Terminal sliding mode control of second-order nonlinear uncertain systems

In this paper, a terminal sliding mode control scheme is proposed for second-order nonlinear uncertain systems. By using a function augmented sliding hyperplane, it is guaranteed that the output tracking error converges to zero in finite time which can be set arbitrarily. In addition, the proposed scheme eliminates the reaching phase problem so that the closed-loop system always shows the invariance property to parameter uncertainties. Copyright © 1999 John Wiley & Sons, Ltd.     

Design of generalized terminal sliding mode control for second-order systems

In this paper, a generalized terminal sliding surface is proposed for second-order systems. It is shown that the proposed scheme guarantees that the system state gets to zero in a finite time, and the proposed generalized terminal sliding surface is a superset of the conventional terminal sliding surfaces. The experimental results are given to show the validity of the main result.     

On the second-order sliding mode control of nonlinear systems with uncertain control direction

This note deals with the implementation of a second-order sliding mode control algorithm for a class of nonlinear systems in which the sign of the high-frequency gain, though constant, is unknown. A specific second-order sliding mode control algorithm, the “Suboptimal” algorithm, is properly modified in order to face the uncertainty in the control direction. It is shown that after a finite time the uncertain sign is identified and the standard finite time convergence takes place from that time on. Simulation results are provided.     

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 ...     

Chattering avoidance by second-order sliding mode control

Relying on the possibility of generating a second-order sliding motion by using, as control, the first derivative of the control signal instead of the actual control, a new solution to the problem of chattering elimination in variable structure control (VSC) is presented. Such a solution, inspired by the classical bang-bang optimal control strategy, is first depicted and expressed in terms of a control algorithm by introducing a suitable auxiliary problem involving a second-order uncertain system with unavailable velocity. Then, the applicability of the algorithm is extended, via suitable modifications, to the case of nonlinear systems with uncertainties of more general types. The proposed algorithm does not require the use of observers and differential inequalities and can be applied in practice by exploiting such commercial components as peak detectors or other approximated methods to evaluate the change of the sign of the derivative of the quantity accounting for the distance to the sliding manifold     

On multi-input chattering-free second-order sliding mode control

A solution to the problem of eliminating the chattering effect, which is always associated with practical implementations of variable structure control, is presented with reference to a class of uncertain multi-input nonlinear systems. The solution procedure relies on the application of an original control approach capable of enforcing a second-order sliding mode (i.e., a sliding regime on a surface s[x(t)]=0 in the system state space, with s˙[x(t)] identically equal to zero, a regime enforced by a control signal depending on s[x(t)], but directly acting only on s¨[x(t)]). Such an approach, in its original formulation, only applies to single-input nonlinear systems with particular types of uncertainties. In the present paper, its validity is extended to multi-input nonlinear systems characterized by uncertainties of more general nature, covering a wide class of real processes     

高阶滑模控制理论综述

滑模控制方法因其结构简单且对系统不确定及外部扰动具有良好的鲁棒性受到人们的广泛关注. 因此, 目前正处于飞速发展阶段. 首先, 本文回顾了滑模控制理论的起源, 简单介绍了传统一阶滑模控制方法的发展; 其次, 列举了几种常用的二阶滑模控制方法, 并介绍了其工作原理; 接着, 总结了高阶滑模控制理论的研究现状, 主要包括齐次性算法和继电–多项式算法的研究成果; 最后, 结合高阶滑模控制方法中需要克服的问题, 讨论了未来可能的研究方向.     

Adaptive second-order sliding mode control with uncertainty compensation

ABSTRACT

This paper endows the second-order sliding mode control (2-SMC) approach with additional capabilities of learning and control adaptation. We present a 2-SMC scheme that estimates and compensates for the uncertainties affecting the system dynamics. It also adjusts the discontinuous control effort online, so that it can be reduced to arbitrarily small values. The proposed scheme is particularly useful when the available information regarding the uncertainties is conservative, and the classical `fixed-gain’ SMC would inevitably lead to largely oversized discontinuous control effort. Benefits from the viewpoint of chattering reduction are obtained, as confirmed by computer simulations.     

Adaptive suboptimal second-order sliding mode control for microgrids

ABSTRACT

This paper deals with the design of adaptive suboptimal second-order sliding mode (ASSOSM) control laws for grid-connected microgrids. Due to the presence of the inverter, of unpredicted load changes, of switching among different renewable energy sources, and of electrical parameters variations, the microgrid model is usually affected by uncertain terms which are bounded, but with unknown upper bounds. To theoretically frame the control problem, the class of second-order systems in Brunovsky canonical form, characterised by the presence of matched uncertain terms with unknown bounds, is first considered. Four adaptive strategies are designed, analysed and compared to select the most effective ones to be applied to the microgrid case study. In the first two strategies, the control amplitude is continuously adjusted, so as to arrive at dominating the effect of the uncertainty on the controlled system. When a suitable control amplitude is attained, the origin of the state space of the auxiliary system becomes attractive. In the other two strategies, a suitable blend between two components, one mainly working during the reaching phase, the other being the predominant one in a vicinity of the sliding manifold, is generated, so as to reduce the control amplitude in steady state. The microgrid system in a grid-connected operation mode, controlled via the selected ASSOSM control strategies, exhibits appreciable stability properties, as proved theoretically and shown in simulation.     

