On adaptive sliding mode control without switching gain overestimation

This paper presents some further results on adaptive sliding mode control (ASMC) for a class of nonlinear systems with bounded uncertain parameters. Given a large initial tracking error, current ASMC design generally produces an unnecessarily large switching gain, consequently leading to a serious chattering problem or a large‐amplitude control jump for the continuous counterpart. To solve such an overadaptation problem, the switching gain adaptation mechanism is first analyzed in this paper, and the adaptation induced by the initial tracking error is suggested to be removed. Then, by exploiting the global sliding mode feature of time‐varying sliding mode control and integral sliding mode control, we present two effective methodologies for ASMC design. The proposed ASMC algorithms ensure that there is no overestimation of the switching gain and the system response is not slowed down when a small switching gain is generated. The validity of the proposed methods is verified by both theoretical analysis and simulation results. Copyright © 2012 John Wiley & Sons, Ltd.     

Discrete time sliding mode control with application to induction motors

This work deals with a sliding mode control scheme for discrete time nonlinear systems. The control law synthesis problem is subdivided into a finite number of subproblems of lower complexity, which can be solved independently. The sliding mode controller is designed to force the system to track a desired reference and to eliminate unwanted disturbances, compensating at the same time matched and unmatched parameter variations. Then, an observer is designed to eliminate the need of the state in the controller implementation. This design technique is illustrated determining a dynamic discrete time controller for induction motors.     

Second order sliding mode block control of single‐phase induction motors

The authors propose a robust nonlinear controller based on a block control linearization technique combined with a second order sliding mode super‐twisting algorithm for controlling the rotor speed of single‐phase induction motors. The block control approach is used to design a sliding manifold in terms of the stator current and its desired value. The super‐twisting sliding mode algorithm is applied then to render the designed manifold be attractive. A nonlinear observer is designed to estimate the unmeasured variables (rotor flux linkages and torque load). Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive sensorless robust control of AC drives based on sliding mode control theory

This paper focuses in the design of a new adaptive sensorless robust control to improve the trajectory tracking performance of induction motors. The proposed design employs the so‐called vector (or field oriented) control theory for the induction motor drives, being the designed control law based on an integral sliding‐mode algorithm that overcomes the system uncertainties. This sliding‐mode control law incorporates an adaptive switching gain in order to avoid the need of calculating an upper limit for the system uncertainties. The proposed design also includes a new method in order to estimate the rotor speed. In this method, the rotor speed estimation error is presented as a first‐order simple function based on the difference between the real stator currents and the estimated stator currents. The stability analysis of the proposed controller under parameter uncertainties and load disturbances is provided using the Lyapunov stability theory. The simulated results show, on the one hand that the proposed controller with the proposed rotor speed estimator provides high‐performance dynamic characteristics, and on the other hand that this scheme is robust with respect to plant parameter variations and external load disturbances. Finally, experimental results show the performance of the proposed control scheme. Copyright © 2006 John Wiley & Sons, Ltd.     

异步电机反馈线性化二阶滑模定子磁链观测器设计

为了提高异步电机定子磁链的观测精度,提出了基于反馈线性化的二阶滑模磁链观测方法,设计了定子磁链观测器,并应用到异步电机直接转矩控制中.为更准确的观测磁链,选取转子磁链为系统输出,运用微分几何理论将异步电机系统的输入/输出线性化,得到以转子磁链为输出的异步电机反馈线性化模型.在此基础上设计基于Super-twisting算法的二阶滑模转子磁链观测器,实现对转子磁链的准确估算,并对所设计的观测器进行稳定性分析.然后再利用转子磁链与定子磁链的关系,估算出定子磁链.将该观测器用于异步电机直接转矩控制中,达到了很好的控制效果.仿真与实验结果验证了该方法的可行性和有效性.     

Decentralized sliding mode control design using overlapping decompositions

This paper discusses overlapping decentralized sliding mode controller design for large-scale continuous-time systems. Design issues, like connective reachability of the sliding manifold and the stability of the sliding mode equations in the expanded and original state spaces are examined. Application of the results to automatic generation control is also discussed briefly.     

