Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 8

lyapunov stability Related Abstracts

8 Sliding Mode Control of Autonomous Underwater Vehicles

Authors: Mohammad Azadi, Ahmad Forouzantabar, Alireza Alesaadi


This paper describes a sliding mode controller for autonomous underwater vehicles (AUVs). The dynamic of AUV model is highly nonlinear because of many factors, such as hydrodynamic drag, damping, and lift forces, Coriolis and centripetal forces, gravity and buoyancy forces, as well as forces from thruster. To address these difficulties, a nonlinear sliding mode controller is designed to approximate the nonlinear dynamics of AUV and improve trajectory tracking. Moreover, the proposed controller can profoundly attenuate the effects of uncertainties and external disturbances in the closed-loop system. Using the Lyapunov theory the boundedness of AUV tracking errors and the stability of the proposed control system are also guaranteed. Numerical simulation studies of an AUV are included to illustrate the effectiveness of the presented approach.

Keywords: Electronics Engineering, Autonomous Underwater Vehicle, lyapunov stability, sliding mode controller

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7 Parallel Particle Swarm Optimization Optimized LDI Controller with Lyapunov Stability Criterion for Nonlinear Structural Systems

Authors: C. Y. Chen, P. W. Tsai, W. L. Hong, C. W. Chen


In this paper, we present a neural network (NN) based approach represent a nonlinear Tagagi-Sugeno (T-S) system. A linear differential inclusion (LDI) state-space representation is utilized to deal with the NN models. Taking advantage of the LDI representation, the stability conditions and controller design are derived for a class of nonlinear structural systems. Moreover, the concept of utilizing the Parallel Particle Swarm Optimization (PPSO) algorithm to solve the common P matrix under the stability criteria is given in this paper.

Keywords: Artificial Intelligence, lyapunov stability, parallel particle swarm optimization, linear differential inclusion

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6 Applied Actuator Fault Accommodation in Flight Control Systems Using Fault Reconstruction Based FDD and SMC Reconfiguration

Authors: A. Ghodbane, M. Saad, C. Thibeault, J. F. Boland


Historically, actuators’ redundancy was used to deal with faults occurring suddenly in flight systems. This technique was generally expensive, time consuming and involves increased weight and space in the system. Therefore, nowadays, the on-line fault diagnosis of actuators and accommodation plays a major role in the design of avionic systems. These approaches, known as Fault Tolerant Flight Control systems (FTFCs) are able to adapt to such sudden faults while keeping avionics systems lighter and less expensive. In this paper, a (FTFC) system based on the Geometric Approach and a Reconfigurable Flight Control (RFC) are presented. The Geometric approach is used for cosmic ray fault reconstruction, while Sliding Mode Control (SMC) based on Lyapunov stability theory is designed for the reconfiguration of the controller in order to compensate the fault effect. Matlab®/Simulink® simulations are performed to illustrate the effectiveness and robustness of the proposed flight control system against actuators’ faulty signal caused by cosmic rays. The results demonstrate the successful real-time implementation of the proposed FTFC system on a non-linear 6 DOF aircraft model.

Keywords: Fault detection and diagnosis, Sliding Mode Control, lyapunov stability, actuators’ faults, fault tolerant flight control, geometric approach for fault reconstruction

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5 Synchronization of Chaotic T-System via Optimal Control as an Adaptive Controller

Authors: Hossein Kheiri, Bashir Naderi, Mohamad Reza Niknam


In this paper we study the optimal synchronization of chaotic T-system with complete uncertain parameter. Optimal control laws and parameter estimation rules are obtained by using Hamilton-Jacobi-Bellman (HJB) technique and Lyapunov stability theorem. The derived control laws are optimal adaptive control and make the states of drive and response systems asymptotically synchronized. Numerical simulation shows the effectiveness and feasibility of the proposed method.