Fast smooth second-order sliding mode control for stochastic systems with enumerable coloured noises

A fast smooth second-order sliding mode control is presented for a class of stochastic systems driven by enumerable Ornstein–Uhlenbeck coloured noises with time-varying coefficients. Instead of treating the noise as bounded disturbance, the stochastic control techniques are incorporated into the design of the control. The finite-time mean-square practical stability and finite-time mean-square practical reachability are first introduced. Then the prescribed sliding variable dynamic is presented. The sufficient condition guaranteeing its finite-time convergence is given and proved using stochastic Lyapunov-like techniques. The proposed sliding mode controller is applied to a second-order nonlinear stochastic system. Simulation results are given comparing with smooth second-order sliding mode control to validate the analysis.     

A multi-regulator sliding mode control strategy for output-constrained systems

This paper proposes a multi-regulator control scheme for single-input systems, where the setpoint of a regulated output must be changed under the constraint that a set of minimum-phase outputs remain within prescribed bounds. The strategy is based on a max–min selector system frequently used in the aerospace field. The regulators used for the regulated and limited outputs are of the sliding mode type, where the sliding variable is defined as the difference between an output and its allowable limit. The paper establishes overall asymptotic stability, as well as invariance properties leading to limit protection. The design methodology is illustrated with a detailed simulation example on thrust control of a turbofan engine.     

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.     

Robust output feedback sampling control based on second-order sliding mode

This paper proposes a new second-order sliding mode output feedback controller. This is developed in the case of finite sampling frequency and uses only output information in order to ensure desired trajectory tracking with high accuracy in a finite time in spite of uncertainties and perturbations. This new strategy is evaluated in simulations on an academic example.     

Super-twisting second-order sliding mode control for a synchronous reluctance motor

This article presents the design and implementation of a super-twisting second-order sliding-mode controller (SOSMC) for a synchronous reluctance motor. Second-order sliding-mode control is an effective tool for the control of uncertain nonlinear systems since it overcomes the main drawbacks of the classical sliding-mode control, i.e., the large control effort and the chattering phenomenon. Its real implementation implies simple control laws, and ensures an improvement in the sliding accuracy with respect to conventional sliding-mode control. This article proposes a novel scheme that is based on the technique of super-twisting second-order sliding-mode control. First, SOSMC is derived mathematically, and then the performance of the proposed method is verified by simulations. The proposed SOSMC shows robustness for variations in the motor parameters and an improvement in the chattering phenomenon.     

Robust dynamic output feedback second-order sliding mode controller for uncertain systems

This paper addresses the problem of designing a dynamic output feedback sliding mode control algorithm to stabilize a linear MIMO uncertain system having relative degree two. Introducing a suitable dynamic compensator into the sliding variable, the additional degree of freedom can be used to robustly guarantee the closed-loop system stability once the system is in the sliding mode. A modified asymptotically stable second-order sliding mode control is analyzed and the proposed controller can obtain the real second-order sliding mode. Finally, the feasibility of the proposed method is illustrated by a numerical example.     

Fixed‐time adaptive sliding mode trajectory tracking control of uncertain mechanical systems

An adaptive fixed‐time trajectory tracking controller is proposed for uncertain mechanical systems in this study. The polynomial reference trajectory is planned for trajectory tracking error. Fractional power of linear sliding mode is applied to design the nonlinear controller, adaptive laws are used to adjust controller parameters. Trajectory planning and fractional power are combined to ensure the tracking‐error convergence in a fixed time. The boundary layer technique is used to suppress the model uncertainties and decrease the chattering phenomenon. The closed‐loop system stability is proved strictly in the Lyapunov framework to show that the trajectory tracking errors and adaptive parameters tend to zero in a fixed time set in advance. Numerical simulation results of robotic manipulators illustrate the effectiveness of the proposed controller.     

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.     

Reduced order observers for the sliding mode control of mechanical systems with elastic joints

In this article the control of mechanical systems with elastic joints is addressed. This kind of system is characterised by a high relative degree. The mechanical control input must be designed to be continuous. Different reduced order observers are introduced and conditions are found to guarantee the exponential convergence of the observation errors. The error stability is ensured provided a certain matrix inequality has a solution. The proposed second-order sliding mode point-to-point controller based on the observed state is proven to stabilise the mechanical system with elastic joints about the desired reference position.     

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.     

A novel robust adaptive second-order sliding mode tracking control technique for uncertain dynamical systems with matched and unmatched disturbances

This paper investigates a robust adaptive second-order sliding mode control method for tracking problem of a class of uncertain linear systems with matched and unmatched disturbances. The fundamental idea of the suggested control method is that the discontinuous sign function is used for the time-derivative of the control signal and hence the smooth control input achieved after an integration process is continuous and removes the chattering problem. Using a PID sliding surface, the finite-time convergence of output tracking errors is obtained. The adaptive gain-tuning control law removes the necessity of gaining information about the upper bounds of the external disturbances. The control system is in the sliding mode and then, tracking errors converge to the origin in a finite time under the presence of the external disturbances. Simulation results on an uncertain numerical system and a turntable servo-system are presented to indicate the effectiveness and feasibility of the proposed scheme.