Higher-order sliding modes,differentiation and output-feedback control

Being a motion on a discontinuity set of a dynamic system, sliding mode is used to keep accurately a given constraint and features theoretically-infinite-frequency switching. Standard sliding modes provide for finite-time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. Yet the relative degree of the constraint has to be 1 and a dangerous chattering effect is possible. Higher-order sliding modes preserve or generalize the main properties of the standard sliding mode and remove the above restrictions. r-Sliding mode realization provides for up to the rth order of sliding precision with respect to the sampling interval compared with the first order of the standard sliding mode. Such controllers require higher-order real-time derivatives of the outputs to be available. The lacking information is achieved by means of proposed arbitrary-order robust exact differentiators with finite-time convergence. These differentiators feature optimal asymptotics with respect to input noises and can be used for numerical differentiation as well. The resulting controllers provide for the full output-feedback real-time control of any output variable of an uncertain dynamic system, if its relative degree is known and constant. The theoretical results are confirmed by computer simulation.     

Global second‐order sliding mode control for nonlinear uncertain systems

Second‐order sliding mode (SOSM) control is used to keep exactly a constraint σ of the second relative degree or to avoid chattering phenomenon. Yet, the traditional SOSM controllers are designed based upon the assumption that the uncertainties or their derivatives are bounded by positive constants. In this paper, a global SOSM controller is designed for a general class of single‐input–single‐output nonlinear systems with uncertainties bounded by positive functions. Moreover, a variable‐gain robust exact differentiator is developed such that the SOSM controllers with finite‐time convergence can also be implemented even when the derivative of the constraint σ is unavailable. Simulation results are given to show the effectiveness of the proposed method.     

UNIVERSAL OUTPUT‐FEEDBACK SISO CONTROLLERS

It is proved in the paper that practically all known higher‐order sliding controllers can be combined with recently developed 2‐sliding‐mode‐based differentiators yielding universal output‐feedback Single‐Input‐Single‐Output (SISO) controllers. These controllers can be applied at least locally, whenever the system relative degree is known. The convergence is global, provided the system relative degree is permanent and few boundedness restrictions hold. No detailed mathematical model of the system is needed. The proposed output‐feedback controller provides for the exact finite‐time‐convergent output tracking of real‐time‐given smooth signals if the output measurements are exact. Otherwise the tracking accuracy is proportional to the magnitude of the sampling noise. The control may be made arbitrarily smooth, thereby removing the chattering effect. The theoretical results are illustrated by computer simulation.     

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.     

Design of sliding mode controllers with bounded L 2 gain performance: an LMI approach

This paper is devoted to the design of robust controllers for sliding mode control systems. A linear fractional transformation (LFT) framework is adopted to describe the systems subject to model uncertainties and external disturbances. A linear matrix inequality (LMI) technique is then developed into the design of both sliding mode and reaching phase control laws. It is shown that by solving a set of LMIs, the switching surface can be designed such that the dynamics in the sliding mode achieve robust stability and bounded L ₂ gain performance with respect to matched and unmatched uncertainties in the presence of disturbances. Furthermore, a reaching phase control law is presented to eliminate the undesirable chattering effect and maintain the robustness property all the time whether the system evolves into its sliding mode in finite time or not. Finally, an observer based control law is also developed to achieve the robust performance during the reaching phase. The results are illustrated by an example.     

Experimental Implementation of New Sliding Mode Control Law applied To a DC–DC Boost Converter

The real implementation of sliding mode controllers (SMCs) to a DC–DC boost converter is a challenge due to the nonminimum phase behavior of these kinds of converters and the SMCs chattering problem. In this paper, new integral sliding mode control laws with linear and proposed nonlinear sliding surfaces are developed to overcome these problems. An experimental comparative study between these SMCs and the classical SMC applied for a DC–DC boost converter is presented.     

Global position regulation of friction manipulators via switched chattering control

Switched position control algorithms are developed to globally stabilize friction mechanical manipulators around a desired position. Both static and dynamic position feedback designs are presented. The controllers constructed, referred to as chattering controllers, do not rely on the generation of sliding motions while providing robustness features similar to those possessed by their sliding mode counterparts. Stability analysis is given within the Lyapunov vector functions framework extended to discontinuous dynamic systems. Performance issues of the chattering controllers are evaluated in an experimental study of a three degrees-of-freedom robot manipulator.     

A survey of applications of second-order sliding mode control to mechanical systems

The effective application of sliding mode control to mechanical systems is not straightforward because of the sensitivity of these systems to chattering. Higher-order sliding modes can counteract this phenomenon by confining the switching control to the higher derivatives of the mechanical control variable, so that the latter results are continuous. Generally, this approach requires the availability of a number of time derivatives of the sliding variable, and, in the presence of noise, this requirement could be a practical limitation. A class of second-order sliding mode controllers, guaranteeing finite-time convergence for systems with relative degree two between the sliding variable and the switching control, could be helpful both in reducing the number of differentiator stages in the controller and in dealing with unmodelled actuator dynamics. In this paper different second-order sliding mode controllers, previously presented in the literature, are shown to belong to the above cited class, and some challenging control problems involving mechanical systems are addressed and solved. Simulations and experimental results are provided throughout the paper.     

