Showing papers on "Terminal sliding mode published in 2008"

Real-time implementation of grey fuzzy terminal sliding mode control for PWM DC-AC converters

Abstract: Classical terminal sliding mode control (TSMC) has finite system state convergence time and is insensitive to disturbances and uncertainties within expected limits. However, TSMC may chatter when uncertainty values are overestimated or may exhibit a steady-state error when uncertainty values are underestimated. An improved TSMC is proposed by the use of a mathematically simple and computationally fast grey prediction (GP) methodology, which is then fine-tuned by the use of fuzzy control methodology for PWM DC–AC converters. First, GP methodology is employed to deal with classical TSMC chattering and steady-state error problems. Fuzzy control is then used to tune the GP forecasting value for improved rise time and overshoot characteristics. The system is evaluated by simulation and also by real experiment. Both evaluation methods confirm that the proposed controller achieves low total harmonic distortion under non-linear loading conditions and fast dynamic response under transient loading conditions. Because the proposed grey-fuzzy TSMC methodology is simpler to implement than prior methods and offers more efficient computation, it will be of interest to designers of related control systems.

A new approach to terminal sliding mode control design

Abstract: In this paper, terminal sliding mode control design is considered. A control method, different from many existing terminal sliding model control design methods, is proposed based on a new switching law and continuous finite-time control ideas. Then terminal sliding mode control laws are constructed for some classes of nonlinear systems.

Second‐order terminal sliding mode control of input‐delay systems

Abstract: This paper proposes a second-order terminal sliding mode control for a class of uncertain input-delay systems. The input-delay systems are firstly converted into the input-delay free systems and further converted into the regular forms. A linear sliding mode manifold is predesigned to represent the ideal dynamics of the system. Another terminal sliding mode manifold surface is presented to drive the linear sliding mode to reach zeros in finite time. In order to eliminate the chattering phenomena, a second-order sliding mode method is utilized to filter the high frequency switching control signal. The uncertainties of the systems are analysed in detail to show the effect to the systems. The simulation results validate the method presented in the paper.

Terminal sliding mode control for coordinated motion of a space rigid manipulator with external disturbance

Abstract: The control problem of coordinated motion of a free-floating space rigid manipulator with external disturbance is discussed. By combining linear momentum conversion and the Lagrangian approach, the full-control dynamic equation and the Jacobian relation of a free-floating space rigid manipulator are established and then inverted to the state equation for control design. Based on the terminal sliding mode control (SMC) technique, a mathematical expression of the terminal sliding surface is proposed. The terminal SMC scheme is then developed for coordinated motion between the base’s attitude and the end-effector of the free-floating space manipulator with external disturbance. This proposed control scheme not only guarantees the existence of the sliding phase of the closed-loop system, but also ensures that the output tracking error converges to zero in finite time. In addition, because the initial system state is always at the terminal sliding surface, the control scheme can eliminate reaching phase of the SMC and guarantee global robustness and stability of the closed-loop system. A planar free-floating space rigid manipulator is simulated to verify the feasibility of the proposed control scheme.

Fuzzy terminal sliding mode control of two-link flexible manipulators

Abstract: This paper proposes a fuzzy terminal sliding mode control method for two-link flexible manipulators. Based on the singular perturbation method and two time-scale decomposition, the flexible manipulator system is firstly decomposed into two subsystems by modeling the joint angles and the corrected flexible modes as the slow and fast variables, respectively. A nonsingular terminal sliding mode manifold is proposed for the slow subsystem to realize fast convergence and better tracking precision. Meanwhile, a hybrid controller for the slow subsystem is proposed to ensure strong robustness, as well as to weaken chattering phenomenon using fuzzy logic. The fast subsystem is stabilized using a LQR control strategy. A reduced-order observer is proposed to estimate the corrected flexible mode variables that can not be measured directly. The simulation results are presented to validate the designed method.

Finite-time consensus algorithm of multi-agent networks

Abstract: This paper is concerned with leader-follower finite-time consensus control of multi-agent networks with input disturbances. Terminal sliding mode control scheme is used to design the distributed control law. A new terminal sliding mode surface is proposed to guarantee finite-time consensus under fixed topology, with the common assumption that the position and the velocity of the active leader is known to its neighbors only. By using the finite-time Lyapunov stability theorem, it is shown that if the directed graph of the network has a directed spanning tree, then the terminal sliding mode control law can guarantee finite-time consensus even under the assumption that the time-varying control input of the active leader is unknown to any follower.

