Use of adaptive fuzzy systems in parameter tuning of sliding-modecontrollers

The paper proposes to combine adaptive fuzzy systems with sliding-mode control (SMC) to solve the chattering problem of SMC for robotic applications. In the design of the controller, special attention is paid to chattering elimination without a degradation of the tracking performance. Furthermore, the a priori knowledge required of the system dynamics for design is kept to a minimum. The paper first considers the basic principles of sliding-mode and fuzzy controllers. Implementation difficulties and most popular solutions are then overviewed. Next, the design of a SMC reported in the literature is outlined and guidelines for the selection of controller parameters for the best tracking performance without chattering are presented. A novel approach based on the introduction of a "chattering variable" is developed. This variable, as a measure of chattering, is used as an input to an adaptive fuzzy system responsible for the minimization. Online tuning of parameters by fuzzy rules is carried out for the SMC. The experimental results obtained are given, and conclusions are presented     

A fuzzy sliding controller for nonlinear systems

It is well known that sliding-mode control can give good transient performance and system robustness. However, the presence of chattering may introduce problems to the actuators. Many chattering elimination methods use a finite DC gain controller which leads to a finite steady-state error. One method to ensure zero steady-state error is using a proportional plus integral (PI) controller. This paper proposes a fuzzy logic controller which combines a sliding-mode controller (SMC) and a PI controller. The advantages of the SMC and the PI controller can be combined and their disadvantages can be removed. The system stability is proved, although there is one more state variable to be considered in the PI subsystem. An illustrative example shows that good transient and steady-state responses can be obtained by applying the proposed controller     

基于模糊神经网络滑模控制器的一类非线性系统自适应控制

本文研究了一类不确定性非线性系统的自适应控制,在模糊神经网络滑模控制器（Ｆｕｚｚｙ ｎｅｒｕａｌ Ｎｅｔｗｏｒｋｓ sｌｉｄｉｎｇ Ｍｏｄｅ Ｃｏｎｔｒｏｌｌｅ ）的基础上提出了一种设计方法,将ＦＮＮＳＭＣ与带死区的滑模控制器（Ｓｌｉｄｉｎｇ ｍｏｄｅ Ｃｏｎｔｒｏｌｌｅｒ ｗｉｔｈ Ｄｅａｄ Ｚｏｎｅ）有机结合,通过平滑切换实现自适应控制,这种方法使系统不仅有好的鲁棒性而且能有效地消除离频动,同时     

A Neuro-Sliding-Mode Control With Adaptive Modeling of Uncertainty for Control of Movement in Paralyzed Limbs Using Functional Electrical Stimulation

During the past several years, several strategies have been proposed for control of joint movement in paraplegic subjects using functional electrical stimulation (FES), but developing a control strategy that provides satisfactory tracking performance, to be robust against time-varying properties of muscle-joint dynamics, day-to-day variations, subject-to-subject variations, muscle fatigue, and external disturbances, and to be easy to apply without any re-identification of plant dynamics during different experiment sessions is still an open problem. In this paper, we propose a novel control methodology that is based on synergistic combination of neural networks with sliding-mode control (SMC) for controlling FES. The main advantage of SMC derives from the property of robustness to system uncertainties and external disturbances. However, the main drawback of the standard sliding modes is mostly related to the so-called chattering caused by the high-frequency control switching. To eliminate the chattering, we couple two neural networks with online learning without any offline training into the SMC. A recurrent neural network is used to model the uncertainties and provide an auxiliary equivalent control to keep the uncertainties to low values, and consequently, to use an SMC with lower switching gain. The second neural network consists of a single neuron and is used as an auxiliary controller. The control law will be switched from the SMC to neural control, when the state trajectory of system enters in some boundary layer around the sliding surface. Extensive simulations and experiments on healthy and paraplegic subjects are provided to demonstrate the robustness, stability, and tracking accuracy of the proposed neuroadaptive SMC. The results show that the neuro-SMC provides accurate tracking control with fast convergence for different reference trajectories and could generate control signals to compensate the muscle fatigue and reject the external disturbance.     

Application of an auto-tuning neuron to sliding mode control

This paper presents a control strategy that incorporates an auto-tuning neuron into the sliding mode control (SMC) in order to eliminate the high control activity and chattering due to the SMC. The main difference between the auto-tuning neuron and the general one is that a modified hyperbolic tangent function with adjustable parameters is employed. In this proposed control structure, an auto-tuning neuron is then used as the neural controller without any connection weights.. The control law will be switched from the sliding control to the neural control, when the state trajectory of system enters in some boundary layer. In this way, the chattering phenomenon will not occur. The results of numerical simulations are provided to show the control performance of our proposed method.     

