Robust control of nonlinear systems by estimating time variantuncertainties

In this paper, robust control design is considered for nonlinear systems with time-variant uncertainties. Instead of assuming that the bounding function on uncertainties is either known or parameterizable in terms of unknown constants, uncertainties or their bounding functions are estimated. It is shown that bounded uncertainties from a known or partially known exo-system can be estimated as a part of a globally stabilizing robust control. The proposed method extends the existing results of adaptive robust control, and it makes robust control more applicable by requiring less information on uncertainties     

非匹配不确定MIMO系统的分数阶终端滑模控制

针对一类非匹配不确定多输入多输出(Multi-input multi-output, MIMO)系统提出一种分数阶终端滑模控制(Fractional-order terminal sliding-mode, FOTSM)策略, 使系统输出收敛到零而非其邻域. 该方法解除传统反步法控制律设计中, 虚拟控制增益右伪逆矩阵必须存在的严苛限制; 对系统不确定性的假设不局限于慢时变和H2范数有界型扰动, 分析控制增益存在摄动情况下系统的控制问题. 分数阶终端滑模面及其控制律的设计使得虚拟和实际控制信号连续, 削弱抖振现象, 利用自适应滑模切换增益技术解决由控制增益矩阵摄动引起的代数环问题. 最后, 仿真分析验证所提方法的正确性和优越性.     

非匹配不确定系统的自适应反步非奇异快速终端滑模控制

针对一类n阶非匹配不确定系统,提出一种自适应反步非奇异快速终端滑模控制方法.控制的前n-1步采用自适应反步控制策略,消除非匹配不确定性的影响;最后一步利用误差的积分构造非奇异快速终端滑模面,设计控制律使系统第n个状态有限时间收敛.该方法对系统中匹配和非匹配不确定项均具有鲁棒性,比自适应反步终端滑模方法具有更快的收敛速度.理论分析证明了闭环系统的稳定性,仿真结果验证了该方法的有效性.     

状态约束下连铸结晶器振动位移系统的抗干扰控制

针对伺服电机驱动的连铸结晶器振动位移系统中存在的机械加工精度误差、摩擦非线性等不确定性和负载转矩扰动等问题,考虑伺服电机单方向变速转动产生的状态约束,提出了一种基于切换函数的抗干扰控制方案。首先,针对系统中状态约束且不可测及前向通道含有非线性周期函数（近似正弦函数,逆解非唯一）传递关系的问题,通过建立偏心轴转角误差与结晶器振动位移之间的函数关系,解决系统自身的状态约束问题。其次,针对系统存在的不确定性和负载转矩扰动问题,设计切换函数重构系统中存在的整体不确定性,通过扩张状态观测器对整体不确定性进行估计,将估计值与滑模控制方法相结合设计输出反馈控制器,实现结晶器振动位移的跟踪控制。最后,通过Lyapunov理论证明了控制系统的稳定性,通过仿真验证了本文所提方法的有效性。     

TORA系统基于自调节滑模干扰补偿器的解耦滑模控制

针对欠驱动TORA系统,提出一种基于自调节滑模干扰补偿器的解耦滑模控制方法。所提出的控制方法无需系统不确定性上界的先验信息,对于系统不确定性具有良好的适应性。该控制方法包括设计一种自调节滑模干扰补偿器和一种新型的双幂次趋近律,所设计的自调节滑模干扰补偿器能够利用切换增益自适应算法准确逼近上界未知的系统不确定性,所提出的新型双幂次趋近律能够保证系统状态的快速趋近并抑制控制器的高频抖动。采用Lyapunov稳定性理论证明闭环控制系统的稳定性,并通过数值仿真实验验证所提出的控制方法的有效性。     

Robust gaze-steering of an active vision system against errors in the estimated parameters

