最大灵敏度指标的分数阶内模控制器设计

针对分数阶控制器设计时参数整定复杂问题,提出一种基于最大灵敏度的分数阶内模控制器设计方法。首先采用粒子群优化算法对原系统模型进行简化处理,在模型简化基础上,根据内模控制原理设计分数阶内模控制器,该控制器仅有一个可调参数,通过这一可调参数可以实现所提控制器的快速整定。最后通过最大灵敏度指标实现分数阶内模控制器的鲁棒整定。仿真结果表明该方法具有良好的控制品质及克服参数摄动的鲁棒性。     

A fractional adaptation law for sliding mode control

This paper presents a novel parameter tuning law that forces the emergence of a sliding motion in the behavior of a multi‐input multi‐output nonlinear dynamic system. Adaptive linear elements are used as controllers. Standard approach to parameter adjustment employs integer order derivative or integration operators. In this paper, the use of fractional differentiation or integration operators for the performance improvement of adaptive sliding mode control systems is presented. Hitting in finite time is proved and the associated conditions with numerical justifications are given. The proposed technique has been assessed through a set of simulations considering the dynamic model of a two degrees of freedom direct drive robot. It is seen that the control system with the proposed adaptation scheme provides (i) better tracking performance, (ii) suppression of undesired drifts in parameter evolution, (iii) a very high degree of robustness and improved insensitivity to disturbances and (iv) removal of the controller initialization problem. Copyright © 2008 John Wiley & Sons, Ltd.     

Adaptive synchronization of fractional‐order complex networks via pinning control

Adaptive synchronization of a class of fractional‐order complex networks is investigated in this paper. On the basis of the fractional‐order system stability theory, adaptive synchronization criteria of fractional‐order complex networks with 0 < q < 1 is achieved. Furthermore, pinning control method is then suggested to control the networks, and adaptive strategy is employed to tune the control gains and coupling strength. Because the nodes with high degree may not be the center of the networks, a new attempt to choose the pinned nodes on the basis of the closeness centrality scheme is proposed. Finally, numerical simulations are given to verify the effectiveness of the proposed approach based on the closeness centrality scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Sliding mode disturbance observer control based on adaptive synchronization in a class of fractional‐order chaotic systems

In this paper, a fractional‐order Dadras‐Momeni chaotic system in a class of three‐dimensional autonomous differential equations has been considered. Later, a design technique of adaptive sliding mode disturbance‐observer for synchronization of a fractional‐order Dadras‐Momeni chaotic system with time‐varying disturbances is presented. Applying the Lyapunov stability theory, the suggested control technique fulfils that the states of the fractional‐order master and slave chaotic systems are synchronized hastily. While the upper bounds of disturbances are unknown, an adaptive regulation scheme is advised to estimate them. The recommended disturbance‐observer realizes the convergence of the disturbance approximation error to the origin. Finally, simulation results are presented in one example to demonstrate the efficiency of the offered scheme on the fractional‐order Dadras‐Momeni chaotic system in the existence of external disturbances.     

Adaptive switching control of uncertain fractional systems: Application to Chua's circuit

Since the introduction of fractional‐order differential equations, there has been much research interest in synthesis and control of oscillatory, periodic, and chaotic fractional‐order dynamical systems. Therefore, in this article, the problem of stabilization and control of nonlinear three‐dimensional perturbed fractional nonlinear systems is considered. The major novelty of this article is handling partially unknown dynamics of nonlinear fractional‐order systems, as well as coping with input saturation along the existence of model variations and high‐frequency sensor noises via just one control input. The method supposes no known knowledge on the upper bounds of the uncertainties and perturbations. It is assumed that the working region of the input saturation function is also unknown. After the introduction of a simple finite‐time stable nonlinear sliding manifold, an adaptive control technique is used to reach the system variables to the sliding surface. Rigorous stability discussions are adopted to prove the convergence of the developed sliding mode controller. The findings of this research are illustrated using providing computer simulations for the control problem of the chaotic unified system and the fractional Chua's circuit model.     

Event-triggered adaptive backstepping tracking control for a class of nonlinear fractional order systems

This article investigates the problem of event-trigger based adaptive backstepping control for a class of nonlinear fractional order systems. By introducing an appropriate transformation of frequency distributed model, the fractional-order indirect Lyapunov method with is obtained. In addition, the event-triggered adaptive controller is developed by employing the event-triggered control approach. Meanwhile, by the proposed adaptive control scheme, all the closed-loop signals are globally uniformly bounded, and the tracking error converges to a small neighborhood of the origin. Finally, simulation results are provided to testify the availability of the presented controller.     

