非对称输入饱和下的非仿射不确定系统自抗扰反演控制

针对一类具有内部动态和外部扰动未知以及非对称输入饱和约束的非仿射系统,提出一种自抗扰反演控制方法.首先基于自抗扰控制思想,通过直接从非仿射项中提取线性控制项,将非仿射系统转化为仿射非线性形式.在此基础上, 在每一步反演控制器设计中,引入扩张状态观测器对系统总的不确定项进行估计,引入跟踪微分器解决虚拟导数的“计算膨胀”问题.在设计真实控制律时,利用双曲正切函数设计一种辅助补偿系统,用来处理输入饱和引起的控制量偏差.基于Lyapunov稳定性定理证明了闭环系统的所有信号有界且跟踪误差可渐近收敛到原点的任意小邻域内.仿真比较结果验证了所提出方法的有效性,体现了一定的工程应用价值.     

一类输入饱和非仿射非线性系统的非线性动态逆控制

输入饱和是实际系统中经常遇到的问题,很多已有的控制方法要求被控系统具有仿射结构.本文针对一类具有输入饱和的非仿射纯反馈非线性系统提出了一种基于奇异值摄动理论的非线性动态逆控制方法.首先构建一个快变子系统,在慢时间尺度下将非仿射非线性系统转换为具有仿射结构的线性系统,从而应用已有的控制算法实现控制目的.为了消除输入饱和带来的影响,建立一个中间子系统对理想控制量与输入饱和限制下控制量的差进行估计和补偿.所提出的控制方法不依赖于被控系统固有的时标分离特性,并能证明闭环系统指数跟踪参考轨迹.该方法具有良好的扩展性,可以根据实际需求与多种控制算法相结合.与动态面控制器和传统近似动态逆控制器的对比仿真结果验证了本文控制方法的有效性.     

非仿射系统的自适应观测器自抗扰控制

研究了一类单输入单输出(SISO)非仿射非线性系统的控制问题,通过微分同胚变换以及自抗扰思想将该类形式转化成含有未知非线性且控制增益未知的仿射形式.引入扩展状态自适应观测器以及Nussbaum-type增益技术,利用积分反演和调节函数技术,设计了自抗扰控制器.从理论上证明了所设计的控制器能够保证闭环系统所有信号全局一致有界,并且证明了跟踪误差渐近收敛到零点的残集内.仿真例子验证了算法的有效性.     

基于反馈线性化的MIMO非最小相位系统指数镇定

针对仿射多输入多输出非线性非最小相位系统,提出了一种新的镇定方案.用反馈线性化解耦系统输入输出关系,通过高增益状态反馈镇定系统外部动态,用模型预测控制镇定内部动态,所设计控制器能保证闭环系统的指数稳定性.仿真结果表明了所提出方法的有效性和优越性.     

一类非仿射非线性时滞系统的动态状态反馈镇定

本文讨论了一类非仿射非线性时滞系统的全局镇定问题.通过引入辅助积分系统和构造合适的LyapunovKrosovskii泛函,提出了一种基于反推法的时滞无关动态状态反馈控制器,所提控制方法无需时滞的任何先验知识.利用Lyapunov稳定性理论证明了该控制策略能够保证非仿射时滞系统状态渐近收敛于原点,且所有闭环信号全局有界.一个仿真实例进一步验证了所得控制方案的可行性与有效性.     

基于神经网络的非仿射块控非线性系统动态反演控制

即使已知非仿射非线性系统的逆存在,利用隐函数定理求解该显式逆仍然非常困难.为此,针对一类不确定块控非仿射系统,将动态反馈、反演、神经网络和反馈线性化技术相结合,提出一种自适应鲁棒控制器的设计方法.利用神经网络来逼近和消除未知函数,并证明了整个闭环系统在李雅普诺夫意义下是稳定的.仿真结果表明了所提出方法的有效性.     

受限的非仿射非线性系统的自适应控制

针对受限的非仿射非线性系统,结合自抗扰思想提出了非仿射系统的扩张状态观测器(ESO)设计,从而将辅助系统设计技巧拓展到了非仿射系统,然后利用反演和指令滤波器设计了自适应控制器,为受限的不确定非仿射系统提供了新的设计思路.为了补偿受限带来的影响,引入了辅助系统,它的状态被用来补偿跟踪误差.指令滤波器用来处理虚拟控制受限问题,同时获得虚拟控制导数的估计,避免了backstepping中对它的繁琐计算,扩张状态观测器被用来估计系统的未知非仿射非线性项和外部干扰.利用输入状态稳定性(ISS)分析了闭环系统的全局一致有界稳定性.最后仿真结果验证了该设计方案的有效性.     

