Fuzzy boundary layer tuning for sliding mode systems as applied to the control of a direct drive robot

Chattering in the control signal is a significant problem in sliding mode control (SMC). The boundary layer approach is one of the many modifications proposed in the literature to avoid the chattering. In this approach, instead of the discontinuous SMC, a continuous feedback control law is employed in a boundary layer around the sliding surface. The thickness of the boundary layer is an important design parameter. This paper proposes a fuzzy online tuning method to adjust the boundary layer thickness for the best system performance without chattering. The method features the measurement of the chattering in the control signal. The paper validates the performance of the algorithm by experiments on a direct drive robot with a range of different payloads.     

A class of second-order sliding mode controller for servo systems

Sliding mode control (SMC) has been widely investigated in recent years.In this paper,a class of secondorder SMC is proposed and used to achieve good tracking performance in servo systems.SMC has good ...     

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。     

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.     

基于粒子群优化的分数阶PID滑模控制参数整定

为了提高系统的控制性能,解决单一控制方法不足,将分数阶PID算法与滑模变结构算法相结合,同时为了规避分数阶PID的滑模变结构算法手动调节参数的复杂性以及不确定性,采用粒子群算法对其参数进行优化,完善分数阶PID的滑模变结构控制器,提高其控制精度.并将新型算法应用于单相全桥逆变器,通过Matlab仿真并与分数阶PID滑模变结构控制函数(PID-SMC)及滑模变结构控制(SMC)方法相比较,研究结果表明,粒子群算法整定参数收敛速度快,较短时间内可以找出最优解,整定后的算法静态误差小,上升速度快,抑制系统抖振能力强,具有较强的鲁棒性.     

State feedback sliding mode control without chattering by constructing Hurwitz matrix for AUV movement

This paper presents a new method to eliminate the chattering of state feedback sliding mode control (SMC) law for the mobile control of an autonomous underwater vehicle (AUV) which is nonlinear and suffers from unknown disturbances system. SMC is a well-known nonlinear system control algorithm for its anti-disturbances capability, while the chattering on switch surface is one stiff question. To dissipate the well-known chattering of SMC, the switching manifold is proposed by presetting a Hurwitz matrix which is deducted from the state feedback matrix. Meanwhile, the best switching surface is achieved by use of eigenvalues of the Hurwitz matrix. The state feedback control parameters are not only applied to control the states of AUV but also connected with coefficients of switching surface. The convergence of the proposed control law is verified by Lyapunov function and the robust character is validated by the Matlab platform of one AUV model.     

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.     

A multitask sliding mode control for mismatched uncertain large-scale systems

A new sliding mode control (SMC) approach, output variables only, single phase only and chattering phenomenon free, is presented for a class of mismatched uncertain large-scale systems. For a new multitask SMC, it is not required that the system states are available. Moreover, the sliding function in this study just depends on output variables. Using an exponential type sliding surface, the system states are always in the sliding mode at the beginning time t = 0. Using a newly appropriate linear matrix inequality stability conditions by the Lyapunov method are derived such that each subsystem in the new sliding mode is completely invariant to matched uncertainties. As a result, robustness of the mismatched uncertain large-scale systems can be assured throughout an entire response of the system starting from the initial time t = 0. In every subsystem, a scheme of decentralised control using only output states is proposed. In addition, a continuous controller is finally designed for chattering removal. Finally, a numerical example is used to demonstrate the efficacy of the proposed method.     

Fault tolerant control based on neural network interval type-2 fuzzy sliding mode controller for octorotor UAV

In this paper, a robust controller for a six degrees of freedom (6 DOF) octorotor helicopter control is proposed in presence of actuator and sensor faults. Neural networks (NN), interval type-2 fuzzy logic control (IT2FLC) approach and sliding mode control (SMC) technique are used to design a controller, named fault tolerant neural network interval type-2 fuzzy sliding mode controller (FTNNIT2FSMC), for each subsystem of the octorotor helicopter. The proposed control scheme allows avoiding difficult modeling, attenuating the chattering effect of the SMC, reducing the number of rules for the fuzzy controller, and guaranteeing the stability and the robustness of the system. The simulation results show that the FTNNIT2FSMC can greatly alleviate the chattering effect, tracking well in presence of actuator and sensor faults.     