薄膜材料的绕组处理的适应失真压力的控制系统

薄膜材料的绕组处理是在一个高度非线性的动态系统中维持应力不变.提出一个为薄膜材料的绕组处理在不同摩擦锟供料速度下的适应模糊应力的控制系统.该提出的适应模糊应力的控制系统包括一个模糊应力控制器和一个适应调谐器.模糊应力控制器是主进度控制器,一个平移宽度的概念和变化模式技术被包括在模糊推论中以矫正模糊现象,而且只有一个参数因素需要被调整.为了对抗在实际应用中的不确定,一个失真压力的控制系统占据着简单控制框架,无震颤的,稳定跟踪性能和对不确定性的鲁棒的优势.与传统的比例积分应力控制方法相比较可提出的这种控制方法有显著的优势.     

Sliding-mode-controlled slider-crank mechanism with fuzzy neuralnetwork

The dynamic response of a sliding-mode-controlled slider-crank mechanism, which is driven by a permanent-magnet (PM) synchronous servo motor, is studied in this paper. First, a position controller is developed based on the principles of sliding-mode control. Moreover, to relax the requirement of the bound of uncertainties in the design of a sliding-mode controller, a fuzzy neural network (FNN) sliding-mode controller is investigated, in which a FNN is adopted to adjust the control gain in a switching control law on line to satisfy the sliding mode condition. In addition, to guarantee the convergence of tracking error, analytical methods based on a discrete-type Lyapunov function are proposed to determine the varied learning rates of the FNN. Numerical and experimental results show that the dynamic behaviors of the proposed controller-motor-mechanism system are robust with regard to parametric variations and external disturbances. Furthermore, compared with the sliding-mode controller, smaller control effort results and the chattering phenomenon is much reduced by the proposed FNN sliding-mode controller     

Comparison of sliding-mode and fuzzy neural network control formotor-toggle servomechanism

A comparative study of sliding-mode control and fuzzy neural network (FNN) control on the motor-toggle servomechanism is presented. The toggle mechanism is driven by a permanent-magnet synchronous servomotor. The rod and crank of the toggle mechanism are assumed to be rigid. First, Hamilton's principle and Lagrange multiplier method are applied to formulate the equation of motion. Then, based on the principles of the sliding-mode control, a robust controller is developed to control the position of a slider of the motor-toggle servomechanism. Furthermore, an FNN controller with adaptive learning rates is implemented to control the motor-toggle servomechanism for the comparison of control characteristics. Simulation and experimental results show that both the sliding-mode and FNN controllers provide high-performance dynamic characteristics and are robust with regard to parametric variations and external disturbances. Moreover, the FNN controller can result in small control effort without chattering     

Total sliding-mode controller for PM synchronous servo motor driveusing recurrent fuzzy neural network

In this paper, the dynamic responses of a recurrent-fuzzy-neural-network (RFNN) sliding-mode-controlled permanent-magnet (PM) synchronous servo motor are described. First, a newly designed total sliding-mode control system, which is insensitive to uncertainties, including parameter variations and external disturbance in the whole control process, is introduced. The total sliding-mode control comprises the baseline model design and the curbing controller design. In the baseline model design, a computed torque controller is designed to cancel the nonlinearity of the nominal plant. In the curbing controller design, an additional controller is designed using a new sliding surface to ensure the sliding motion through the entire state trajectory. Therefore, in the total sliding-mode control system, the controlled system has a total sliding motion without a reaching phase. Then, to overcome the two main problems with sliding-mode control, i.e., the assumption of known uncertainty bounds and the chattering phenomena in the control effort, an RFNN sliding-mode control system is investigated to control the PM synchronous servo motor. In the RFNN sliding-mode control system, an RFNN bound observer is utilized to adjust the uncertainty bounds in real time. To guarantee the convergence of tracking error, analytical methods based on a discrete-type Lyapunov function are proposed to determine the varied learning rates of the RFNN. Simulated and experimental results due to periodic step and sinusoidal commands show that the dynamic behaviors of the proposed control systems are robust with regard to uncertainties     

Fuzzy supervisory sliding-mode and neural-network control for robotic manipulators

Highly nonlinear, highly coupled, and time-varying robotic manipulators suffer from structured and unstructured uncertainties. Sliding-mode control (SMC) is effective in overcoming uncertainties and has a fast transient response, while the control effort is discontinuous and creates chattering. The neural network has an inherent ability to learn and approximate a nonlinear function to arbitrary accuracy, which is used in the controllers to model complex processes and compensate for unstructured uncertainties. However, the unavoidable learning procedure degrades its transient performance in the presence of disturbance. A novel approach is presented to overcome their demerits and take advantage of their attractive features of robust and intelligent control. The proposed control scheme combines the SMC and the neural-network control (NNC) with different weights, which are determined by a fuzzy supervisory controller. This novel scheme is named fuzzy supervisory sliding-mode and neural-network control (FSSNC). The convergence and stability of the proposed control system are proved by using Lyapunov's direct method. Simulations for different situations demonstrate its robustness with satisfactory performance.     