非仿射纯反馈系统的间接自适应神经网络控制

针对非仿射纯反馈系统,提出了一种新的设计方案.与现有文献中方法不同,该方案不是直接利用逼近技巧构建理想的反馈控制器.首先通过自抗扰思想将非仿射纯反馈系统转化成含有未知控制系数以及未知非线性的仿射系统,并且证明了可行性.然后结合微分器和全调节径向基函数神经网络,利用自适应反演技巧设计了自抗扰控制器,微分器的引入避免了传统反演的计算复杂性.最后,从理论上证明了所设计的控制器能够保证闭环系统所有信号半全局一致有界,并且证明了系统状态渐进收敛到零点的残集内.仿真例子验证了算法的有效性.     

线性自抗扰控制的适用性及整定

线性自抗扰控制将被控对象看成串级积分系统,把其他信息都当成不确定性.这种处理方法简单,但是对什么样的系统有效,目前还没有理论给出确定的答案.本文证明任何带有积分行为的严格正则传递函数都可以由线性自抗扰控制的反馈控制器等价实现,从而表明线性自抗扰控制具有广泛的适用性,即只要其他线性控制方法能够控制的系统,线性自抗扰控制同样可以适用.为简化线性自抗扰控制器参数整定,本文针对工业过程中广泛存在的PID控制器,提出将PID参数转化为二阶自抗扰控制参数的方法.该方法转化的线性自抗扰参数以带宽形式表示,从而保留了传统线性自抗扰简单易调的特性,为线性自抗扰控制在工业过程的应用准备了基础.     

基于反馈线性化的MIMO非最小相位系统指数镇定

针对仿射多输入多输出非线性非最小相位系统,提出了一种新的镇定方案.用反馈线性化解耦系统输入输出关系,通过高增益状态反馈镇定系统外部动态,用模型预测控制镇定内部动态,所设计控制器能保证闭环系统的指数稳定性.仿真结果表明了所提出方法的有效性和优越性.

     

Adaptive fuzzy output-feedback fault-tolerant tracking control of a class of uncertain nonlinear switched systems

ABSTRACT

This paper considers the output-feedback fault-tolerant tracking control problem for a class of uncertain nonlinear switched systems with nonlinear faults and strict-feedback form, where the faults which are nonaffine occur on the actuator. As a kind of specialised function approximating tool, fuzzy logic systems (FLSs), are employed to approximate the unknown smooth nonlinear functions. A switched fuzzy observer is designed to address the problem of unmeasurable states, filtered signals are used to address algebraic loop problem and the average dwell time (ADT) method is further utilised to prove the stability of the resulting closed-loop systems under a type of slowly switching signals. Based on the backstepping recursive design technique and Lyapunov function method, an adaptive fuzzy output-feedback control scheme is developed. The developed control method can ensure all the signals are semi-globally uniformly ultimately bounded (SGUUB) and the system output tracks the reference signal tightly even if unknown fault occurs. A simulation carried on an example demonstrates the validity of the obtained control scheme.     

Output feedback performance recovery in the presence of uncertainties

We propose an output-feedback tracking controller for uncertain, nonaffine, nonlinear systems. The output feedback controller results in a closed-loop system with a three-time-scale structure; an extended high-gain observer estimates unmeasured states and uncertainties in the fastest time scale and dynamic inversion is used to deal with nonaffine inputs and input uncertainties in the intermediate time scale while the plant dynamics evolves in the slowest time scale. The dynamic inversion algorithm is based on sector conditions and results in exponential convergence of the inputs. Together with the extended high-gain observer, dynamic inversion results in performance recovery of a target system. The singular perturbation method is used to analyze the stability and performance of the system and numerical simulations are used to demonstrate the effectiveness of the control design.     

Globally Stabilizing a Class of Underactuated Mechanical Systems on the Basis of Finite-Time Stabilizing Observer

Globally exponentially stabilizing a class of underactuated mechanical systems (UMS) with nonaffine nonlinear dynamics is investigated in this paper. The considered UMS has a nonaffine nonlinear subsystem that can be globally asymptotically stabilized by saturated feedbacks, but the saturated feedback cannot be analytically expressed in closed-form. This obstacle limits the real-time applications of most controllers presented in literatures. In this paper, a hybrid feedback strategy is presented to globally exponentially stabilize the UMS with nonaffine and strict-feedback canonical forms. The hybrid feedback strategy is characterized by the composition of partial states feedback and partial virtual outputs feedback based on a higher-order finite-time stabilizing observer. The presented hybrid feedback controller can be synthesized by applying Lyapunov stability theory. Some numerical simulations associated with two underactuated nonlinear systems, the Acrobot system and the Inertia-Wheel-Pendulum (IWP) system, are employed to demonstrate the effectiveness of the proposed controller. The presented control strategy can be applied in real time, thus providing a new feasible dynamic model other than the differential flatness systems for synthesizing the mechanical systems of general underactuated legged robots.     

