A new fractional-order sliding mode controller via a nonlinear disturbance observer for a class of dynamical systems with mismatched disturbances

This paper investigates the stabilization and disturbance rejection for a class of fractional-order nonlinear dynamical systems with mismatched disturbances. To fulfill this purpose a new fractional-order sliding mode control (FOSMC) based on a nonlinear disturbance observer is proposed. In order to design the suitable fractional-order sliding mode controller, a proper switching surface is introduced. Afterward, by using the sliding mode theory and Lyapunov stability theory, a robust fractional-order control law via a nonlinear disturbance observer is proposed to assure the existence of the sliding motion in finite time. The proposed fractional-order sliding mode controller exposes better control performance, ensures fast and robust stability of the closed-loop system, eliminates the disturbances and diminishes the chattering problem. Finally, the effectiveness of the proposed fractional-order controller is depicted via numerical simulation results of practical example and is compared with some other controllers.     

Adaptive super-twisting sliding mode observer based robust backstepping sensorless speed control for IPMSM

This paper proposes a higher-order sliding mode observer based robust backstepping control to realize high-performance sensorless speed regulation for the interior permanent magnet synchronous motor (IPMSM). A new robust adaptive super-twisting higher-order sliding mode based observer is proposed to estimate the rotor position. The proposed observer has advantages of sliding chattering reduction and robustness against uncertainties. And, a new robust integral adaptive backstepping control with sliding mode actions is designed to achieve precise speed regulation. The uncertainties with unknown bounds can be stabilized by the sliding mode actions. And both transient and steady performance can be achieved by using the sliding mode and integral actions simultaneously. Then, a sensorless scheme is put forward to by combining the presented observer and the proposed controller. The stability of the observer and controller are verified. Simulation and experiment results validate the proposed approach.     

阀控缸系统有限时间滑模控制

针对阀控缸系统稳态跟踪误差的收敛时间均为非有限时间内收敛到0的问题，提出了一种终端滑模控制方法。解决了液压系统非有限时间收敛问题，使得跟踪误差在有限时间内收敛到0。首先，运用终端滑模控制方法通过构造终端函数方式引入非线性项，设计终端滑模面来保证系统的全局鲁棒性和稳定性；其次，基于Lyapunov稳定性理论设计终端滑模控制器，保证位置跟踪误差在有限时间内收敛到0并验证其稳定性；最后，利用阀控缸系统模型以正弦信号及其衍生信号为参考信号对控制策略进行Simulink仿真，表明了终端滑模控制方法的可行性与有效性。     

Continuous higher-order sliding mode control with time-varying gain for a class of uncertain nonlinear systems

This paper presents a continuous higher-order sliding mode (HOSM) control scheme with time-varying gain for a class of uncertain nonlinear systems. The proposed controller is derived from the concept of geometric homogeneity and super-twisting algorithm, and includes two parts, the first part of which achieves smooth finite time stabilization of pure integrator chains. The second part conquers the twice differentiable uncertainty and realizes system robustness by employing super-twisting algorithm. Particularly, time-varying switching control gain is constructed to reduce the switching control action magnitude to the minimum possible value while keeping the property of finite time convergence. Examples concerning the perturbed triple integrator chains and excitation control for single-machine infinite bus power system are simulated respectively to demonstrate the effectiveness and applicability of the proposed approach.     

A new continuous sliding mode control approach with actuator saturation for control of 2-DOF helicopter system

The 2-degree of freedom (DOF) helicopter system is a typical higher-order, multi-variable, nonlinear and strong coupled control system. The helicopter dynamics also includes parametric uncertainties and is subject to unknown external disturbances. Such complicated system requires designing a sophisticated control algorithm that can handle these difficulties. This paper presents a new robust control algorithm which is a combination of two continuous control techniques, composite nonlinear feedback (CNF) and super-twisting control (STC) methods. In the existing integral sliding mode (ISM) based CNF control law, the discontinuous term exhibits chattering which is not desirable for many practical applications. As the continuity of well known STC reduces chattering in the system, the proposed strategy is beneficial over the current ISM based CNF control law which has a discontinuous term. Two controllers with integral sliding surface are designed to control the position of the pitch and the yaw angles of the 2- DOF helicopter. The adequacy of this specific combination has been exhibited through general analysis, simulation and experimental results of 2-DOF helicopter setup. The acquired results demonstrate the good execution of the proposed controller regarding stabilization, following reference input without overshoot against actuator saturation and robustness concerning to the limited matched disturbances.     