Keywords: Adaptive Control, Optimal Control, Chaos, Synchronization, lyapunov stability

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4 Sliding Mode Control of Bilateral Teleoperation System with Time Delay

Authors: Mohammad Azadi, Ahmad Forouzantabar


This paper presents sliding mode controller for bilateral teleoperation systems with robotic master and slave under constant communication delays. We extend the passivity-based coordination architecture to enhance position and force tracking in the presence of offset in initial conditions, environmental contacts and unknown parameters such as friction coefficient. To address these difficulties, a nonlinear sliding mode controller is designed to approximate the nonlinear dynamics of master and slave robots and improve both position and force tracking. Using the Lyapunov theory, the boundedness of master- slave tracking errors and the stability of the teleoperation system are also guaranteed. Numerical simulations show that proposed controller position and force tracking performances are superior to that of conventional coordination controller tracking performances.

Keywords: Time Delay, lyapunov stability, sliding mode controller, teleoperation system

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3 Fault Tolerant Control System Using a Multiple Time Scale SMC Technique and a Geometric Approach

Authors: Ghodbane Azeddine, Saad Maarouf, Boland Jean-Francois, Thibeault Claude


This paper proposes a new design of an active fault-tolerant flight control system against abrupt actuator faults. This overall system combines a multiple time scale sliding mode controller for fault compensation and a geometric approach for fault detection and diagnosis. The proposed control system is able to accommodate several kinds of partial and total actuator failures, by using available healthy redundancy actuators. The overall system first estimates the correct fault information using the geometric approach. Then, and based on that, a new reconfigurable control law is designed based on the multiple time scale sliding mode technique for on-line compensating the effect of such faults. This approach takes advantages of the fact that there are significant difference between the time scales of aircraft states that have a slow dynamics and those that have a fast dynamics. The closed-loop stability of the overall system is proved using Lyapunov technique. A case study of the non-linear model of the F16 fighter, subject to the rudder total loss of control confirms the effectiveness of the proposed approach.

Keywords: Fault detection and diagnosis, Sliding Mode Control, lyapunov stability, fault tolerant flight control, geometric approach for fault reconstruction, actuator faults, multiple time scale approximation

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2 Nonlinear Control of Mobile Inverted Pendulum: Theory and Experiment

Authors: V. Sankaranarayanan, V. Amrita Sundari, Sunit P. Gopal


This paper presents the design and implementation of a nonlinear controller for the point to point control of a mobile inverted pendulum (MIP). The controller is designed based on the kinematic model of the MIP to stabilize all the four coordinates. The stability of the closed-loop system is proved using Lyapunov stability theory. The proposed controller is validated through numerical simulations and also implemented in a laboratory prototype. The results are presented to evaluate the performance of the proposed closed loop system.

Keywords: Nonlinear Systems, lyapunov stability, mobile inverted pendulum, switched control

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1 Balancing a Rotary Inverted Pendulum System Using Robust Generalized Dynamic Inverse: Design and Experiment

Authors: Ibrahim M. Mehedi, Uzair Ansari, Ubaid M. Al-Saggaf, Abdulrahman H. Bajodah


This paper presents a methodology for balancing a rotary inverted pendulum system using Robust Generalized Dynamic Inversion (RGDI) under influence of parametric variations and external disturbances. In GDI control, dynamic constraints are formulated in the form of asymptotically stable differential equation which encapsulates the control objectives. The constraint differential equations are based on the deviation function of the angular position and its rates from their reference values. The constraint dynamics are inverted using Moore-Penrose Generalized Inverse (MPGI) to realize the control expression. The GDI singularity problem is addressed by augmenting a dynamic scale factor in the interpretation of MPGI which guarantee asymptotically stable position tracking. An additional term based on Sliding Mode Control is appended within GDI control to make it robust against parametric variations, disturbances and tracking performance deterioration due to generalized inversion scaling. The stability of the closed loop system is ensured by using positive definite Lyapunov energy function that guarantees semi-global practically stable position tracking. Numerical simulations are conducted on the dynamic model of rotary inverted pendulum system to analyze the efficiency of proposed RGDI control law. The comparative study is also presented, in which the performance of RGDI control is compared with Linear Quadratic Regulator (LQR) and is verified through experiments. Numerical simulations and real-time experiments demonstrate better tracking performance abilities and robustness features of RGDI control in the presence of parametric uncertainties and disturbances.

Keywords: Sliding Mode Control, lyapunov stability, generalized dynamic inversion, rotary inverted pendulum system

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