A neuro-fuzzy-sliding mode controller using nonlinear sliding surface applied to the coupled tanks system

The aim of this paper is to develop a neuro-fuzzy-sliding mode controller （NFSMC） with a nonlinear sliding surface for a coupled tank system. The main purpose is to eliminate the chattering phenomenon and to overcome the problem of the equivalent control computation. A first-order nonlinear sliding surface is presented, on which the developed sliding mode controller （SMC） is based. Mathematical proof for the stability and convergence of the system is presented. In order to reduce the chattering in SMC, a fixed boundary layer around the switch surface is used. Within the boundary layer, where the fuzzy logic control is applied, the chattering phenomenon, which is inherent in a sliding mode control, is avoided by smoothing the switch signal. Outside the boundary, the sliding mode control is applied to drive the system states into the boundary layer. Moreover, to compute the equivalent controller, a feed-forward neural network （NN） is used. The weights of the net are updated such that the corrective control term of the NFSMC goes to zero. Then, this NN also alleviates the chattering phenomenon because a big gain in the corrective control term produces a more serious chattering than a small gain. Experimental studies carried out on a coupled tank system indicate that the proposed approach is good for control applications.     

Chattering reduction of sliding mode control by low‐pass filtering the control signal

The conventional approach to reducing control signal chattering in sliding mode control is to use the boundary layer design. However, when there is high‐level measurement noise, the boundary layer design becomes ineffective in chattering reduction. This paper, therefore, proposes a new design for chattering reduction by low‐pass filtering the control signal. The new design is non‐trivial since it requires estimation of the sliding variable via a disturbance estimator. The new sliding mode control has the same performance as the boundary layer design in noise‐free environments, and outperforms the boundary layer design in noisy environments. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Sliding Mode Control with Adaptive Fuzzy Immune Feedback Reaching Law

In this paper, a novel adaptive fuzzy immune feedback reaching law (AFIFRL) based sliding mode control (SMC) strategy is proposed for uncertain nonlinear systems with time-varying disturbances. First, a nonlinear immune feedback reaching law (IFRL) inspired by biological immune feedback regulation mechanism is designed to alleviate chattering effect without losing the robustness against disturbances. Second, an improved IFRL is developed in a thin boundary layer to enhance tracking performance. Then, the applied fuzzy controller adjusts the boundary layer online to further improve control performance despite large system uncertainties and disturbances. Furthermore, an adaptive law is employed to estimate the unknown bound of uncertainties, which can effectively attenuate chattering and minimize control effort. The stability analysis is derived by Lyapunov stability theorem. Finally, numerical simulations are conducted to evidence the effectiveness and superiority of the proposed AFIFRL based SMC scheme.     

Trajectory Tracking with Parallel Robots Using Low Chattering,Fuzzy Sliding Mode Controller

This paper proposes a trajectory tracking scheme which belongs to the sliding mode control (SMC) for the 4-degree-of-freedom (DOF) parallel robots. Two fuzzy logic systems (FLS) are first put forward to replace the constant switching control gain and the width of the boundary layer. The fuzzy adaptive supervisory controller (FASC) is combined with the fuzzy sliding mode control (FSMC) to further reduce the chattering. The design is simple and less fuzzy rules are required. The simulation results demonstrate that the chattering of the SMC is reduced greatly and the parallel robot realizes the trajectory tracking with very good robustness to the parameter uncertainties and external disturbances.     

Neuro-sliding mode control with its applications to seesaw systems

This paper proposes an approach of cooperative control that is based on the concept of combining neural networks and the methodology of sliding mode control (SMC). The main purpose is to eliminate the chattering phenomenon. Next, the system performance can be improved by using the method of SMC. In the present approach, two parallel Neural Networks are utilized to realize a neuro-sliding mode control (NSMC), where the equivalent control and the corrective control are the outputs of neural network 1 and neural network 2, respectively. Based on expressions of the SMC, the weight adaptations of neural network can be determined. Furthermore, the gradient descent method is used to minimize the control force so that the chattering phenomenon can be eliminated. Finally, experimental results are given to show the effectiveness and feasibility of the approach.     