Design of first- and second-order sliding mode observers for induction motors using a stator-flux model

We extend current research in the area of ‘sensorless’ control of induction motors by presenting two observers based on first- and second-order sliding mode control theories for the simultaneous estimation of flux and speed. We base the observers on the stator-flux model of the motor instead of the usual rotor-flux model mainly because of the uncertain rotor resistance that plays a significant role in the latter. By designing the observers as if they are sliding mode controllers, we lend the properties of parameter insensitive closed-loop dynamics and finite time convergence to the stator flux and speed estimation schemes. We also present simulation and experimental results to validate the operation of the observers.     

Sliding mode control of wind-induced vibrations using fuzzy sliding surface and gain adaptation

Although fuzzy/adaptive sliding mode control can reduce the chattering problem in structural vibration control applications, they require the equivalent control and the upper bounds of the system uncertainties. In this paper, we used fuzzy logic to approximate the standard sliding surface and designed a dead-zone adaptive law for tuning the switching gain of the sliding mode control. The stability of the proposed controller is established using Lyapunov stability theory. A six-storey building prototype equipped with an active mass damper has been used to demonstrate the effectiveness of the proposed controller towards the wind-induced vibrations.     

Trajectory tracking for an autonomous airship using fuzzy adaptive sliding mode control

We present a novel control approach for trajectory tracking of an autonomous airship.First,the dynamics model and the trajectory control problem of an airship are formulated.Second,the sliding mode control law is designed to track a time-varying reference trajectory.To achieve better control performance,fuzzy adaptive sliding mode control is proposed in which the control gains are tuned according to fuzzy rules,and an adaptation law is used to guarantee that the control gains can compensate for model uncertainties of the airship.The stability of the closed-loop control system is proven via the Lyapunov theorem.Finally,simulation results illustrate the effectiveness and robustness of the proposed control scheme.     

Robust control of delay systems: a sliding mode control design via LMI

This paper considers the sliding mode control of uncertain systems with single or multiple, constant or time-varying state-delays, submitted to additive perturbations. The sliding surface is designed so to maximize the calculable set of admissible delays. The conditions for the existence of the sliding regime are studied by using Lyapunov–Krasovskii functionals and Lyapunov-Razumikhin functions. LMIs are used for the optimization procedure. Two examples illustrate the proposed method.     

动力定位的分数阶双环自适应终端滑模控制

为了解决具有非线性和环境干扰的船舶动力定位系统的控制问题,本文提出了一种基于分数阶双环自适应快速终端滑模控制算法,证明了闭环系统的稳定性,设计了自适应控制律,计算了滑模的收敛时间。控制系统由外环位置姿态环和内环速度环构成,外环滑模控制实现自动定位于期望位置和姿态,内环滑模控制实现对速度和角速度的定位。通过切换函数的设计,对不确定性和外加干扰具有较强的鲁棒性,避免系统出现抖振现象。对双环滑模控制器进行仿真,计算出动力定位外界环境扰动的变速运动情况下的前进位置、横荡位置、艏向角度、前进速度、横荡速度、艏向角速度、前进控制力、横荡控制力和艏向控制力矩等。对外环控制率增益λ2等参数对控制性能的影响进行了比较分析。结果表明,分数阶双环自适应终端滑模控制动态响应要稍快于传统双环控制,且超调量小,调整时间更短,所设计的控制器对有非线性和环境干扰的船舶动力定位系统都具有较强的鲁棒性。本算法为不确定性系统的变结构控制提供了新的解决方案,扩展了滑模控制算法的应用领域。     

一类非线性系统的模糊自适应滑模输出反馈控制

针对一类非线性系统，提出一种新的模糊自适应滑模输出反馈控制方法，该方法不需要非线性系统的状态可测的假设。基于李亚普诺夫函数方法，给出了模糊自适应输出反馈控制律以及在线调节的参数自适应律，证明了模物闭环系统的稳定性和跟踪误差的收敛性。     

Robust sliding mode control of uncertain nonlinear systems

A dynamic sliding mode controller design method is proposed for multiple input-output systems with additive uncertainties. A previous result on the stability of triangular systems is generalised to the case of uniform ultimate boundedness of controlled triangular systems. This is used to prove the stability of the overall closed-loop system. The uncertain system with appropriately chosen sliding mode control is shown to be ultimately bounded if the zero dynamics of the nominal system are uniformly asymptotically (exponentially) stable. The design method is demonstrated with two examples.     

