线性滞后广义系统的二阶滑模控制方法

讨论了时滞广义系统在不同条件下的变结构控制,根据终端滑模控制的特点,提出了一种由线性滑模与终端滑模构成的二阶终端滑模及相应控制策略.研究结果表明,该方法能够有效地清除系统的高频抖振,同时保证闭环系统的渐近稳定,实现滑模运动.举例说明了设计的合理性和有效性.     

A sliding mode control for linear fractional systems with input and state delays

In this paper, a sliding mode control design for fractional order systems with input and state time-delay is proposed. First, we consider a fractional order system without delay for which a sliding surface is proposed based on fractional integration of the state. Then, a stabilizing switching controller is derived. Second, a fractional system with state delay is considered. Third, a strategy including a fractional state predictor input delay compensation is developed. The existence of the sliding mode and the stability of the proposed control design are discussed. Numerical examples are given to illustrate the theoretical developments.     

基于组合智能控制的柔性臂微机控制系统研究

针对难以控制的柔性机械臂，设计了强鲁棒性、强自适应能力的模糊滑模控制策略；并针对控制对象与控制算法的复杂性，设计了基于DSP＋FPGA的控制系统，保证了系统的实时性和精确度。     

Adaptive backstepping sliding mode control for chaos synchronization of two coupled neurons in the external electrical stimulation

In this paper, a robust control system combining backstepping and sliding mode control techniques is used to realize the synchronization of two gap junction coupled chaotic FitzHugh-Nagumo (FHN) neurons in the external electrical stimulation. A backstepping sliding mode approach is applied firstly to compensate the uncertainty which occur in the control system. However, the bound of uncertainty is necessary in the design of the backstepping sliding mode controller. To relax the requirement for the bound of uncertainty, an adaptive backstepping sliding mode controller with a simple adaptive law to adapt the uncertainty in real time is designed. The adaptive backstepping sliding mode control system is robust for time-varying external disturbances. The simulation results demonstrate the effectiveness of the control scheme.     

Event-triggered sliding mode control for switched genetic regulatory networks with persistent dwell time

This paper focus on the event-triggered sliding mode controller design for discrete-time switched genetic regulatory networks (GRNs) with persistent dwell time (PDT) switching. Firstly, the observation error dynamics of switched GRNs with PDT is constructed in the light of event-triggered sliding mode control (SMC) scheme. Next, sufficient conditions are derived to ensure the exponential stability of the augmented plant. Moreover, an event-triggered SMC law is synthesized to impel the system trajectories onto the sliding surface in a finite time. Finally, a verification example is provided to illustrate the effectiveness and potential of the proposed method.     

Control uncertain Genesio–Tesi chaotic system: Adaptive sliding mode approach

An adaptive sliding mode control (ASMC) technique is introduced in this paper for a chaotic dynamical system (Genesio–Tesi system). Using the sliding mode control technique, a sliding surface is determined and the control law is established. An adaptive sliding mode control law is derived to make the states of the Genesio–Tesi system asymptotically track and regulate the desired state. The designed control scheme can control the uncertain chaotic behaviors to a desired state without oscillating very fast and guarantee the property of asymptotical stability. An illustrative simulation result is given to demonstrate the effectiveness of the proposed adaptive sliding mode control design.     

Fractional terminal sliding mode control design for a class of dynamical systems with uncertainty

A novel type of control strategy combining the fractional calculus with terminal sliding mode control called fractional terminal sliding mode control is introduced for a class of dynamical systems subject to uncertainties. A fractional-order switching manifold is proposed and the corresponding control law is formulated based on the Lyapunov stability theory to guarantee the sliding condition. The proposed fractional-order terminal sliding mode controller ensures the finite time stability of the closed-loop system. Finally, numerical simulation results are presented and compared to illustrate the effectiveness of the proposed method.     

Dynamics and chaos control in nonlinear electrostatic transducers

In this paper, we analyze the dynamics of a system consisting of two coupled nonlinearly Duffing oscillators, obtained from a nonlinear electrostatic device which is a prototype of emitters and receivers in communication engineering. Inverse or backward period doubling cascades and sudden transition to chaos are observed. A sliding mode controller is applied to control the electrostatic transducers system. The sliding surface used is one dimension higher than the traditional surface and guarantees its passage through the initial states of the controlled system. By means of the design of sliding mode dynamics characteristics, the controlled system performance is arbitrarily determined by assigning the switching gain of the sliding mode dynamics. Therefore, using the characteristic of this sliding mode we aim to design a controller that can meet the desired specification and use less control energy by comparing with the result in the current literature. The results show that the proposed controller can steer electrostatic transducers to the desired reference trajectory without chattering phenomenon and abrupt state change.     