二级直线倒立摆系统的实物控制

针对二级直线倒立摆系统,采用拉格朗日方程法建立其理论模型,分别使用线性二次最优控制（Linear Quadratic Regulator,LQR）及基于趋近律的滑模控制（Sliding Mode Control,SMC）算法来实现干扰存在情况下倒立摆的平衡控制。对于LQR算法,研究了矩阵[Q]和矩阵[R]与反馈控制矩阵[K]的定性关系,并经过反复多次实验,不断试凑,得到一组良好的控制参数,实现了倒立摆的稳定控制。SMC算法采用基于指数趋近律的控制方法进行了滑模变结构控制器的设计,并利用边界层法来进一步削弱抖振。最后通过仿真及实验,实现了倒立摆的实物平衡控制。     

GBF-CMAC和滑模控制的柔性结构系统控制

针对一类不确定系统的跟踪控制,设计了一种将GBF-CMAC（cerebellar model articulation controller with Gauss basis function）与滑模控制相结合的控制系统。利用符号距离和分层结构减少了神经网络所需存储器的数量,并提出了一种神经网络参数的自适应学习律。将设计的控制器用于含有不确定性和欠驱动结构的高阶柔性直线结构系统的跟踪控制,并与一般滑模控制和积分滑模控制进行了比较。实验结果表明,所设计的控制器不仅具有较好的鲁棒性,而且改善了滑模控制存在的抖振问题。同时通过调整神经网络的参数对抖振进行控制,实现了抖振和跟踪性能之间的最优选择。     

Discussions on Smooth Modifications of Integral Sliding Mode Control

Sliding mode control (SMC) contains two phases, namely reaching and sliding phases, where the invariance of SMC is not guaranteed during the reaching phase. Integral SMC (ISMC) eliminates the reaching phase such that the invariance is guaranteed from the initial time instant. Several smoothing techniques have been applied to reduce chattering in the ISMC, including boundary layer, high-order SMC, low-pass filtering, etc. In this study, we discuss pros and cons of these techniques and suggest a simple and effective solution to attenuate chattering in the ISMC. In the suggested solution, the discontinuous part of the ISMC law is smoothed by a low-pass filter based on the equivalent control method. The resultant ISMC can not only avoid the trade-off among chattering, tracking accuracy, and robustness, but also act as a disturbance observer to exactly estimate and reject uncertainties. Numerical results have been provided to verify the arguments of this study.     

基于NDOB的匹配/非匹配不确定性系统滑模控制

针对一类n阶匹配与非匹配不确定性和扰动共存的系统,提出了一种新颖的基于非线性干扰观测器的滑模控制方法。将非匹配扰动的估计值融入到滑模面,设计了集成扰动观测的滑模控制。与传统的滑模控制方法相比,该方法在匹配与非匹配不确定性和扰动出现时具有较好的抑制能力,并能有效地抑制切换增益所引起的抖振现象。利用李雅普诺夫理论和输入-输出稳定性概念严格证明了闭环系统的稳定性。最后通过两个仿真实例验证了所提控制方法的有效性。     

Adaptive Chattering Free Neural Network Based Sliding Mode Control for Trajectory Tracking of Redundant Parallel Manipulators

In this paper, an adaptive chattering free neural network‐based sliding mode control (ACFN‐SMC) method is proposed for tracking trajectories of redundant parallel manipulators. ACFN‐SMC combines adaptive chattering free radial basis function neural networks (RBFN), sliding mode control with online updating the robust term parameters, and a nonlinear compensation item for reducing tracking errors. The stability of the closed‐loop system with modeling uncertainties, frictional uncertainties, and external disturbances is ensured by using the Lyapunov method. The proposed controller has a simple structure and little computation time while securing dynamic performance with expected quality in tracking trajectories of redundant parallel manipulators. In addition, the ACFN‐SMC strategy does not need to know the upper bound of any uncertainties. From the simulation results, it is evident that the proposed control strategy not only has significantly higher robustness capability for uncertainties but also can achieve better chattering elimination when compared with those using existing intelligent control schemes.     

Frequency domain analysis of noise‐induced control chattering in sliding mode controls

The switching sliding mode control is robust with respect to disturbances, but its control signal has the so‐called chattering phenomenon that can damage the actuator and the system. To remove the chattering phenomenon, it has been proposed that one can use a continuous boundary layer design to replace the switching control. This paper shows, via the frequency domain analysis, that even when a boundary layer design is used, stochastic measurement noise can still induce the chattering phenomenon in control signals. Such noise‐induced chattering is almost unavoidable in noisy environments when the control accuracy requirement is high. Copyright © 2010 John Wiley & Sons, Ltd.     

Chattering in sliding mode control systems with boundary layer approximation of discontinuous control

It has been a widely accepted notion that approximation of discontinuous control by certain continuous function in a boundary layer results in chattering elimination in sliding mode control systems. It is shown through three different types of analysis that in the presence of parasitic dynamics, this approach to chattering elimination would work only if the slope of the continuous nonlinear function within the boundary layer is low enough, which may result in the deterioration of performance of the system. A few examples are provided. An approach to robust stability of linear systems from the consideration of the saturating control is proposed.     