Chattering and stability analysis of the sliding mode control using inverse hyperbolic function

Chattering is a known issue in sliding mode control (SMC) and much research has been carried out to mitigate the chattering and its effects. In this work the chattering and stability analysis of the inverse hyperbolic function (IHF) based reaching law (RL) has been carried out. The work mathematically formulates the reaching time and calculates the describing function (DF) for the IHF based RL, which is used to formulate the conditions for chattering avoidance. The bound for the gain of RL has been calculated that will result in the chattering avoidance. Finally the proposed scheme has been used to control the speed of DC motor. Experimental results show avoidance of chattering and reduction in the reaching time.     

基于改进型PI趋近律的无刷直流电机滑模控制

针对无刷直流电机模型参数时变的特性,为解决传统PID控制易受模型参数变化影响的弊端与传统滑模控制(SMC)的抖振问题,将分数阶PI与变速趋近律结合,提出了一种改进型PI趋近律的无刷直流电机滑模控制算法。该算法通过对趋近律的改进,既避免了模型参数变化的影响,又减小了系统输出的抖振。仿真与实验结果表明,与传统滑模控制、传统PI控制相比,具有响应快、鲁棒性强、超调小、抖振小等优点,是一种更优的控制方法。     

Sliding mode control of uncertain switched delay systems via hysteresis switching strategy

This paper investigates the robust sliding mode control (SMC) problem for a class of uncertain switched systems with time-varying delay. The sliding surface is constructed such that the sliding motion is completely invariant to all admissible uncertainties. For the case of the known delay-derivative upper bound, by using the multiple Lyapunov functions method, the Hysteresis switching law dependent on the state and the previous value of switching signal are designed to stabilize the sliding motion and avoid the chattering. Variable structure controllers are developed to drive the state of switched systems to reach the sliding surface in finite time and remain on it thereafter. For the case of the unknown delay-derivative upper bound, based on the single Lyapunov function method, the conditions of stabilization are obtained. Finally, a numerical example is given to illustrate the effectiveness of the proposed methods.     

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.     

无抖振离散滑模趋近律

针对离散滑模趋近律形式多样且容易产生高频抖振的问题,提出了离散滑模趋近律的一般形式,并给出了无抖振的到达条件及其理论证明,从一般意义上为离散滑模趋近律的设计提供了理论依据。针对满足匹配条件的不确定系统,给出了切换函数收敛域的推导方法,推导了无抖振的最小收敛域。以典型的高氏指数趋近律为例,利用无抖振的到达条件,对其一般形式进行了无抖振改进,验证了所提出方法的有效性。     

Robust adaptive control of a bio-inspired robot manipulator using bat algorithm

This paper proposes a novel adaptive fractional order PID sliding mode controller (AFOPIDSMC) using a Bat algorithm to control of a Caterpillar robot manipulator. A fractional order PID (FOPID) control is applied to improve both trajectory tracking and robustness. Sliding mode controller (SMC) is one of the control methods which provides high robustness and low tracking error. Using hybridization, a new combined control law is proposed for chattering reduction by means of FOPID controller and high trajectory tracking through using SMC. Then, an adaptive controller design motivated from the SMC is applied for updating FOPID parameters. A metaheuristic approach, the Bat search algorithm based on the echolocation behavior of bats is applied for optimal design of the Caterpillar robot in order to tune the parameter AFOPIDSMC controllers (BA-AFOPIDSMC). To study the effectiveness of Bat algorithm, its performance is compared with five other controllers such as PID, FOPID, SMC, AFOPIDSMC and PSO-AFOPIDSMC. The stability of the AFOPIDSMC controller is proved by Lyapunov theory. Numerical simulation results completely indicate the advantage of BA-AFOPIDSMC for trajectory tracking and chattering reduction.     