Suppression of chaotic behavior in horizontal platform systems based on an adaptive sliding mode control scheme

This work presents an adaptive sliding mode control scheme to elucidate the robust chaos suppression control of non-autonomous chaotic systems. The proposed control scheme utilizes extended systems to ensure that continuous control input is obtained in order to avoid chattering phenomenon as frequently in conventional sliding mode control systems. A switching surface is adopted to ensure the relative ease in stabilizing the extended error dynamics in the sliding mode. An adaptive sliding mode controller (ASMC) is then derived to guarantee the occurrence of the sliding motion, even when the chaotic horizontal platform system (HPS) is undergoing parametric uncertainties. Based on Lyapunov stability theorem, control laws are derived. In addition to guaranteeing that uncertain horizontal platform chaotic systems can be stabilized to a steady state, the proposed control scheme ensures asymptotically tracking of any desired trajectory. Furthermore, the numerical simulations verify the accuracy of the proposed control scheme, which is applicable to another chaotic system based on the same design scheme.     

Robust observer design for uncertain Itô neutral stochastic time-delay systems via sliding mode control

This paper deals with the output feedback sliding mode control for uncertain Itô neutral stochastic time-delay systems. The system states are unmeasured, and the uncertainties are unmatched. A sliding mode control scheme is proposed based on the state estimates. By utilizing a novel switching function, the derivative of the switching function is ensured to have a finite variation. It is shown that the sliding mode in the estimation space can be attained in finite time. A sufficient condition for the asymptotic stability (in probability) of the overall closed-loop stochastic system is derived. Finally, a simulation example is given to illustrate the proposed method.     

不确定电液位置伺服系统的自适应终端滑模控制

为了解决非线性、不确定电液伺服系统的位置跟踪控制问题,提出了一种基于反步法的自适应终端滑模控制方法.该方法将自适应控制和终端滑模方法结合在一起,一方面,提出的自适应控制律可以对电液伺服系统中的不确定性参数进行有效在线估计和补偿;另一方面,通过引入误差吸引子到滑模趋近律中得到变系数趋近律,设计的终端滑模控制律不仅能够消除普通终端滑模控制律中的非奇异项,还大大降低了滑模面的抖震.最终,根据Lyapunov稳定性理论,位置跟踪误差的有限时间稳定性得以严格证明.将该方法与积分反步滑模控制和线性滑模控制方法进行了对比研究,仿真结果验证了该方法在电液伺服系统位置跟踪控制方面良好的鲁棒性和跟踪精度.     

Sliding Mode Control of an Underactuated Two-Link Manipulator

We consider a horizontally mounted two-link manipulator of which only the first joint is actuated and the friction in the second joint is neglected. As a consequence, predefined equilibrium points are difficult to reach and point-to-point control is a challenging task. Starting from a partially feedback linearized model, a transformation to Byrnes-Isidori normal form is presented. Based on this decomposition, the projection into a two-dimensional subspace reveals certain similarities to a double integrator. Modifying an existing sliding mode approach for that system, a control law which steers the manipulator to an equilibrium point can be deduced. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Control of non‐integer‐order dynamical systems using sliding mode scheme

This article deals with the problem of control of canonical non‐integer‐order dynamical systems. We design a simple dynamical fractional‐order integral sliding manifold with desired stability and convergence properties. The main feature of the proposed dynamical sliding surface is transferring the sign function in the control input to the first derivative of the control signal. Therefore, the resulted control input is smooth and without any discontinuity. So, the harmful chattering, which is an inherent characteristic of the traditional sliding modes, is avoided. We use the fractional Lyapunov stability theory to derive a sliding control law to force the system trajectories to reach the sliding manifold and remain on it forever. A nonsmooth positive definite function is applied to prove the existence of the sliding motion in a given finite time. Some computer simulations are presented to show the efficient performance of the proposed chattering‐free fractional‐order sliding mode controller. © 2015 Wiley Periodicals, Inc. Complexity 21: 224–233, 2016     

Optimal Sliding Mode Robust Control for Fractional-Order Systems with Application to Permanent Magnet Synchronous Motor Tracking Control

This paper presents an optimal sliding mode output tracking control scheme for a class of fractional-order uncertain systems. Firstly, an augmented fractional-order system, composed of the original system and the external system, is constructed to transform the optimal output tracking issue into the design problem of linear quadratic regulator. The optimal tracking control problem for the nominal augmented fractional-order system is then studied. Secondly, the fractional-integral sliding mode controller is introduced to robustify the augmented fractional-order system, which satisfy the matching conditions. As a result, the original system output can track the external system output trajectory effectively even the uncertainties exist. Finally, the developed design techniques are applied to the tracking control of fractional-order permanent magnet synchronous motor. The simulation results demonstrate the validity of this approach.     