Integral backstepping sliding mode control for underactuated systems: Swing-up and stabilization of the Cart–Pendulum System

In this paper an integral backstepping sliding mode controller is proposed for controlling underactuated systems. A feedback control law is designed based on backstepping algorithm and a sliding surface is introduced in the final stage of the algorithm. The backstepping algorithm makes the controller immune to matched and mismatched uncertainties and the sliding mode control provides robustness. The proposed controller ensures asymptotic stability. The effectiveness of the proposed controller is compared against a coupled sliding mode controller for swing-up and stabilization of the Cart–Pendulum System. Simulation results show that the proposed integral backstepping sliding mode controller is able to reject both matched and mismatched uncertainties with a chattering free control law, while utilizing less control effort than the sliding mode controller.     

Sliding mode control with PID sliding surface and experimental application to an electromechanical plant

In this study, a sliding mode control system with a proportional+integral+derivative (PID) sliding surface is adopted to control the speed of an electromechanical plant. A robust sliding mode controller is derived so that the actual trajectory tracks the desired trajectory despite uncertainty, nonlinear dynamics, and external disturbances. The proposed sliding mode controller is chosen to ensure the stability of overall dynamics during the reaching phase and sliding phase. The stability of the system is guaranteed in the sense of the Lyapunov stability theorem. The chattering problem is overcome using a hyperbolic function for the sliding surface. Experimental results that are compared with the results of conventional PID verify that the proposed sliding mode controller can achieve favorable tracking performance, and it is robust with regard to uncertainties and disturbances.     

复合滑模控制在精密PMLSM激光切割运动平台的应用

针对永磁直线同步电机激光切割运动平台的位置伺服控制低抖振、高精度、强鲁棒的要求,在传统双幂次滑模趋近律的基础上,提出一种变边界层的双幂次滑模趋近律带滑模扰动观测器的复合趋近律滑摸控制方法。变边界层方法是对控制系统的控制精度要求和降低抖振的权衡,而所提出的方法又继承了传统双幂次滑模趋近律方法的有限时间收敛特性。为了降低控制系统设计的保守性,设计了一种基于超螺旋算法的滑模扰动观测器对系统的未知扰动进行估计,并在此算法中添加一个幂指数,通过仿真实验证明了提高幂指数的数值可加快未知扰动的估计值的收敛速度。结合Lyapunov稳定性理论,证明了闭环系统的稳定性。最后,搭建了用于激光切割的永磁直线同步电机平移试验台对所提出的控制器进行测试。实验结果表明:本文所提出的控制器的位置跟踪误差不超过1μm,且误差波动较小,能够满足伺服控制系统的要求。     

存在死区的双柔杆空间机器人有限时间控制与抑振

探讨了存在关节力矩输出死区情况下,基于有限时间的漂浮基双柔杆空间机器人系统的轨迹跟踪与柔性抑振问题。采用奇异摄动理论,将系统的动力学方程分解为慢变与快变子系统,分别表示刚性运动与柔性振动。针对模型存在不确定性和死区参数未知的慢变子系统,设计了死区预补偿器和一种基于名义模型的有限时间控制器。引入了具有有限时间收敛特性的积分式滑模面,它与传统渐近收敛控制方法相比,具有更快的收敛速度、更好的鲁棒性和抗干扰特性。对于快变子系统,采用线性二次最优控制方法主动抑制其振动,以保证系统良好的稳定性。结合有限时间稳定性引理,采用李雅普诺夫理论证明了所提控制算法能使跟踪误差在有限时间内收敛到原点。仿真算例验证了所提方法的有效性。     

磁悬浮控制力矩陀螺高速转子的高精度位置控制

在受到陀螺效应、动框架效应等影响后产生的磁力非线性问题是磁悬浮控制力矩陀螺(MSCMG)高速转子位置精度下降的主要因素。为解决以上问题,提高转子位置精度,本文分析了转子所受磁力的特性,建立了转子系统非线性动力学模型,提出了神经网络滑模控制方法。设计滑模控制律,采用径向基函数神经网络逼近控制律中的非线性模型,自适应算法根据误差在线调整神经网络的权值,同时可以保证整个系统的稳定性。仿真和实验结果表明,所提出方法的转子位置精度达到99%,稳态误差为0.000 2 mm。神经网络滑模控制可以实现MSCMG转子系统的高精度位置控制。     

