BACKSTEPPING CONTROL STRATEGY FOR AN UNDERACTUATED X4-AUV

2015 ◽  
Vol 74 (9) ◽  
Author(s):  
Zainah Md. Zain ◽  
Nur Fadzillah Harun
Keyword(s):  
Nonlinear Control ◽  
Lyapunov Stability ◽  
Control Strategy ◽  
Stability Theory ◽  
Degrees Of Freedom ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Backstepping Control ◽  
Six Degrees Of Freedom ◽  
Nonlinear Control Method

A nonlinear control method is considered for stabilizing all attitudes and positions (x, y or z) of an underactuated X4-AUV with four thrusters and six degrees-of-freedom (DOFs), in which the positions are stabilized according to the Lyapunov stability theory and angles are stabilized using backstepping control method. A dynamical model is first derived, and then a sequential nonlinear control strategy is implemented for the X4-AUV, composed of translational and rotational subsystems. A controller for the translational subsystem stabilizes one position out of x-, y-, and z-coordinates, whereas controllers for the rotational subsystems generate the desired roll, pitch and yaw angles. Thus, the rotational controllers stabilize all the attitudes of the X4-AUV at a desired (x-, y- or z-) position of the vehicle. Some numerical simulations are conducted to demonstrate the effectiveness of the proposed controllers.

scholarly journals On Full-State Hybrid Projective Synchronization of General Discrete Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Adel Ouannas
Keyword(s):  
Lyapunov Stability ◽  
Discrete Time ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Full State ◽  
Hybrid Projective Synchronization ◽  
Nonlinear Control Method

The problems of full-state hybrid projective synchronization (FSHPS) and inverse full-state hybrid projective synchronization (IFSHPS) for general discrete chaotic systems are investigated in 2D. Based on nonlinear control method and Lyapunov stability theory, new controllers are designed to study FSHPS and IFSHPS, respectively, for 2D arbitrary chaotic systems in discrete-time. Numerical example and simulations are used to validate the main results of this paper.

scholarly journals Adaptive Terminal Synergetic Synchronization of Hyperchaotic Systems

2021 ◽  
Vol 54 (5) ◽  
pp. 789-795
Author(s):  
Yamina Haddadji ◽  
Mohamed Naguib Harmas ◽  
Abdlouahab Bouafia ◽  
Ziyad Bouchama
Keyword(s):  
Nonlinear Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Initial Conditions ◽  
Lyapunov Stability Theory ◽  
Slave System ◽  
Unknown Parameters ◽  
Master System ◽  
Simulation Results ◽  
Hyperchaotic Systems

This research paper introduces an adaptive terminal synergetic nonlinear control. This control aims at synchronizing two hyperchaotic Zhou systems. Thus, the adaptive terminal synergetic control’s synthesis is applied to synchronize a hyperchaotic i.e., slave system with unknown parameters with another hyperchaotic i.e., master system. Accordingly, simulation results of each system in different initial conditions reveal significant convergence. Moreover, the findings proved stability and robustness of the suggested scheme using Lyapunov stability theory.

Coordination Control Strategy for Active and Reactive Power of DFIG Based on Exact Feedback Linearization under Grid Fault Condition

2011 ◽  
Vol 48-49 ◽  
pp. 335-344
Author(s):  
Meng Zeng Cheng ◽  
Zhen Lan Dou ◽  
Xu Cai
Keyword(s):  
Nonlinear Control ◽  
Power System ◽  
Control Strategy ◽  
Feedback Linearization ◽  
Transient Stability ◽  
Reactive Power ◽  
Control Method ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Nonlinear Control Method

In this paper, a control strategy for operation of rotor side converter (RSC) of Doubly Fed Induction Generators (DFIG) is developed by injecting reactive power into the grid in order to support the grid voltage during and after grid fault events. The novel nonlinear control method is based on differential geometry theory, and exact feedback linearization is applied for control system design of DFIG. Then the optimal control for the linearized system is obtained through introducing the linear quadratic regulator (LQR) design method. Simulation results on a single machine infinite bus power system show that the proposed nonlinear control method can inject reactive power to fault grid rapidly, reduce the oscillation of active power and improve the transient stability of power system.