Gaze-steering is often used to broaden the viewing range of an active vision system. Gaze-steering procedures are usually based on estimated parameters such as image position, image velocity, depth and camera calibration parameters. However, there may be uncertainties in these estimated parameters because of measurement noise and estimation errors. In this case, robust gaze-steering cannot be guaranteed. To compensate for such problems, this paper proposes a gaze-steering method based on a linear matrix inequality (LMI). In this method, we first propose a proportional derivative (PD) control scheme on the unit sphere that does not use depth parameters. This proposed PD control scheme can avoid uncertainties in the estimated depth and camera calibration parameters, as well as inconveniences in their estimation process, including the use of auxiliary feature points and highly non-linear computation. Furthermore, the control gain of the proposed PD control scheme on the unit sphere is designed using LMI such that the designed control is robust in the presence of uncertainties in the other estimated parameters, such as image position and velocity. Simulation results demonstrate that the proposed method provides a better compensation for uncertainties in the estimated parameters than the contemporary linear method and steers the gaze of the camera more steadily over time than the contemporary non-linear method.     

舰船混沌运动的单输入自适应变结构控制

针对在舰船混沌运动控制中由模型不确定性及外部扰动无法确知所引起的控制结果无法保证的问题,采用自适应控制与滑模变结构控制相结合的方法,在设计切换函数时,将符号函数转移到控制输入的一阶导数当中,有效抑制了变结构控制中的抖振问题,并提出了一种单输入自适应滑模变结构控制方法.实验结果表明,与传统滑模变结构控制相比,新方法能够在系统模型具有不确定性及未知外部扰动的情况下实现舰船混沌运动的良好控制,为舰船混沌运动控制提供了一种可靠的工程实现途径.     

ROBUST VIBRATION CONTROL FOR FLEXIBLE ARMS USING THE SLIDING MODE METHOD

The vibration control of flexible arms is accomplished here using the sliding mode method, where the traditional discontinuous approach is modified by a differentiable one. The higher order modes of the flexible arm are treated as disturbances and are compensated by introducing a disturbance observer. Simplified expressions of the motor angular and the strain moment for the flexible arm with a disturbance observer are obtained, where the remaining disturbance and the model uncertainties are considered as system uncertainties. The robustness of the sliding mode control is effectively employed to cope with the system uncertainties, where the bounds of the uncertainties are adaptively updated. The proposed control law simultaneously causes the motor angular to track a desired signal and the strain moment to approach zero. The stability of the controlled flexible arm is analyzed based on the obtained important fact that a part of the control input is the approximate estimate of a special signal generated by the uncertainty. The motor angular tracking error and the converging speed of the controlled signals are determined by means of design parameters. Experimental results demonstrate the robustness of the proposed method.     

Adaptive Chattering Free Neural Network Based Sliding Mode Control for Trajectory Tracking of Redundant Parallel Manipulators

In this paper, an adaptive chattering free neural network‐based sliding mode control (ACFN‐SMC) method is proposed for tracking trajectories of redundant parallel manipulators. ACFN‐SMC combines adaptive chattering free radial basis function neural networks (RBFN), sliding mode control with online updating the robust term parameters, and a nonlinear compensation item for reducing tracking errors. The stability of the closed‐loop system with modeling uncertainties, frictional uncertainties, and external disturbances is ensured by using the Lyapunov method. The proposed controller has a simple structure and little computation time while securing dynamic performance with expected quality in tracking trajectories of redundant parallel manipulators. In addition, the ACFN‐SMC strategy does not need to know the upper bound of any uncertainties. From the simulation results, it is evident that the proposed control strategy not only has significantly higher robustness capability for uncertainties but also can achieve better chattering elimination when compared with those using existing intelligent control schemes.     

Robust formation control of electrically driven nonholonomic mobile robots via sliding mode technique

This paper proposes a sliding mode formation control method for electrically driven nonholonomic mobile robots in the presence of model uncertainties and disturbances. We use the kinematic model based on the leader-following approach for the formation control of multiple robots. Unlike many researches considering only the kinematic model, we also consider the dynamic model including actuator dynamics to obtain the voltage input because it is more realistic to use the voltage as input than the velocity. Then, the sliding mode control method is used to deal with model uncertainties and disturbances acting on the mobile robots. The stability of the proposed control system is proven using Lyapunov stability theory. Finally, we perform computer simulations to demonstrate the performance of the proposed control system.     