Model-free adaptive integral terminal sliding mode predictive control for a class of discrete-time nonlinear systems

In this paper, a new model-free adaptive digital integral terminal sliding mode predictive control scheme is proposed for a class of nonlinear discrete-time systems with disturbances. The characteristic of the proposed control approach is easy to be implemented because it merely adopts the input and output data model of the system based on compact form dynamic linearization (CFDL) data-driven technique, while the technique of perturbation estimation is applied to estimate the disturbance term of the system. Moreover, by means of combining model predictive control and CFDL digital integral terminal sliding mode control (CFDL-DITSMC), the CFDL digital integral terminal sliding mode predictive control (CFDL-DITSMPC) method is proposed, which can further improve the tracking accuracy and disturbance rejection performance in comparison with the CFDL model-free adaptive control, neural network quasi-sliding mode control and the CFDL-DITSMC scheme. Meanwhile, the stability of the proposed approach is guaranteed by theoretical analysis, and the effectiveness of the proposed method is also illustrated by numerical simulations and the experiment on the two-tank water level control system.     

Dynamic output feedback sliding mode control for uncertain mechanical systems without velocity measurements

For MIMO mechanical systems using position measurements only, this paper presents a dynamic output feedback sliding mode control algorithm in which an additional dynamics is introduced into the design of the sliding surface. Although the system has the mismatched uncertainty and external disturbance, once the system is in the sliding mode, the proposed method can guarantee robust stabilization and sustain the nature of performing disturbance attenuation through utilizing H_∞ control analytical technique. A controller is then designed to drive the system to the sliding surface in a finite time and stay on it thereafter. Finally, a numerical example is explained for demonstrating the applicability of the proposed scheme.     

A novel adaptive sliding mode control with application to MEMS gyroscope

This paper presents a new adaptive sliding mode controller for MEMS gyroscope; an adaptive tracking controller with a proportional and integral sliding surface is proposed. The adaptive sliding mode control algorithm can estimate the angular velocity and the damping and stiffness coefficients in real time. A proportional and integral sliding surface, instead of a conventional sliding surface is adopted. An adaptive sliding mode controller that incorporates both matched and unmatched uncertainties and disturbances is derived and the stability of the closed-loop system is established. The numerical simulation is presented to verify the effectiveness of the proposed control scheme. It is shown that the proposed adaptive sliding mode control scheme offers several advantages such as the consistent estimation of gyroscope parameters including angular velocity and large robustness to parameter variations and external disturbances.     

Optimal second order sliding mode control for linear uncertain systems

In this paper an optimal second order sliding mode controller (OSOSMC) is proposed to track a linear uncertain system. The optimal controller based on the linear quadratic regulator method is designed for the nominal system. An integral sliding mode controller is combined with the optimal controller to ensure robustness of the linear system which is affected by parametric uncertainties and external disturbances. To achieve finite time convergence of the sliding mode, a nonsingular terminal sliding surface is added with the integral sliding surface giving rise to a second order sliding mode controller. The main advantage of the proposed OSOSMC is that the control input is substantially reduced and it becomes chattering free. Simulation results confirm superiority of the proposed OSOSMC over some existing.     

基于干扰观测器的弹丸协调臂Terminal滑模控制

为了解决某火炮弹丸协调臂电液伺服系统位置控制精度问题和鲁棒性问题,提出了一种基于扰动观测器的弹丸协调臂Terminal滑模控制策略。推导出弹丸协调臂电液伺服系统的动力学方程,将系统的参数不确定性以及外界扰动处理为干扰项。采用指数趋近的干扰观测器进行在线观测并在控制律中进行补偿,提高了系统的鲁棒性。同时为了克服传统滑模控制在线性滑模面条件下状态渐进收敛导致无法在有限时间内到达平衡状态的特点,设计了一种全局快速Terminal滑动模态,使系统在有限时间内到达滑模面,系统状态在有限时间内迅速收敛到平衡状态,最后利用Lyapunov证明全局稳定性。仿真结果证明,该控制策略能对电液伺服系统不确定性和干扰具有很好的鲁棒性,且能明显提高弹丸协调臂动态精度与稳态精度。     