Hybrid terminal sliding mode observer design method for permanent magnet synchronous motor control system

Abstract: This paper proposes a hybrid terminal sliding mode observer based on the nonsingular terminal sliding mode and the high-order sliding mode for the rotor position and speed estimation in the permanent magnet synchronous motor control system. A nonsingular terminal sliding mode manifold is utilized to realize both fast convergence and better tracking precision. Meanwhile, a high-order sliding mode control law is designed to guarantee the stability of the observer and eliminate the chattering. Therefore, the smooth back electromotive force (EMF) signals can be obtained without a low pass filter. According to the back EMF equations, the rotor position and speed can be calculated. Simulation results show that, compared to the conventional sliding mode observer, the hybrid terminal sliding mode observer avoids the phase lag in the back EMF signals, and improves the estimation precision of the rotor position and speed.

Non-singular terminal sliding mode backstepping control for the uncertain chaotic systems

Abstract: The paper proposes a non-singular terminal sliding mode control for a class of uncertain chaotic systems based on backstepping method. Through defining the error variables between the states of chaotic system and virtual feedback variables, a special non-singular terminal sliding mode and the control strategy are proposed. Then verified that the proposed control method can guarantee the error variables reach the non-singular terminal sliding mode manifold in finite time. Followed address the output of the chaotic system can track the arbitrary desired trajectory by using backstepping method. The simulations verified the effectiveness of the proposed method in the paper.

On singularity free recursive fast terminal sliding mode control

Abstract: A novel singularity free fast recursive terminal sliding mode structure is proposed in this paper, which results in fast and finite time convergence. Dynamical properties of the structure are given and a fast terminal sliding mode control scheme is proposed for a class of nonlinear systems.

Control of chaos in nonlinear circuits and systems

Abstract: Nonlinear circuits and systems, such as electronic circuits (Chapter 5), power converters (Chapter 6), human brains (Chapter 7), phase lock loops (Chapter 8), sigma delta modulators (Chapter 9), etc, are found almost everywhere. Understanding nonlinear behaviours as well as control of these circuits and systems are important for real practical engineering applications. Control theories for linear circuits and systems are well developed and almost complete. However, different nonlinear circuits and systems could exhibit very different behaviours. Hence, it is difficult to unify a general control theory for general nonlinear circuits and systems. Up to now, control theories for nonlinear circuits and systems are still very limited. The objective of this book is to review the state of the art chaos control methods for some common nonlinear circuits and systems, such as those listed in the above, and stimulate further research and development in chaos control for nonlinear circuits and systems. This book consists of three parts. The first part of the book consists of reviews on general chaos control methods. In particular, a time-delayed approach written by H. Huang and G. Feng is reviewed in Chapter 1. A master slave synchronization problem for chaotic Lur’e systems is considered. A delay independent and delay dependent synchronization criteria are derived based on the H performance. The design of the time delayed feedback controller can be accomplished by means of the feasibility of linear matrix inequalities. In Chapter 2, a fuzzy model based approach written by H.K. Lam and F.H.F. Leung is reviewed. The synchronization of chaotic systems subject to parameter uncertainties is considered. A chaotic system is first represented by the fuzzy model. A switching controller is then employed to synchronize the systems. The stability conditions in terms of linear matrix inequalities are derived based on the Lyapunov stability theory. The tracking performance and parameter design of the controller are formulated as a generalized eigenvalue minimization problem which is solved numerically via some convex programming techniques. In Chapter 3, a sliding mode control approach written by Y. Feng and X. Yu is reviewed. Three kinds of sliding mode control methods, traditional sliding mode control, terminal sliding mode control and non-singular terminal sliding mode control, are employed for the control of a chaotic system to realize two different control objectives, namely to force the system states to converge to zero or to track desired trajectories. Observer based chaos synchronizations for chaotic systems with single nonlinearity and multi-nonlinearities are also presented. In Chapter 4, an optimal control approach written by C.Z. Wu, C.M. Liu, K.L. Teo and Q.X. Shao is reviewed. Systems with nonparametric regression with jump points are considered. The rough locations of all the possible jump points are identified using existing kernel methods. A smooth spline function is used to approximate each segment of the regression function. A time scaling transformation is derived so as to map the undecided jump points to fixed points. The approximation problem is formulated as an optimization problem and solved via existing optimization tools. The second part of the book consists of reviews on general chaos controls for continuous-time systems. In particular, chaos controls for Chua’s circuits written by L.A.B. Torres, L.A. Aguirre, R.M. Palhares and E.M.A.M. Mendes are discussed in Chapter 5. An inductorless Chua’s circuit realization is presented, as well as some practical issues, such as data analysis, mathematical modelling and dynamical characterization, are discussed. The tradeoff among the control objective, the control energy and the model complexity is derived. In Chapter 6, chaos controls for pulse width modulation current mode single phase H-bridge inverters written by B. Robert, M. Feki and H.H.C. Iu are discussed. A time delayed feedback controller is used in conjunction with the proportional controller in its simple form as well as in its extended form to stabilize the desired periodic orbit for larger values of the proportional controller gain. This method is very robust and easy to implement. In Chapter 7, chaos controls for epileptiform bursting in the brain written by M.W. Slutzky, P. Cvitanovic and D.J. Mogul are discussed. Chaos analysis and chaos control algorithms for manipulating the seizure like behaviour in a brain slice model are discussed. The techniques provide a nonlinear control pathway for terminating or potentially preventing epileptic seizures in the whole brain. The third part of the book consists of reviews on general chaos controls for discrete-time systems. In particular, chaos controls for phase lock loops written by A.M. Harb and B.A. Harb are discussed in Chapter 8. A nonlinear controller based on the theory of backstepping is designed so that the phase lock loops will not be out of lock. Also, the phase lock loops will not exhibit Hopf bifurcation and chaotic behaviours. In Chapter 9, chaos controls for sigma delta modulators written by B.W.K. Ling, C.Y.F. Ho and J.D. Reiss are discussed. A fuzzy impulsive control approach is employed for the control of the sigma delta modulators. The local stability criterion and the condition for the occurrence of limit cycle behaviours are derived. Based on the derived conditions, a fuzzy impulsive control law is formulated so that the occurrence of the limit cycle behaviours, the effect of the audio clicks and the distance between the state vectors and an invariant set are minimized supposing that the invariant set is nonempty. The state vectors can be bounded within any arbitrary nonempty region no matter what the input step size, the initial condition and the filter parameters are. The editors are much indebted to the editor of the World Scientific Series on Nonlinear Science, Prof. Leon Chua, and to Senior Editor Miss Lakshmi Narayan for their help and congenial processing of the edition.