Global mode method for dynamic modeling of a flexible-link flexible-joint manipulator with tip mass

In this paper, the global mode method (GMM) is proposed to obtain a reduced-order analytical dynamic model for a signal flexible-link flexible-joint (SFF) manipulator. Firstly, the nonlinear partial differential equations (PDE) that govern the motion of the flexible link and flexible joint, respectively, are derived by applying the Hamilton principle. By combining the linearized governing equations of motion for a flexible link and the equation of motion for the flexible joint, the characteristic equation is obtained for the whole system. The natural frequencies and global mode shapes of the linearized model of the SFF manipulator are determined, and orthogonality relations of the global mode shapes are established. Then, the global mode shapes and their orthogonality relations are used to truncate the nonlinear PDEs of the SFF manipulator to a nonlinear ordinary differential equation with a few degrees-of-freedom (DOF). For comparison, two other dynamic models of the SFF are derived by employing the assumed mode method (AMM) and finite element method (FEM). To verify the method proposed, the results from the GMM are compared with those obtained from the FEM. The effects of the link length and payload mass on the convergence of AMM model for the first two frequencies are investigated. Based on the dynamic models, obtained by GMM and AMM, dynamical responses for the system with different numbers of modes are worked out numerically, which are compared with those obtained from FEM. These comparisons show a good agreement between the results of the GMM and that of the FEM model, which indeed proved the accuracy and applicability of the GMM model.     

Unidirectional synchronization for Hindmarsh–Rose neurons via robust adaptive sliding mode control

This paper presents an adaptive neural network (NN) based sliding mode control for unidirectional synchronization of Hindmarsh–Rose (HR) neurons in a master–slave configuration. We first give the dynamics of single HR neuron which may exhibit spike-burst chaotic behaviors. Then we formulate the problem of unidirectional synchronization control of two HR neurons and propose a NN based sliding mode controller. The controller consists of two simple radial basis function (RBF) NNs which are used to approximate the desired sliding mode controller and the uncertain nonlinear part of the error dynamical system, respectively. The control scheme is robust to the uncertainties such as approximate errors, ionic channel noise and external disturbances. The simulation results demonstrate the validity of the proposed control method.     

Suboptimal Integral Sliding Mode Controller Design for a Class of Affine Systems

This paper proposes an nth-order suboptimal integral sliding mode controller for a class of nonlinear affine systems. First, a general form of integral sliding mode is given. An extended Theta-D method is developed for the optimal control problems characterized by a quadratic cost function with a cross term. Then the extended Theta-D method is employed to determine a suboptimal integral sliding mode. Rigorous proof shows that the controller guarantees semi-global asymptotical stability of affine systems. To verify the accuracy of the extended Theta-D method, a numerical example is provided. To verify the effectiveness of the proposed suboptimal integral sliding mode controller, a numerical example and an application example of an overhead crane system are provided.     

Chaos suppression of a class of unknown uncertain chaotic systems via single input

This paper deals with the design of a robust adaptive control scheme for chaos suppression of a class of chaotic systems. We assume that model uncertainties and external disturbances disturb the system’s dynamics. The bounds of both model uncertainties and external disturbances are assumed to be unknown in advance. Moreover, it is assumed that the nonlinear terms of the chaotic system dynamics are unknown bounded. Based on the global boundedness feature of the chaotic systems’ trajectories, a simple one input adaptive sliding mode control approach is proposed to suppress the chaos of the uncertain chaotic system. Furthermore, using a dynamical sliding manifold the discontinuous sign function in the control input is diverted to the first derivative of the control input to eliminate the chattering. Finally, the robustness of the proposed approach is mathematically proved and numerically illustrated.     

Optimal sliding mode control for nonlinear systems with time-delay

This paper is concerned with the sliding mode control (SMC) for a class of nonlinear systems with time-delay. A novel optimal sliding mode is proposed by using the successive approximation approach (SAA). The stability of the nonlinear sliding mode is analyzed. The switching manifold ensures that the state trajectories of the closed-loop system converge to zero in an optimal fashion on the ideal sliding surface. Furthermore, the convergence velocity of every state trajectory on the ideal sliding surface can be adjusted through choosing the parameters of the quadratic performance index. A numerical simulation is given to show the effectiveness of the proposed design approach.     

EID-based sliding mode investment policy design for fuzzy stochastic jump financial systems

This paper proposes a sliding mode investment policy design for nonlinear stochastic financial systems which can be represented by the well-known Takagi–Sugeno fuzzy model. When modeling the financial systems, it is more important to consider the unpredictable investment changes and worldwide unpredictable events which can be regarded as external disturbances. The equivalent-input-disturbance (EID) approach combined with sliding mode investment policy design is implemented to reject the unpredictable investment changes for having better investment. Moreover, the Luenberger state observer is constructed for the addressed financial system to estimate the unpredictable investment changes and worldwide unpredictable events. More precisely, a sliding mode investment policy design is developed by solving the obtained linear matrix inequality (LMI)-based constrained algorithm. Finally, the obtained results of the addressed fuzzy stochastic financial system are verified through numerical simulation to show efficiency of the proposed sliding mode investment policy design.