Robust chattering-free sliding mode control of space robot in task space

This paper studies the tracking control problem of a free-floating space robot in a task space. Considering the model uncertainties and external disturbance, a robust sliding mode controller is proposed using the Lyapunov direct method and dissipative theory. To eliminate the chattering phenomenon, an radial basis function （RBF） neural network is applied to replace the discontinuous part of the control signal. A novel on-line learning method of the weights and parameters of the RBF neural network established using Lyapunov function assures the stability of the system. It is proved that the proposed controller can guarantee that the L2 gain from disturbance to tracking error is lower than the given index y. Simulation results show that the control method is valid.     

Robust chattering-free sliding mode control of space robot in task space

This paper studies the tracking control problem of a free-floating space robot in a task space. Considering the model uncertainties and external disturbance, a robust sliding mode controller is proposed using the Lyapunov direct method and dissipative theory. To eliminate the chattering phenomenon, an radial basis function (RBF) neural network is applied to replace the discontinuous part of the control signal. A novel on-line learning method of the weights and parameters of the RBF neural network established using yapunov function assures the stability of the system. It is proved that the proposed controller can guarantee that the L(/sub 2) gain from isturbance to tracking error is lower than the given index γ. Simulation results show that the control method is valid.     

Non-linear adaptive sliding mode switching control with average dwell-time

In this article, an adaptive integral sliding mode control scheme is addressed for switched non-linear systems in the presence of model uncertainties and external disturbances. The control law includes two parts: a slide mode controller for the reduced model of the plant and a compensation controller to deal with the non-linear systems with parameter uncertainties. The adaptive updated laws have been derived from the switched multiple Lyapunov function method, also an admissible switching signal with average dwell-time technique is given. The simplicity of the proposed control scheme facilitates its implementation and the overall control scheme guarantees the global asymptotic stability in the Lyapunov sense such that the sliding surface of the control system is well reached. Simulation results are presented to demonstrate the effectiveness and the feasibility of the proposed approach.     

New variable gain super-twisting sliding mode observer for sensorless vector control of nonsinusoidal back-EMF PMSM

This paper presents a new discrete-time super-twisting sliding mode observer with variable gains for sensorless nonsinusoidal vector control of permanent magnet synchronous motors. This observer is adopted to estimate the back electromotive forces (back-EMF) that are required for the rotor speed estimation and for the nonsinusoidal vector control. In addition, their gains are time-varying to minimize the chattering. So, they are adjusted based on internal states of the super-twisting algorithm. The stability analysis is investigated from the Lyapunov theory for discrete-time systems. Finally, simulation and experimental results are presented to demonstrate the good performance and the effectiveness of the proposed observer.     

Vector control for induction motor drives based on adaptive variable structure control algorithm

This paper presents a new adaptive robust control for induction motor drives. The proposed control scheme is based on the so‐called field oriented control theory that allows to control the induction motor like a separately excited direct current motor drive, where the field flux (produced by the field current) and the armature flux (produced by the armature current) are decoupled. The robust control law is based on the sliding mode control theory, but unlike the traditional sliding mode control schemes, the proposed design incorporates an adaptive switching gain that avoids the need of calculating an upper limit of the system uncertainties. Moreover the proposed control law is smoothed out in order to avoid the high control activity inherent to the switching control laws. The resulting closed loop system is proven to be stable using the Lyapunov stability theory. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Dynamic sliding mode control design using attracting ellipsoid method

A methodology for the design of sliding mode controllers for linear systems subjected to matched and unmatched perturbations is proposed. It is considered that the control signal is applied through a first-order low-pass filter. The technique is based on the existence of an attracting (invariant) ellipsoid such that the convergence to a quasi-minimal region of the origin using the suboptimal control signal is guaranteed. The design procedure is given in terms of the solution of a set of Matrix Inequalities. A benchmark example illustrating the design is given.     

一种用于异步电机矢量控制的新型滑模转子磁链观测器研究

针对异步电机矢量控制需要实现定、转子电路解耦的一个关键问题是准确地观测转子磁链.提出了一种以异步电机在两相同步旋转坐标系下的定子电流和转子磁链为状态变量的基于滑模变结构思想的转子磁链观测器,对滑模变结构输入控制信号的设计使得滑模运动速度与轨迹和滑模面的距离相关联,并利用李亚普诺夫理论证明了算法的收敛性.通过仿真表明,该方法具有较高的转子磁链观测准确度,对转子电阻的变化具有很强的鲁棒性,能够改善异步电机矢量控制调速系统的动静态性能.