A new terminal sliding mode tracking control for a class of nonminimum phase systems with uncertain dynamics

Abstract: In this paper, a new terminal sliding mode tracking control scheme is developed for a class of nonminimum phase systems with uncertainties. It is shown that, unlike conventional linear or terminal sliding mode controls, the Lyapunov stability theory in this paper is used to determine the upper and the lower bounds of the control signal and its derivative. A dynamic control signal can then be designed, subject to the bounded conditions, to drive the terminal sliding variable to converge to zero, and, on the terminal sliding mode surface, the tracking error is guaranteed to converge to zero in a finite time. A simulation example is presented in support of the proposed robust tracking control scheme.

Terminal sliding mode control for flexible manipulators with uncertain parameters

Abstract: A terminal sliding mode control method based on genetic algorithm is proposed for the end-tip control of two- link flexible manipulators with uncertain parameters The output of the manipulator system is redefined By input-output linearization, the system is decomposed into an input-output subsystem and an internal subsystem A terminal sliding mode control strategy is designed to make the input-output subsystem converge to zero in finite time The internal subsystem is converted into a zero dynamic subsystem A genetic algorithm is adopted to optimize the parameters of the zero dynamic subsystem to guarantee its asymptotical convergence to the neighborhood of the equilibrium point The error range of end-tip output is calculated by Lyapunov stability theorem Simulation results are presented to validate the design

Robust terminal sliding mode control for ASV re-entry mode

Abstract: A robust adaptive flight control based terminal sliding mode is proposed,which eliminates the reaching phase of common sliding mode control,and guarantees the tracking errors converge to zero in finite time.The effects caused by modeling errors,uncertainties and disturbances are cancelled by RBF neural network through adaptive tuning its weights and without any assumptions.Simulation shows the effectiveness of the presented method.

Sliding mode control for trajectory tracking on mobile manipulators

Abstract: This paper proposes a sliding mode control approach for a wheeled mobile manipulator. The wheeled mobile manipulator composed of a four-wheeled mobile platform and a three-degree of freedom onboard manipulator. The dynamic models are established and the sliding mode control methods are employed. The entire control system is decomposed into two subsystems, including the sliding mode control of the mobile platform and the non-singular terminal sliding mode control of the manipulator. The simulation results are shown at last and demonstrate the effectiveness of the presented algorithm.

