Chattering reduction using multiphase sliding mode control

For the system with sliding mode controllers operated by on/off switches, ‘chattering’ appears in the output of the system when its switching frequency is restricted. In power systems, the switching frequency is commonly limited to prevent power losses, and chattering or ‘ripple’ appears especially in the system current. Common methods to decrease such ripple are based on ‘harmonic cancellation’ using the multiple number of phase channels having the desired phase shift that brings cancellation in the sum of outputs from the individual channels. In this article, a design principle of sliding mode control for a multiphase controller is proposed. The methodology is originated from the concept of multidimensional sliding mode and provides desired phase shifts between phases with the help of adaptive width for the hysteresis loops in switching elements. The chattering suppression effect is demonstrated by simulations for the DC–DC converter systems in various situations.     

Variable structure control with sliding mode prediction for discrete-time nonlinear systems

A new variable structure control algorithm based on sliding mode prediction for a class of discrete-time nonlinear systems is presented. By employing a special model to predict future sliding mode value, and combining feedback correction and receding horizon optimization methods which are extensively applied on predictive control strategy, a discrete-time variable structure control law is constructed. The closed-loop systems are proved to have robustness to uncertainties with unspecified boundaries. Numerical simulation and pendulum experiment results illustrate that the closed-loop systems possess desired performance, such as strong robustness, fast convergence and chattering elimination.     

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.     

Robust discrete-time chattering free sliding mode control

A new control algorithm based on discrete-time variable structure systems theory is proposed. The basic feature of this algorithm is that trajectories reach the sliding manifold in finite time, without chattering. Apart from stability, the robustness of the algorithm with respect to parameter uncertainties, as well as external disturbances is considered. It is demonstrated that the robustness is improved by decreasing the sampling period. The theory is illustrated on a DC servo-position system.     

引入趋近律的功率因数校正滑模控制仿真研究

提出一种引入趋近律的滑模变结构控制(SMVSC)方法来实现有源功率因数校正(APFC),减少电流的谐波成分.SMVSC是一种解决非线性时变系统(如APFC系统)问题的良好办法,但是实际应用中SMVSC的"抖振"现象问题必须要解决好.引入趋近律来削弱APFC系统在滑模控制中的"抖振"现象,并且依此推导出了控制APFC系统中的功率开关的PWM占空比.采用Matlab平台进行仿真验证控制策略控制APFC电路几乎得到单位功率因数,同时超调减小、响应时间缩短.     

基于模糊扰动观测器的PMSM积分滑模控制研究

为了克服传统永磁同步电机(Permanent magnet synchronous motor,PMSM)的滑模控制增益大容易产生抖振的问题,提出基于模糊观测器的PMSM积分滑模控制策略。采用新型趋近律设计积分滑模控制器取代传统的滑模控制器,提高系统的动态响应性能。结合模糊控制与自适应控制的特点,设计模糊扰动观测器,能够迅速有效地观测系统内部参数变化和外部扰动,并对积分滑模速度控制器进行前馈补偿,削弱系统抖振的同时提高了系统的鲁棒性。通过李雅普诺夫理论证明了该控制系统的稳定性。仿真及实验结果验证了该方法具有较强的鲁棒性,可以实现良好的跟踪效果并且无抖动。     

Sliding mode control of a discrete system

Conventional sliding mode control designed on the basis of a continuous system is known to be robust to the plant uncertainties. A realized digital system, however, not only yields chattering, but also may become unstable by a long sampling interval. This paper presents a stable discrete sliding mode control insensitive to the choice of sampling interval and not yielding chattering. The control system is designed on the basis of a discrete Lyapunov function and a sufficient condition of the control gain to make the system stable is given. Contrary to the continuous case, the derived switching plane of the control law is different from the sliding mode, and in its neighborhood, the control law is given by the linear state feedback. Simulations show the effectiveness of the proposed method.     

SLIDING MODE PREDICTION TRACKING CONTROL DESIGN FOR UNCERTAIN SYSTEMS

In this paper, a tracking control algorithm based on sliding mode prediction for a class of discrete‐time uncertain systems is presented. By creating a special model to predict the future sliding mode function value and by combining feedback correction and receding horizon optimization approaches, which are extensively applied in predictive control strategy, a discrete‐time sliding mode control law for tracking problem is constructed. With the designed control law, closed‐loop systems have strong robustness to matched or unmatched uncertainties as they eliminate chattering. Besides, in the robustness analysis, the boundary condition for uncertainties, which is a universal presupposition in sliding mode control method, is not required. Numerical simulation and cart‐pendulum experiment results illustrate the validity of the proposed algorithm.     

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.     

电动汽车TCS滑模控制器设计

针对电动汽车在冰雪低附着极端工况极易出现的驱动轮过度滑转问题,以电动汽车驱动电机转矩为控制变量,设计了一种电动汽车驱动防滑防牵引力控制系统(Traction control system,TCS)滑模控制器,控制器通过调节驱动电机转矩,将滑转率控制在目标值附近,使汽车持续获得最大路面附着,防止车轮过度滑转,对应用滑模控制出现的抖振问题,设计了一种改进的指数型趋近律,用以削弱系统抖振。仿真结果表明,设计的TCS滑模控制器通过控制驱动电机转矩能将汽车的滑转率控制在目标值附近,使得汽车持续获得最大的路面附着,充分抑制汽车打滑,提高了汽车行驶稳定性,在整个控制过程中驱动电机转矩和状态变量收敛快速且十分平滑,抖振削弱效果良好。     

Proportional-integral based fuzzy sliding mode control of the milling head

A-axis (that is, the milling head) is an essential assembly in the five-axis CNC machine tools, positioning precision of which directly affects the machining accuracy and surface qualities of the processed parts. Considering the influence of nonlinear friction and uncertain cutting force on the control precision of the A-axis, a novel fuzzy sliding mode control (FSMC) based on the proportional-integral (PI) control is designed according to the parameters adaptation. Main idea of the control scheme is employing the fuzzy systems to approximate the unknown nonlinear functions and adopting the PI control to eliminate the input chattering. Simulation analyses and experimental results illustrate that the designed control strategy is robust to the uncertain load and the parameters perturbation.     