非线性摩擦干扰下的电动舵机滑模变结构控制

针对电动舵机非线性摩擦干扰和传统滑模变结构控制高频抖振问题,设计了一个基于新型趋近律的滑 模变结构控制器．仿真结果表明,所设计的控制器能很好地消除非线性摩擦所引起的低速“爬行”和“平顶”现象, 并能有效降低抖振,改善动态品质．     

Chattering‐free sliding mode control for a class of nonlinear mechanical systems

Second‐order sliding mode control (2‐smc) and dynamic sliding mode control (dsmc) eliminate the disturbing characteristic of chattering in static sliding mode control under the assumption that the derivative of the sliding surface is available or complex inequalities at the acceleration level can be constructed. In this paper, passivity‐based adaptive and non‐adaptive chattering‐free sliding mode controllers are proposed assuming that the upper bound of the norm of the derivative of the sliding surface is available, a weaker and easy to implement assumption in comparison to those of 2‐smc and dsmc. The closed‐loop system accounts explicitly for the invariance condition without reaching phase, and therefore for a desired transient response with global exponential convergence of tracking errors. Preliminary experiments are presented. Copyright © 2001 John Wiley & Sons, Ltd.     

离散时间系统的滑模控制器设计与仿真研究*

针对不确定性离散时间系统,分析和设计了一类变结构控制器。当存在外界干扰和不确定性时,系统状态也是全局有界稳定的。一个新的切换面作为系统的输出信号被提出,特别用来设计滑模控制器。系统状态一旦进入到准滑动模态,就对设备参数变化和外界干扰显示出强的鲁棒性,因为控制器的设计完全考虑了边界层的影响。外推法被用来估计不确定离散时间系统的不确定值。两种方法均有效地消除了系统的抖振,确保了系统的稳定性,且保证了变结构控制系统良好的品质。最后,仿真结果证实了所提出方法的有效性。     

Some remarks on the boundedness and convergence properties of smooth sliding mode controllers

Conventional sliding mode controllers are based on the assumption of switching control, but a well-known drawback of such controllers is the chattering phenomenon. To overcome the undesirable chattering effects, the discontinuity in the control law can be smoothed out in a thin boundary layer neighboring the switching surface. In this paper, rigorous proofs of the boundedness and convergence properties of smooth sliding mode controllers are presented. This result corrects flawed conclusions previously reached in the literature. An illustrative example is also presented in order to confirm the convergence of the tracking error vector to the defined bounded region.     

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.     

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.     

Design of a chatter-free terminal sliding mode controller for nonlinear fractional-order dynamical systems

This paper investigates the problem of robust control of nonlinear fractional-order dynamical systems in the presence of uncertainties. First, a novel switching surface is proposed and its finite-time stability to the origin is proved. Subsequently, using the sliding mode theory, a robust fractional control law is proposed to ensure the existence of the sliding motion in finite time. We use a fractional Lyapunov stability theory to prove the stability of the system in a given finite time. In order to avoid the chattering, which is inherent in conventional sliding mode controllers, we transfer the sign function of the control input into the fractional derivative of the control signal. The proposed chattering-free sliding mode technique is then applied for stabilisation of a broad class of three-dimensional fractional-order chaotic systems via a single variable driving control input. Simulation results reveal that the proposed fractional sliding mode controller works well for chaos control of fractional-order hyperchaotic Chen, chaotic Lorenz and chaotic Arneodo systems with no-chatter control inputs.     

Risk assessment in control of fractional-order coronary artery system in the presence of external disturbance with different proposed controllers

In this study, different controllers for control of fractional-order coronary artery system in the presence of external disturbance are designed. Using sliding mode, the proposed type 1 and type 2 fuzzy methods, the suitable controllers are proposed. In sliding mode control, a fractional sliding surface is presented and the control signal is modified to prevent chattering in the control system. With mathematical analysis, a type of membership function is suggested which has better performance in the fractional order system. Also, a rule-base is presented which leads to better results in type 1 and type 2 fuzzy controllers. The risk of the proposed controllers in different conditions is analyzed. Finally, according to the other analyzing methods, it is shown that this analyzing method has more accurate results.     

Speed control of induction motors using a novel fuzzy sliding-modestructure

This paper presents a new approach to indirect vector control of induction motors. Two nonlinear controllers, one of sliding mode type and the other PI-fuzzy logic-based, define a new control structure. Both controllers are combined by means of an expert system based on Takagi-Sugeno fuzzy reasoning. The sliding-mode controller acts mainly in a transient state while the PI-like fuzzy controller acts in the steady state. The new structure embodies the advantages that both nonlinear controllers offer: sliding-mode controllers increasing system stability limits, and PI-like fuzzy logic based controllers reducing the chattering in permanent state. The scheme has been implemented and experimentally validated     

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.     

一种新型的滑模变结构增益调度控制器设计方法

研究影响一般滑动模态变结构控制性能的因素,并给出了根据切换函数选择滑动模态系数、边界层厚度以及控制器增益系数的一般要求．针对一类含参数不确定性的非线性系统,采用新型增益调度变结构控制策略进行控制,以切换函数作为调度变量对滑动模态系数、边界层厚度以及控制器增益系数进行调度,以提高滑动模态变结构控制系统的控制性能,抑制颤振,降低控制能耗．仿真算例验证了所提出控制策略的有效性．     

大型空间飞行器的高阶滑模姿态控制律设计

针对大型空间飞行器的大角度姿态控制问题,考虑航天器惯量矩阵中的不确定性和外部扰动力矩,应用高阶滑模控制方法设计了姿态跟踪控制律.采用的二阶滑模控制方法改善了系统针对不确定性及外部扰动的鲁棒性,并减弱了振颤现象.针对所设计的控制器进行了仿真验证,并与一阶滑模控制进行了对比,仿真结果表明了所提出方法的有效性.