考虑扰动与输入饱和的机械臂连续非奇异快速终端滑模控制

针对机械臂控制过程中由于扰动与输入饱和造成的控制精度低的问题,提出一种连续非奇异快速终端滑模控制算法.首先,针对输入饱和问题,设计饱和补偿系统以消除输入饱和特性;其次,为避免滑模控制的抖振问题,设计二阶模型不确定与扰动估计器(UDE)对扰动项进行估计;同时,为进一步提高控制精度,采用自适应方法对扰动估计误差进行控制;在...     

Sliding Mode Control of Coupled Tank Systems Using Conditional Integrators

For the problem of set point regulation of the liquid level in coupled tank systems, we present a continuous sliding mode control(SMC) with a "conditional integrator", which only provides integral action inside the boundary layer. For a special choice of the controller parameters, our design can be viewed as a PID controller with anti-windup and achieves robust regulation.The proposed controller recovers the transient response performance without control chattering. Both full-state feedback as well as output-feedback designs are presented in this work. Our output-feedback design uses a high-gain observer(HGO) which recovers the performance of a state-feedback design where plant parameters are assumed to be known. We consider both interacting as well as non-interacting tanks and analytical results for stability and transient performance are presented in both the cases. The proposed controller continuous SMC with conditional integrators(CSMCCI) provides superior results in terms of the performance measures as well as performance indices than ideal SMC, continuous SMC(CSMC) and continuous SMC with conventional integrator(CSMCI). Experimental results demonstrate good tracking performance in spite of unmodeled dynamics and disturbances.     

Adaptive fuzzy-neural-network control for maglev transportation system

A magnetic-levitation (maglev) transportation system including levitation and propulsion control is a subject of considerable scientific interest because of highly nonlinear and unstable behaviors. In this paper, the dynamic model of a maglev transportation system including levitated electromagnets and a propulsive linear induction motor (LIM) based on the concepts of mechanical geometry and motion dynamics is developed first. Then, a model-based sliding-mode control (SMC) strategy is introduced. In order to alleviate chattering phenomena caused by the inappropriate selection of uncertainty bound, a simple bound estimation algorithm is embedded in the SMC strategy to form an adaptive sliding-mode control (ASMC) scheme. However, this estimation algorithm is always a positive value so that tracking errors introduced by any uncertainty will cause the estimated bound increase even to infinity with time. Therefore, it further designs an adaptive fuzzy-neural-network control (AFNNC) scheme by imitating the SMC strategy for the maglev transportation system. In the model-free AFNNC, online learning algorithms are designed to cope with the problem of chattering phenomena caused by the sign action in SMC design, and to ensure the stability of the controlled system without the requirement of auxiliary compensated controllers despite the existence of uncertainties. The outputs of the AFNNC scheme can be directly supplied to the electromagnets and LIM without complicated control transformations for relaxing strict constrains in conventional model-based control methodologies. The effectiveness of the proposed control schemes for the maglev transportation system is verified by numerical simulations, and the superiority of the AFNNC scheme is indicated in comparison with the SMC and ASMC strategies.     

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。     

Decentralized sliding mode adaptive controller design based on fuzzy neural networks for interconnected uncertain nonlinear systems

A new type controller, fuzzy neural networks sliding mode controller (FNNSMC), is developed for a class of large-scale systems with unknown bounds of high-order interconnections and disturbances. Although sliding mode control is simple and insensitive to uncertainties and disturbances, there are two main problems in the sliding mode controller (SMC): control input chattering and the assumption of known bounds of uncertainties and disturbances. The FNNSMC, which incorporates the fuzzy neural networks (FNNs) and the SMC, can eliminate the chattering by using the continuous output of the FNN to replace the "discontinuous" sign term in the SMC. The bounds of uncertainties and disturbances are also not required in the FNNSMC design. Two examples are presented to support the validity of the new controller. The simulation results show that the FNNSMC is more robust than the SMC.