非匹配不确定系统的终端滑模分解控制

针对非匹配多变量模型不确定系统,提出了一种终端滑模分解控制方法.通过状态变换和去耦合处理将系统转换为块能控标准型,它由匹配扰动的值域空间子系统和稳定的非匹配扰动的零动态子系统组成.提出了特殊的终端滑模超曲面,采用滑模控制策略,使值域空间子系统的状态在有限时间内收敛至平衡点,随后非匹配扰动的零动态子系统渐近收敛至平衡点附近的邻域内,且建立了该邻域的范围与系统的非匹配不确定性范围之间的数学关系,并用于系统的设计与分析.所提方法对于维数较高的非匹配不确定系统的控制具有较大的意义,可简化设计,实现递阶控制.仿真实     

Fuzzy neural-based control for nonlinear time-varying delay systems.

In this paper, a partially known nonlinear dynamic system with time-varying delays of the input and state is approximated by N fuzzy-based linear subsystems described by a state-space model with average delay. To shape the response of the closed-loop system, a set of fuzzy reference models is established. Similarly, the same fuzzy sets of the system rule are employed to design a fuzzy neural-based control. The proposed control contains a radial-basis function neural network to learn the uncertainties caused by the approximation error of the fuzzy model (e.g., time-varying delays and parameter variations) and the interactions resulting from the other subsystems. As the norm of the switching surface is inside of a defined set, the learning law starts; in this situation, the proposed method is an adaptive control possessing an extra compensation of uncertainties. As it is outside of the other set, which is smaller than the aforementioned set, the learning law stops; under this circumstance, the proposed method becomes a robust control without the compensation of uncertainties. A transition between robust control and adaptive control is also assigned to smooth the possible discontinuity of the control input. No assumption about the upper bound of the time-varying delays for the state and the input is required. However, two time-average delays are needed to simplify the controller design: 1) the stabilized conditions for every transformed delay-free subsystem must be satisfied; and 2) the learning uncertainties must be relatively bounded. The stability of the overall system is verified by Lyapunov stability theory. Simulations as compared with a linear transformed state feedback with integration control are also arranged to consolidate the usefulness of the proposed control.     

PI Adaptive Fuzzy Control With Large and Fast Disturbance Rejection for a Class of Uncertain Nonlinear Systems

Design of controllers for uncertain systems is inherently paradoxical. Adaptive control approaches claim to adapt system parameters against uncertainties, but only if these uncertainties change slowly enough. Alternatively, robust control methodologies claim to ensure system stability against uncertainties, but only if these uncertainties remain within known bounds. This is while, in reality, disturbances and uncertainties remain faithfully uncertain, i.e., may be both fast and large. In this paper, a PI-adaptive fuzzy control architecture for a class of uncertain nonlinear systems is proposed that aims to provide added robustness in the presence of large and fast but bounded uncertainties and disturbances. While the proposed approach requires the uncertainties to be bounded, it does not require this bound to be known. Lyapunov analysis is used to prove asymptotic stability of the proposed approach. Application of the proposed method to a second-order inverted pendulum system demonstrates the effectiveness of the proposed approach. Specifically, system responses to fast versus slow and large versus small disturbances are considered in the presented simulation studies.     

Parametrized guaranteed cost method with prescribed performance via critic-only ADP for uncertain nonlinear systems and disturbances

In this paper, a novel parametrized guaranteed cost control (PGCC) method with prescribed performance control (PPC) is proposed for nonlinear systems with unknown bounded uncertainties and external disturbances described by Euler-Lagrange (EL) equations. The proposed method is capable of ensuring a robust optimal performance in the presence of dynamics constraints without the specific information of nonlinear perturbation. As a consequence, the conditions in the form of disturbances and uncertainties are also relaxed. The augmented model is converted by transforming the uncertainties and disturbances in the original system to a mismatched term using asymmetric PPC. By designing and modifying the novel guaranteed cost function to account for the maximum value of the nonlinear perturbation, an infinite-horizon PGCC problem is proposed by the unconstrained stationary optimal control problem. The relevant proposed linear parametrized Hamilton-Jacobian-Bellman (PHJB) equation is approximated to solve by a critic-only neural network (NN) with efficient computationally. Uniformly ultimately bounded stability is guaranteed via a Lyapunov-based stability analysis. Finally, numerical simulation results demonstrate the effectiveness of the proposed control scheme.     