基于误差反馈学习的永磁同步电机变负载有限时间速度控制

针对传统永磁同步电机调速系统面对变负载和大范围调速时,P、I参数需要频繁调整且速度跟踪不理想的问题,提出了一种基于误差反馈学习结构的永磁同步电机有限时间速度控制方法。在对永磁同步电机运动方程分析的基础上,使用非线性PI和径向基神经网络建立了速度环控制器模型。前者保证控制系统收敛和稳定,其输出作为神经网络的误差学习参数;后者基于终端滑模理论设计参数调整律,加快神经网络的参数收敛速度,使得神经网络的输出逐渐取代非线性PI成为控制系统的主要控制器。利用李雅普诺夫稳定判据分析了控制器的收敛性,并在永磁同步电机调速系统上进行了试验。研究结果表明,基于误差反馈学习结构的有限时间控制策略能够减小系统静态误差和抖振,具有一定的抗干扰能力。     

Sliding mode disturbance observer-based control of a twin rotor MIMO system

This work proposes a robust tracking controller for a helicopter laboratory setup known as the twin rotor MIMO system (TRMS) using an integral sliding mode controller. To eliminate the discontinuity in the control signal, the controller is augmented by a sliding mode disturbance observer. The actuator dynamics is handled using a backstepping approach which is applicable due to the continuous chattering-free nature of the command signals generated using the disturbance observer based controller. To avoid the complexity of analytically differentiating the command signals, a first order sliding mode differentiator is used. Stability analysis of the closed loop system and the ultimate boundedness of the tracking error is proved using Lyapunov stability arguments. The proposed controller is validated by several simulation studies and is compared to other schemes in the literature. Experimental results using a hardware-in-the-loop system validate the robustness and effectiveness of the proposed controller.     

Chaos synchronization of uncertain chaotic systems using composite nonlinear feedback based integral sliding mode control

This paper proposes a combination of composite nonlinear feedback and integral sliding mode techniques for fast and accurate chaos synchronization of uncertain chaotic systems with Lipschitz nonlinear functions, time-varying delays and disturbances. The composite nonlinear feedback method allows accurate following of the master chaotic system and the integral sliding mode control provides invariance property which rejects the perturbations and preserves the stability of the closed-loop system. Based on the Lyapunov- Krasovskii stability theory and linear matrix inequalities, a novel sufficient condition is offered for the chaos synchronization of uncertain chaotic systems. This method not only guarantees the robustness against perturbations and time-delays, but also eliminates reaching phase and avoids chattering problem. Simulation results demonstrate that the suggested procedure leads to a great control performance.     

Robust finite time cooperative control of second order agents:A Multi-input Multi-output higher order super-twisting based approach

This paper studies the formation of multiple mobile agents with double integrator dynamics and their target tracking. An algorithm consisting of an observer and a feedback control law of the nonsmooth type is proposed for the purpose of achieving finite-time formation and target tracking. The development is based on the Multi-input Multi-output (MIMO) super-twisting like approach aiming at finite time convergence without chattering. In addition to the formation; tracking, chattering prevention and robustness is also provided by the sliding mode mechanism which is demonstrated by simulations.     

基于RBF网络滑模的电动助力制动系统液压力控制

针对汽车电动助力制动系统（Electro-booster,EBooster）的液压力控制中液压负载的非线性和不一致性问题,提出一种基于径向基函数（Radial based function,RBF）神经网络的滑模变结构控制方法。设计EBooster系统压力控制架构,建立液压制动系统等效结构简化模型,据此设计基于RBF网络滑模变结构的液压力控制方法,通过设计RBF网络的自适应律来实现系统滑模控制参数的自适应调整,并利用李雅普诺夫函数方法分析算法的稳定性。最后搭建电动助力制动系统的快速原型试验平台来验证算法的有效性。试验结果表明,采用RBF神经网络滑模变结构的控制策略对电动助力制动系统液压力的控制误差在2%以内,具有良好的控制效果。研究成果为EBooster系统的压力控制提出一种具有良好自适应性的算法设计思路。