Hybrid Terminal Sliding-Mode Observer Design Method for a Permanent-Magnet Synchronous Motor Control System

This paper proposes a hybrid terminal sliding-mode observer based on the nonsingular terminal sliding-mode (NTSM) and the high-order sliding-mode (HOSM) for the rotor position and speed estimation in the permanent-magnet synchronous motor control system. An NTSM manifold is utilized to realize both fast convergence and better tracking precision. In addition, a derivative estimator is used to obtain the derivative of the sliding-mode function. Meanwhile, an HOSM control law is designed to guarantee the stability of the observer and eliminate the chattering, so that 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 of the motor can be calculated. Simulation and experimental results are presented to validate the proposed method.      

FPGA-Based Adaptive Backstepping Sliding-Mode Control for Linear Induction Motor Drive

A field-programmable gate array (FPGA)-based adaptive backstepping sliding-mode controller is proposed to control the mover position of a linear induction motor (LIM) drive to compensate for the uncertainties including the friction force. First, the dynamic model of an indirect field-oriented LIM drive is derived. Next, a backstepping sliding-mode approach is designed to compensate the uncertainties occurring in the motion control system. Moreover, the uncertainties are lumped and the upper bound of the lumped uncertainty is necessary in the design of the backstepping sliding-mode controller. However, the upper bound of the lumped uncertainty is difficult to obtain in advance of practical applications. Therefore, an adaptive law is derived to adapt the value of the lumped uncertainty in real time, and an adaptive backstepping sliding-mode control law is the result. Then, an FPGA chip is adopted to implement the indirect field-oriented mechanism and the developed control algorithms for possible low-cost and high-performance industrial applications. The effectiveness of the proposed control scheme is verified by some experimental results. With the adaptive backstepping sliding-mode controller, the mover position of the FPGA-based LIM drive possesses the advantages of good transient control performance and robustness to uncertainties in the tracking of periodic reference trajectories.     

Integral sliding-mode control of a magnetically suspended balancebeam: analysis, simulation, and experiment

This paper presents a sliding-mode controller with integral compensation for a magnetic suspension balance beam system. The control scheme comprises an integral controller which is designed for achieving zero steady-state error under step disturbances, and a sliding-mode controller which is designed for enhancing robustness under plant uncertainties. A procedure is developed for determining the coefficients of the switching plane such that the overall closed-loop system has stable eigenvalues. A proper continuous design signal is introduced to overcome the chattering problem. The performance of the balance beam control system is illustrated by simulation and experimental results showing that the proposed integral sliding-mode controller method is effective under external step disturbances and input channel parameter variations     

Robust fuzzy neural network sliding mode control scheme for IPMSM drives

This article proposes a robust fuzzy neural network sliding mode control (FNNSMC) law for interior permanent magnet synchronous motor (IPMSM) drives. The proposed control strategy not only guarantees accurate and fast command speed tracking but also it ensures the robustness to system uncertainties and sudden speed and load changes. The proposed speed controller encompasses three control terms: a decoupling control term which compensates for nonlinear coupling factors using nominal parameters, a fuzzy neural network (FNN) control term which approximates the ideal control components and a sliding mode control (SMC) term which is proposed to compensate for the errors of that approximation. Next, an online FNN training methodology, which is developed using the Lyapunov stability theorem and the gradient descent method, is proposed to enhance the learning capability of the FNN. Moreover, the maximum torque per ampere (MTPA) control is incorporated to maximise the torque generation in the constant torque region and increase the efficiency of the IPMSM drives. To verify the effectiveness of the proposed robust FNNSMC, simulations and experiments are performed by using MATLAB/Simulink platform and a TI TMS320F28335 DSP on a prototype IPMSM drive setup, respectively. Finally, the simulated and experimental results indicate that the proposed design scheme can achieve much better control performances (e.g. more rapid transient response and smaller steady-state error) when compared to the conventional SMC method, especially in the case that there exist system uncertainties.     