Integral Sliding Mode Fault‐Tolerant Control for Spacecraft With Uncertainties and Saturation

An integral sliding mode fault‐tolerant control method is proposed to deal with faults with matched uncertainties, unmatched uncertainties, and input saturation. Integral sliding mode, control allocation, and parameter identification are included in this method. The Lyapunov stability conditions of the integral sliding mode control for uncertainties and input saturation, respectively, are obtained, which denote the robustness extent of the controller. The direct method for control allocation is improved by adding a judgement before calculating for each facet. Finally, the fault‐tolerant scheme is applied to a six‐wheel spacecraft and simulations are given to show its effectiveness.     

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.     

基于模型信息的电静液作动器降阶线性自抗扰控制

针对电静液作动器(electro-hydrostatic actuators, EHA)系统存在内外部扰动、参数不确定性和变控制增益等问题,提出一种基于模型信息的降阶线性自抗扰位置控制方法.首先,基于系统模型信息选取控制增益.其次,通过降阶线性扩张观测器对系统总扰动进行估计,并在控制器中加入扰动项进行补偿.利用奇异摄动理论证明所提控制器可使闭环系统是半全局最终一致有界的,并且当观测器带宽足够大时,所提出的控制器理论上可以使系统输出以所需精度跟踪期望轨迹.仿真结果表明,所提控制方法响应速度较快,控制精度较高,对外部扰动和参数不确定性具有较强的鲁棒性.     

基于扰动观测器的机器人自适应神经网络跟踪控制研究

为解决机器人动力学模型未知问题并提升系统鲁棒性,本文基于扰动观测器,考虑动力学模型未知的情况,设计了一种自适应神经网络（Neural network,NN）跟踪控制器.首先分析了机器人运动学和动力学模型,针对模型已知的情况,提出了刚体机械臂通用模型跟踪控制策略;在考虑动力学模型未知的情况下,利用径向基函数（Radial basis function,RBF）神经网络设计基于全状态反馈的自适应神经网络跟踪控制器,并通过设计扰动观测器补偿系统中的未知扰动.利用李雅普诺夫理论证明所提出的控制策略可以使闭环系统误差信号半全局一致有界（Semi-globally uniformly bounded,SGUB）,并通过选择合适的增益参数可以将跟踪误差收敛到零域.仿真结果证明所提出算法的有效性并且所提出的控制器在Baxter机器人平台上得到了实验验证.     

基于扩张状态观测器的永磁同步电机重复学习控制

本文针对非参数不确定永磁同步电机系统,提出一种基于扩张状态观测器的重复学习控制方法,实现对周期期望轨迹的高精度跟踪.首先,将永磁同步电机中的非参数不确定性分为周期不确定与非周期不确定两部分.其次,构造包含周期不确定的未知期望控制输入,并设计重复学习律估计未知期望控制输入并补偿系统周期不确定.在此基础上,设计扩张状态观测器,估计系统未知状态和补偿非周期性不确定,进而提高系统鲁棒性.与已有的部分限幅学习律相比,本文提出的全限幅重复学习律可以保证估计值的连续性且能够被限制在指定的界内.最后,基于李雅普诺夫方法分析误差的收敛性能,并给出仿真和实验结果验证本文所提方法的有效性.     

基于块控原理的变结构控制

针对一类非匹配不确定性的线性系统 ,基于块控原理 ,提出了一种变结构控制设计方法 .利用反演设计方法来处理系统中的非匹配不确定性 ,再用变结构控制方法来改善系统的性能 .仿真实例证明了所提出的方法的正确性和有效性