Linear adaptive control of a class of SISO nonaffine nonlinear systems

This paper addresses the problem of linear adaptive control for a class of uncertain continuous-time single-input single-output (SISO) nonaffine nonlinear dynamic systems. Using the implicit function theory, the existence of an ideal controller which can achieve control objectives is firstly demonstrated. However, this ideal controller cannot be known and computed even if the system model is well known. The aim of our work is to construct this unknown ideal controller using a simple linear controller with the free parameters updated online by a stable adaptation mechanism designed to minimise the error between the unknown ideal controller and the used linear controller. Since the mathematical model of the system is assumed unknown in this work, the proposed control scheme can be regarded as a simple model free controller for the studied class of nonaffine systems. We prove that the closed-loop system is stable and all the signals are bounded. An application of the proposed linear adaptive controller for a nonaffine system is illustrated through the simulation results to demonstrate the effectiveness of the proposed control scheme.     

一阶时滞系统线性自抗扰控制器参数稳定域分析

当使用线性自抗扰控制器(linear active disturbance rejection controller,LADRC)控制时滞系统时,闭环系统的稳定性与控制器参数的选取有较大的关系.如何定量求取线性自抗扰针对时滞系统的参数稳定域还没有有效的方法.本文针对线性自抗扰控制器控制一阶时滞系统,利用双轨迹法精确求解出了线性自抗扰控制器参数的稳定域.该方法利用双轨迹的图形性质,有效地将求解具有时滞的控制系统闭环特征方程根的分布问题转化为求解双轨迹交点频率的问题,从而得到能够保证闭环系统稳定性的控制器参数稳定域.求得的稳定域为时滞系统线性自抗扰控制器的整定提供了理论依据.仿真结果验证了所提出方法的有效性.     

一类轻载电液位置伺服系统线性自抗扰控制

为解决一类轻载电液位置伺服系统线性自抗扰控制器设计过程中面临的阶次选择问题,本文从系统特性、频域等角度,分析自抗扰框架中“积分器串联结构”与轻载电液位置伺服系统之间的内在联系,得到轻载电液位置伺服系统在自抗扰控制框架下是本质“一阶”系统的结论,从而合理设计了1阶线性自抗扰控制器.在此基础上,提出了有效的控制器参数整定方法,并分析了闭环系统的稳定性.仿真和试验结果表明,与高阶相比1阶线性自抗扰控制器可以更好地控制动态过程较快、负载较轻的惯性负载电液位置伺服系统,为自抗扰控制在液压伺服领域的工程应用提供了参考.     

Adaptive neural network control for a class of low-triangular-structured nonlinear systems

In this paper, a class of unknown perturbed nonlinear systems is theoretically stabilized by using adaptive neural network control. The systems, with disturbances and nonaffine unknown functions, have low triangular structure, which generalizes both strict-feedback uncertain systems and pure-feedback ones. There do not exist any effective methods to stabilize this kind of systems. With some new conclusions for Nussbaum-Gain functions (NGF) and the idea of backstepping, semiglobal, uniformal, and ultimate boundedness of all the signals in the closed-loop is proved at equilibrium point. The two problems, control directions and control singularity, are well dealt with. The effectiveness of proposed scheme is shown by simulation on a proper nonlinear system.     

Adaptive Dynamic Surface Control for Stabilization of Parametric Strict-Feedback Nonlinear Systems With Unknown Time Delays

The robust stabilization method via the dynamic surface control (DSC) is proposed for uncertain nonlinear systems with unknown time delays in parametric strict-feedback form. That is, the DSC technique is extended to state time delay nonlinear systems with linear parametric uncertainties. The proposed control system can overcome not only the problem of ldquoexplosion of complexityrdquo inherent in the backstepping design method but also the uncertainties of the unknown time delays by choosing appropriate Lyapunov-Krasovskii functionals. In addition, we prove that all the signals in the closed-loop system are semiglobally uniformly bounded. Finally, an example is provided to illustrate the effectiveness of the proposed control system.     

具有输入约束和输出噪声的不确定系统级联线性自抗扰控制EI北大核心CSCD

针对一类具有输入约束和输出噪声的SISO(Single input single output)不确定非线性系统,提出了一种基于误差补偿和工程滤波的抗饱和级联线性自抗扰控制(Linear active disturbance rejection control,LADRC)方法.首先针对高频量测噪声,分析了线性扩张状态观测器(Linear extended state observer,LESO)对噪声的放大机理及其与观测器增益的定量关系,进而设计了一种基于工程滤波器的级联LADRC方法,在滤除噪声的同时有效补偿了因滤波所造成的输出幅值和相位损失,确保了闭环系统的跟踪精度.然后继续考虑输入饱和的问题,利用LADRC的实时估计/补偿能力,通过将饱和差值信号引入LESO,设计了一种基于误差补偿的抗饱和LADRC方法,有效减小了系统设计控制量,避免了系统长时间陷入饱和.通过实时仿真比较,验证了所提出方法的有效性.