Sliding-mode control in voltage source inverter-based higher-order circuits

In this article, a new control methodology of sliding-mode control (SMC) for voltage source inverter (VSI)-based higher-order circuit is proposed. In this method, the SMC is used at the inner terminals for stable tracking of the voltage and current variables. An outer voltage control loop is included to reduce the steady-state error in tracking the reference load voltage. It is shown that when the SMC is applied on the load voltage terminal for higher-order VSI circuits, it leads to the instability. However, it well stabilises the system when the controller is implemented on the inner shunt capacitor terminals. Additional outer voltage control loop with proportional plus integral controller will ensure regulated voltage across the load. It has been shown that the controller is able to achieve good tracking accuracy with an acceptable stability margins. The performance of the proposed SMC has been verified on the fourth-order VSI circuit.     

Continuous variable structure controller for BLDDSM positioncontrol with prescribed tracking performance

The continuous, accurate, and robust sliding mode tracking controller based on a disturbance observer for a brushless direct drive servo motor (BLDDSM) is presented. Although the conventional sliding mode control (SMC) or variable structure control (VSC) can give the desired tracking performance, there exists an inevitable chattering problem in control which is undesirable for a direct drive system. With the proposed algorithm, not only are the chattering problems removed, but also the prescribed tracking performance can be obtained by using the efficient compensation of the disturbance observer. The design of the sliding mode tracking controller for the prescribed, accurate, and robust tracking performance without the chattering problem is given based on the results of the detailed stability analysis. The usefulness of the proposed algorithm is demonstrated through the computer simulations for a BLDDSM under load variations     

Second-order sliding-mode control of DC drives

One of the most recent topics in variable-structure systems theory is represented by the second-order sliding-mode control (2-SMC) methodology. This approach guarantees the same robustness and dynamic performance of traditional first-order SMC algorithms, and, at the same time, attenuates the chattering phenomenon, which is the main drawback in the actual implementation of this technique. In the present paper, a recently-proposed 2-SMC algorithm is used to synthesize a robust dc-drive control system which does not require current feedback and demands only rough information about the actual motor parameters. Stability and performance are analyzed, and an experimental comparison with a proportional-integral-based control scheme is reported.     

Design and implementation of an adaptive sliding-mode dynamic controller for wheeled mobile robots

This paper designs an adaptive sliding-mode dynamic controller for wheeled mobile robots to implement the trajectory-tracking mission. First, a kinematic controller is introduced for the wheeled mobile robot. Secondly, the adaptive sliding-mode dynamic controller is proposed to make the real velocity of the wheeled mobile robot reach the desired velocity command, although the wheeled mobile robot is even with system uncertainties and disturbances. The convergence of the complete equations of motion of the wheeled mobile robot is proved by the Lyapunov stability theory. Computer simulation results illustrate the effectiveness of the proposed control schemes. Finally, the real-time experiments of the adaptive sliding-mode dynamic controller on the test ground demonstrate the feasibility of practical wheeled mobile robot maneuvers.     

Design of a perturbation estimator using the theory ofvariable-structure systems and its application to magnetic levitationsystems

A perturbation estimator using the theory of variable structure systems is proposed to enhance the robustness of a pole-placement controller design. In its ideal form, the pole-placement design using feedback-linearization technique achieves a desired performance in nonlinear time-varying systems. However, its performance deteriorates rapidly with the presence of disturbance and parametric uncertainties, referred to as perturbation. The estimate generated by the proposed perturbation estimator is incorporated as an additional input to rectify the uncertainties in the nominal control model of the pole-placement design. The proposed scheme requires neither the measurement of the time derivative of the state vector nor the precise knowledge of system parameters, hut rather the bounds on system perturbation. Chatter and the adverse effects of conservative bounds on system perturbation, often encountered in conventional sliding-mode control (SMC), are alleviated for the controlled plant by the proposed scheme. The benefits of this scheme are demonstrated in this study practically on a magnetic levitation system and its performance is compared with that of the conventional SMC scheme     

液压伺服系统自适应模糊变结构控制

结合变结构控制、自适应控制和模糊技术等特点,提出一种自适应模糊变结构控制方法.首先,设计一个带积分开关平面函数的变结构控制器,并构造一个二维模糊边界层宽度调节器以削弱抖振.其次,基于Lyapunov稳定性理论,引入一自适应算法,自适应调节变结构控制参数.应用于液压伺服系统的控制实验结果表明,所提出的控制方法能削弱抖振,改善液压伺服系统稳态控制精度,具有较强的鲁棒自适应综合性能.