to reduce the upper bound of both the uncertainty and interference of the sliding mode controller. This approach presents an added value compared to the new sliding control methods in terms of overshoot and speed of convergence which is designed to control the vertical position of the proposed system. By using rigorous mathematical transformation associated with the adaptation laws in the frequency domain, a sufficient condition is drawn for the stability of the dynamical error based on the Lyapunov theory. This allows us a great possibility for interpreting the operation of the maglev train system. Numerical results are presented to show the effectiveness of our proposed control scheme.

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