An LTR-observer-based dynamic sliding mode control for chattering reduction

Two important approaches to alleviation of control chattering in sliding mode control are the boundary layer control (BLC) and the dynamic sliding mode control (DSMC). The DSMC is superior to the BLC since in DSMC chattering is alleviated without sacrificing the control accuracy. However, the design of DSMC is more challenging because its sliding variable contains an unknown system uncertainty. This paper proposes a robust two-dimensional LTR observer for estimation of the state-dependent uncertainty in the sliding variable. This paper also shows, via simulation examples, that the DSMC can better reduce chattering than the BLC especially in noisy environments.     

On frequency-domain criterion of finite-time convergence of second-order sliding mode control algorithms

Transient processes in the systems controlled by the twisting second-order sliding mode (SOSM) control algorithm and certain generic SOSM given by the describing function are analyzed in the frequency domain. The analysis is based on the approximate describing function method. The relationship between the frequency response (Nyquist plot) of the plant, the shape of the negative reciprocal describing function of the controller, and the transient process convergence rate is investigated. A simple criterion of the existence of finite-time convergence is proposed. It is shown that the convergence rate in a system controlled by a SOSM controller depends on the angle between the high-frequency asymptote of the Nyquist plot of the plant and the low-amplitude asymptote of the negative reciprocal of the describing function of the controller, which is named the phase deficit.     

Coordinating optimization-based sliding mode variable structure control for electro-hydraulic servo system

A sliding mode variable structure control （SMVSC） based on a coordinating optimization algorithm has been developed. Steady state error and control switching frequency are used to constitute the system performance indexes in the coordinating optimization, while the tuning rate of boundary layer width （BLW） is employed as the optimization parameter. Based on the mathematical relationship between the BLW and steady-state error, an optimized BLW tuning rate is added to the nonlinear control term of SMVSC. Simulation experiment results applied to the positioning control of an electro-hydraulic servo system show the comprehensive superiority in dynamical and static state performance by using the proposed controller is better than that by using SMVSC without optimized BLW tuning rate. This succeeds in coordinately considering both chattering reduction and high-precision control realization in SMVSC.     

Sliding mode control of singularly perturbed systems and its application in quad-rotors

This paper presents a sliding mode control scheme for tracking control of nonlinear singularly perturbed systems in the presence of model errors and external disturbances. A dual-loop feedback control is developed to provide accurate tracking capability and sufficient robustness to system uncertainties. A sliding mode controller is proposed in the outer-loop feedback design such that the plant states are stabilised for given reference trajectories, while an additional robust controller is designed in the inner loop to increase the adaptability to uncertainties, and reduce the effect of unmodelled high-frequency dynamics on plant dynamics. An appealing feature of the control scheme is the attenuation of chattering. The effectiveness and merits of the new control scheme developed are shown via a verification example of velocity control of a quad-rotor.     

Coordinating optimization-based sliding mode variable structure control for electro-hydraulic servo system

A sliding mode variable structure control (SMVSC) based on a coordinating optimization algorithm has been developed. Steady state error and control switching frequency are used to constitute the system performance indexes in the coordinating optimization, while the tuning rate of boundary layer width (BLW) is employed as the optimization parameter. Based on the mathematical relationship between the BLW and steady-state error, an optimized BLW tuning rate is added to the nonlinear control term of SMVSC. Simulation experiment results applied to the positioning control of an electro-hydraulic servo system show the comprehensive superiority in dynamical and static state performance by using the proposed controller is better than that by using SMVSC without optimized BLW tuning rate. This succeeds in coordinately considering both chattering reduction and high-precision control realization in SMVSC.     

无抖振离散滑模输出反馈控制方法及仿真研究

针对离散时间系统,提出了一种基于多速率采样输出反馈和幂次函数趋近律的离散滑模控制方法;理论分析表明,通过引入幂次函数可消除离散滑模控制系统的抖振;采用多速率采样技术,运用不同采样速率下的系统输出值表示系统状态,实现了仅用系统输入输出采样值完成离散滑模控制器的设计,减轻了控制系统设计的复杂性;仿真结果表明,控制器的输出、切换函数、系统的输出均不存在抖振现象,而且控制系统表现出了良好的动态特性。     

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     

MIMO非线性不确定系统二阶滑模控制

提出了一种基于有限状态机切换策略的多输入多输出二阶滑模控制算法。算法保证了传统滑模控制对参数变化和扰动不灵敏的特点,削弱了滑模控制的“抖动”现象。在上界未知的测量噪声和参数变化的情况下,算法通过滑模量及其微分的符号构成控制律,实现了系统的镇定。仿真结果表明算法在噪声环境下能保证系统的稳定性,对参数不确定具有较强的鲁棒性。算法结构简单,便于实现。