基于动态边界层的水下航行器滑模轨迹跟踪

滑模控制方法的不变性和鲁棒性特性能够克服水下航行器轨迹跟踪过程中的参数不确定性以及摄动的影响,但在实际应用中存在执行器受限问题常常会导致滑动模态的丧失.为了抑制执行器的速率与幅值限制对滑模控制器的影响,采用二阶滑模控制的水下航行器轨迹跟踪控制,并用了边界层厚度动态控制的方法解决存在速率和幅值限制的有限带宽的执行器的滑模控制器的设计,通过增加边界层厚度,控制器的轨迹跟踪能力有所减弱.但是系统状态仍然保持在边界层内,保证了系统的稳定性.通过仿真证明了水下航行器的姿态角跟踪控制仿真证明了上述结论的正确性.     

Robust sliding mode control using adaptive switching gain for induction motors

A robust sliding mode approach combined with a field oriented control （FOC） for induction motor （IM） speed control is presented. The proposed sliding mode control （SMC） design uses an adaptive switching gain and an integrator. This approach guarantees the same robustness and dynamic performance of traditional SMC algorithms. And at the same time, it attenuates the chattering phenomenon, which is the main drawback in actual implementation of this technique. This approach is insensitive to uncertainties and permits to decrease the requirement for the bound of these uncertainties. The stability and robustness of the closed- loop system are proven analytically using the Lyapunov synthesis approach. The proposed method attenuates the effect of both uncertainties and external disturbances. Experimental results are presented to validate the effectiveness and the good performance of the developed method.     

Improving asynchronous motor speed and flux loop control by using hybrid fuzzy-SMC controllers

This paper presents a new method combining sliding mode control (SMC) and fuzzy logic control (FLC) to enhance the robustness and performance for a class of non-linear control systems. This fuzzy sliding mode control (FSMC) is developed for application in the area for controlling the speed and flux loops of asynchronous motors. The proposed control law can solve those problems associated with the conventional control by sliding mode control, such as high current, flux and torque chattering, variable switching frequency and variation of parameters, in which a robust fuzzy logic controller replaces the discontinuous part of the classical sliding mode control law. Simulation results of the proposed FSMC technique on the speed and flux rotor controllers present good dynamic and steady-state performances compared to the classical SMC in terms of reduction of the torque chattering, quick dynamic torque response and robustness to disturbance and variation of parameters.     

Adaptive sliding controller synthesis for non-linear systems

Classical ‘sliding mode control’, as investigated mostly in Soviet literature, features excellent robustness properties in relation to parametric uncertainty, but presents several important drawbacks that severely limit its practical applicability. These drawbacks, including large control authority and control chattering, were remedied by Slotine and Sastry (1983) and Slotine (1984) by replacing control switching at a fixed sliding surface by a smooth control interpolation in a boundary layer neighbouring a time-varying sliding surface. This avoids the excitation of high-frequency unmodelled dynamics, and leads to an explicit trade-off between model uncertainty and controller tracking performance. The present paper examines how to further improve performance by effectively coupling on-line parameter estimation to sliding controller design. The boundary layer concept leads to a compact measure of the quality of parameter estimation, and provides a consistent rule on when to stop adaptation. The approach is demonstrated by simulations.     

An O(T2) boundary layer in sliding mode for sampled-datasystems

The use of a discontinuous control law (typically, sign functions) in a sampled-data system will bring about chattering phenomenon in the vicinity of the sliding manifold, leading to a boundary layer with thickness O(T), where T is the sampling period. However, by proper consideration of the sampling phenomenon in the discrete-time sliding mode control design, the thickness of the boundary layer can be reduced to O(T²). In contrast to discontinuous control for continuous-time VSS, the discrete-time sliding mode control need not be of switching type     

Sliding mode-like fuzzy logic control with self-tuning the deadzone parameters

In this paper, a fuzzy logic controller (FLC) is designed based on the similarity between the FLC and the sliding mode control (SMC). The proposed scheme provides the sliding mode-like FLC with fast self-tuning the dead-zone parameters (boundary layer thickness) under parameter variations of the controlled system. To show the validity and the effectiveness of the proposed control method, simulations are performed for the position control of a rotary inverted pendulum     

A survey on sliding mode control strategies for induction motors

A state of the art review of control and estimation methods for induction motor (IM) based on conventional approaches, sliding mode control (SMC) and sensorless SMC is presented. The objective of this survey paper is to summarize the different control approaches for IMs including field oriented control (FOC), direct torque control (DTC), speed observer, observer based flux estimation, sliding mode (SM) flux and speed observer, current regulation by SMC, sensorless SMC, etc. The applications of SMC to IMs has been widespread in recent years. The increasing interest in SMC is because of its interesting features such as invariance, robustness, order reduction and control chattering. Particularly robustness of SM approach with respect to parameter variations and external disturbance is vital for the control system. The review covers the sensorless SMC schemes by integrating controller and observer design to guarantee convergence of the estimates to the real states. It also covers the chattering problems, encountered often in SMC area dealt by using an asymptotic observer.