A revised Terminal Sliding Mode controller design for servo implementation

Abstract: Terminal sliding mode (TSM) control is known for its high gain property nearby the vicinity of the equilibrium while retaining reasonably low gain elsewhere. This is desirable in digital implementation where the limited sampling frequency may incur chattering if the controller gain is overly high. In this work we integrate a linear switching surface with a terminal switching surface. The mixed switching surface can be designed according to the precision requirement. The analysis, simulations and experimental investigation show that the mixed SMC design outperforms the linear SMC as well as the pure TSMC.

Composite disturbance-observer-based control and terminal sliding mode control for complex models

Abstract: A novel type of control scheme combined the distance-observer-based control (DOBC) with terminal sliding mode control is proposed for a class of continuous complex models subject to disturbances. The disturbances are supposed to include two parts. One in the input channel is generated by an exogenous system with uncertainty, which can represent the harmonic signals with modeling perturbations. The other is supposed to have the bounded H2 norm. The disturbance observers based on regional pole placement and D-stability theory are presented, which can be designed separately from the controller design. By integrating DOBC with terminal sliding mode control laws, the disturbances can be rejected and the desired dynamic performances can be guaranteed for complex systems with known and unknown nonlinear dynamics, respectively. Simulations for a flight control system are given to demonstrate the effectiveness of the results and compare the proposed results with the previous schemes.

Terminal sliding mode control for vehicle longitudinal following in automated highway system

Abstract: In this paper, based on the nonlinear dynamical coupled model of string of vehicles, by the design method of terminal sliding mode control, the longitudinal following control of string of vehicles in automated highway system is studied, the control law for each vehicle in the platoon is designed Simulation results showed that the convergence rate of spacing errors of the vehicle platoon is fast

Adaptive fast terminal sliding mode control for a class of nonlinear systems with time-varying uncertainties via LMI approach

Abstract: This paper proposes an adaptive fast terminal sliding mode control for a class of multiple input nonlinear systems with time-varying mismatched uncertainties via LMI approach. First, a novel fast terminal sliding surface design method for a class of nonlinear systems is proposed based on Lyapunov method. The sufficient conditions are provided for the uncertain system on the sliding surface, such that the terminal sliding motion is finite stable. Second, the corresponding new adaptive reaching law is constructed based on the Lyapunov method, which can drive the state trajectory of the close-loop system onto the sliding surface within limited time. The chattering around the sliding surface can be allevated by the proposed approach. In addition, on-line adaptive laws of the control system are also derived based on the gradient descent method. Simulation results validate the effectiveness of the proposed control scheme for multiple input nonlinear systems with unknown uncertainties.

Terminal sliding mode control for lane keeping with parametric uncertainties

Abstract: The lane keeping control law with parametric uncertainties for automated highway systems was studied.With the assumption of the boundness of such uncertain parameters as the mass of vehicle,moment of inertia and tire cornering stiffness,etc,the dynamic equations for vehicle lateral position error and yaw angle error were established based on the look-ahead scheme and vehicle lateral dynamic model.The variable structure control law for lane keeping was designed by using the terminal sliding mode,and Lyapunov stability theory was used to analyze stability of the control systems.Simulation results show that the control method designed here has fast convergence rate for the lateral displacement error and yaw angle error.

Terminal sliding mode control of coordinated motion of free-floating space robot with dual-arms

Abstract: The control problem of coordinated motion of free-floating dual-arm space robot with external disturbance is discussed. Combined the linear momentum conversation and the Lagrangian approach, the full-controlled dynamic equations of free-floating space robot with dual-arms is established and then inverted to the state equation for control design. Based on the terminal sliding mode control (SMC) technique, a mathematical expression of the terminal sliding surface is proposed, and the terminal SMC scheme of coordinated motion between the basepsilas attitude and the armspsila joints of free-floating dual-arm space robot with external disturbance is developed. This proposed control scheme not only guarantees that the sliding phase of the closed-loop system exists, but also ensures that the output tracking error converges to zero in finite time. In addition, the control scheme eliminates the reaching phase of SMC and guarantees the global robustness and stability of the closed-loop system, because the initial state of system is always at the terminal sliding surface. A planar free-floating space robot with dual-arms is simulated to verify the feasibility of the proposed control scheme.