Robust Finite-Time Stabilization of Fractional-Order Chaotic Systems based on Fractional Lyapunov Stability Theory

2012 ◽  
Vol 7 (2) ◽  
Author(s):  
Mohammad Pourmahmood Aghababa
Keyword(s):  
Fractional Order ◽  
Lyapunov Stability ◽  
Finite Time ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Convergence Time ◽  
Control Approach ◽  
Finite Time Stability

This paper concerns the problem of stabilization of uncertain fractional-order chaotic systems in finite time. On the basis of fractional Lyapunov stability theory, a robust finite-time fractional controller is introduced to control chaos of fractional-order chaotic systems in the presence of system uncertainties. The finite-time stability of the closed-loop system is analytically proved. An estimation of the convergence time is also given. Some numerical simulations are provided to illustrate the usefulness and applicability of the proposed robust finite-time control approach. It is worth noting that the proposed fractional control method is applicable for stabilizing a broad range of uncertain fractional-order nonlinear systems in a given finite time.

scholarly journals Hybrid Chaos Synchronization of Four–Scroll Systems via Active Control

2014 ◽  
Vol 65 (2) ◽  
pp. 97-103 ◽  
Author(s):  
Rajagopal Karthikeyan ◽  
Vaidyanathan Sundarapandian
Keyword(s):  
Numerical Simulations ◽  
Active Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Hybrid Synchronization ◽  
Active Control Method

Abstract This paper investigates the hybrid chaos synchronization of identical Wang four-scroll systems (Wang, 2009), identical Liu-Chen four-scroll systems (Liu and Chen, 2004) and non-identical Wang and Liu-Chen four-scroll systems. Active control method is the method adopted to achieve the hybrid chaos synchronization of the four-scroll chaotic systems addressed in this paper and our synchronization results are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the active control method is effective and convenient to hybrid synchronize identical and different Wang and Liu-Chen four-scroll chaotic systems. Numerical simulations are also shown to illustrate and validate the hybrid synchronization results derived in this paper.

ANTI-SYNCHRONIZATION OF UNIFIED HYPERCHAOTIC SYSTEMS

2014 ◽  
Vol 28 (05) ◽  
pp. 1450014
Author(s):  
PI LI ◽  
XING-YUAN WANG ◽  
PENG SUN ◽  
CHAO LUO ◽  
XIU-KUN WANG
Keyword(s):  
Adaptive Control ◽  
Active Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Control Methods ◽  
System Parameters ◽  
Hyperchaotic Systems ◽  
Active Control Method

In this paper, active control and adaptive control methods are applied, respectively. Adaptive control method is implemented when system parameters are unknown and active control method is applied when system parameters are known. Based on the Lyapunov stability theory, the controllers are designed to realize anti-synchronization, meanwhile, the update laws of parameters are proposed. The theoretical proof is given. And two groups of examples are shown to verify the effectiveness of the proposed schemes.

Outer synchronization of general colored networks with different-dimensional node via sliding mode control

2018 ◽  
Vol 32 (31) ◽  
pp. 1850342 ◽  
Author(s):  
Shuang Liu ◽  
Qingyun Wang
Keyword(s):  
Lyapunov Stability ◽  
Stability Theory ◽  
Control Method ◽  
Sliding Mode ◽  
Lyapunov Stability Theory ◽  
Sliding Mode Controller ◽  
Network Systems ◽  
Colored Complex ◽  
System Parameters ◽  
Linear Subsystem

In this paper, a separated sliding mode strategy is proposed for the synchronization of network systems. To break the predicament caused by the inhomogeneity of nodes coupling in complex network, a colored network with different node systems and edges is given. According to the nonlinear subsystem of the colored complex networks, a separated sliding mode controller is designed, while for the linear subsystem, some appropriate system parameters are established to implement synchronization. Then, based on the Lyapunov stability theory, the performance of the sliding mode controller is appraised through the synchronization for the colored networks consisting of different-dimensional systems and nonidentical interactions. In the end, two simulation illustrations are employed to demonstrate the presented control method.

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