An adaptive terminal sliding mode control and its applications

Abstract: A novel adaptive Terminal sliding mode control based on fast fuzzy disturbance observer is designed for a high order MIMO(multiple-input multiple-out-put) nonlinear system.To solve the shortcoming of learning slowly of traditional fuzzy disturbance observer when the approximation errors are very small,a fast fuzzy disturbance observer is designed.It is strictly proved that the tracking errors and approximation errors converge to very small regions in finite time.Finally,simulation results of ASV(aerospace vehicle) re-entry demonstrate the effectiveness of presented control scheme.

High-order terminal sliding mode based mechanical resonance suppressing method in servo system

Abstract: This paper proposes a mechanical resonance suppressing method based on high-order sliding mode and non-singular terminal sliding mode for servo system. Non-singular terminal sliding mode manifolds are designed for load speed and stator currents of the permanent magnet synchronous motor to realize both fast convergence and better tracking precision. A state observer is utilized to estimate the shaft torsion angle and the load speed. And a high-order sliding mode control law is designed to eliminate the chattering and guarantee the stability of the system. Simulation results show that, compared with the acceleration feedback and the notch filter method, the proposed method in this paper can suppress mechanical resonance more effectively, and the motor speed converges fast without overshoot.

A novel fuzzy neural network approximator with exponential fast terminal sliding mode

Abstract: A new learning algorithm for fuzzy neural network (FNN) systems to approximate unknown nonlinear continuous functions is proposed. The concept of exponential fast terminal sliding mode is introduced into the learning algorithm to improve approximation ability. The Lyapunov stability analysis guarantees that the approximation is stable and converges to the unknown function with improved speed. The proposed FNN approximator is then applied in the control of an unstable nonlinear system. Simulation results demonstrate that the proposed method can obtain good approximation ability and tracing control of nonlinear dynamic system.

A Terminal Sliding Mode Tracking Control Algorithm for Mobile Robots

Abstract: This paper presents a new trajectory tracking control algorithm to uncertain mobile robot with nonholonomic constraints. This algorithm is based on the non-singular terminal sliding mode technique, which can eliminate the singularity problem caused by conventional terminal sliding mode control. The system state vector is designed using backstepping method, this method breaks down nonlinear systems into low dimensional systems and simplifies the controller design. By combining Lyapunov method, it is proved that under this control law, the pose errors converge to zero, the mobile robot can track the desired trajectory when the desired velocity satisfies some assumptions. Simulation results validate the theoretical analysis.

Space RVD Terminal Approach to Attitude Tracking by Terminal Sliding Mode Control

Abstract: For the attitude control problem of terminal approach phase of RVD,the feedback linear theory was adopted to linearize nonlinear attitude dynamics,and a phase-variable states space model was deducedThe terminal sliding mode control theory considering the disturbances was used on the basis of the deduced modelFurthermore,this paper introduces a controller which implements the attitude tracking and controls the states tracking errors convergent to zero in the finite timeFor the example given,the control results satisfy the terminal time constrain and the tracking errors were convergent to zero,and this demonstrates that the controller is robust

The optimal design of terminal sliding controller for flexible manipulators based on chaotic genetic algorithm

Abstract: To deal with the non-minimum-phase characteristic,a terminal sliding mode control strategy is proposed for a two-link flexible manipulator.The system output is redefined as a function of the joint angles and the variables of the flexible modes.Through input-output linearization,the system is decomposed into input-output subsystems and zero-dynamics subsystems.A terminal sliding mode control strategy is designed to make the outputs of the input-output subsystems converge in a finite time.By adjusting the parameters in the optimal controller,which is designed by chaotic genetic algorithm,the outputs of the zero-dynamics subsystems will be made asymptotically stable at the equilibrium point. Thus,the original two-link flexible manipulator control system is guaranteed to be asymptotically stable.The control design procedure is simple and easy to be implemented.Simulation results are presented to validate the design.

Adaptive Algorithm to Vehicle Following Control in Intelligent Transportation System

Abstract: In this paper, the Lyapunov second method is used to derive adaptive control laws that can be used to control the spacing between vehicles in a platoon. The decentralized adaptive algorithm to compensate for parametric variations is investigated and the terminal sliding mode longitudinal control laws for each vehicle in the platoon are designed. From the simulation of the vehicle platoon, convergence rate of spacing errors of the vehicle platoon is fast.