Fractional order model reference adaptive control for anesthesia

The design of a fractional order model reference adaptive control for anesthesia based on a fractional order model is proposed in the paper. This model gets around many difficulties in controller designs based on the pharmacokinetic/pharmacodynamic model, commonly used for anesthesia for theses purposes, and allows to design a simple adaptive controller with stability and positivity of the system ensured via Lyapunov analysis. Also, the convergence of the tracking error to zero is established by applying an extension of the Barbalat lemma, proven in the paper. Simulations illustrate the effectiveness and robustness of the proposed control.     

Mittag‐Leffler state estimator design and synchronization analysis for fractional‐order BAM neural networks with time delays

This paper deals with the extended design of Mittag‐Leffler state estimator and adaptive synchronization for fractional‐order bidirectional associative memory neural networks with time delays. By the aid of Lyapunov direct approach and Razumikhin‐type method, a suitable fractional‐order Lyapunov functional is constructed and a new set of novel sufficient condition are derived to estimate the neuron states via available output measurements such that the ensuring estimator error system is globally Mittag‐Leffler stable. Then, the adaptive feedback control rule is designed, under which the considered FBNNs can achieve Mittag‐Leffler adaptive synchronization by means of some fractional‐order inequality techniques. Moreover, the adaptive feedback control may be utilized even when there is no ideal information from the system parameters. Finally, two numerical simulations are given to reveal the effectiveness of the theoretical consequences.     

Application of adaptive lattice filters to internal model control

An adaptive internal model control (IMC) framework is proposed in this article for infinite impulse response systems. The innovation in this study stems from the relaxed assumption that the controller needs to know a priori the system order. To bypass this restriction, a lattice filter identifies the system's order as well as its reflection coefficients. Within the IMC structure, a lattice‐based controller is utilized in the forward path in cascade with a low‐pass detuning filter. The controller self‐configures its structure according to the estimated system order, while the filter's bandwidth increases as the identifier estimates more accurately the system dynamics. Copyright © 2007 John Wiley & Sons, Ltd.     

交流调速系统的单神经元自适应内模控制

针对感应电机速度控制器的传统设计方法所存在的缺点,提出了单神经元自适应内模速度控制器.首先依据内模控制原理设计出内模速度控制器,该控制器具有PI结构,但只有一个可调参数,且该参数与控制系统的动态特性直接相关,再利用单神经元对此参数进行实时在线调节,实现了系统的自适应控制.在理论分析的基础上,将此控制器应用到基于数字信号处理器实现的交流电机矢量控制系统中.实验结果表明:该方法是一种有效的实时控制策略,它能使调速系统不仅具有良好的动、静态性能,而且具有很强的鲁棒性和自学习能力.     

Robust adaptive passivity-based PIλD control

In this article, we develop proportional, fractional-integral, and derivative () controllers for the regulation and tracking problems of nonlinear systems. The analytic results are obtained by extending the passivity-based approach to include fractional operators. Robustness under parametric uncertainty is dealt with by a combination with an adaptive scheme. It is also shown their robustness under additive noise and their robustness under uncertainty in the derivation order. The advantages in the controlled system performance and in the control energy consumption in comparison to classic PI and proportional integral derivative controllers are illustrated for the quadratic boost converter and a benchmark system in the literature.     

Memory‐based IMC tuning of PID controllers for nonlinear systems

This paper describes a new memory‐based proportional, integral, derivative (PID) controller design. These PID parameters are tuned by the IMC‐PID method, which is derived from the relationship between the internal model control (IMC) and PID control. The IMC‐PID has a user‐specified parameter that greatly influences the control performance. The authors have already proposed a system identification scheme based on the memory‐based approach. In this paper, a new controller design scheme is discussed, whose system parameters and the corresponding suitable user‐specified parameter are simultaneously computed. Finally, the behavior of the newly proposed control scheme is examined in a simulation example. © 2006 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Fractional‐order multivariable composite model reference adaptive control

A novel multivariable composite model reference adaptive control scheme is developed for multivariable fractional‐order systems with arbitrary relative degree. Firstly, by introducing right gain matrix to substitute left gain matrix, the stringent symmetry assumption is no longer required. The design procedures of controller with certain and uncertain high‐frequency gain matrix are then provided, respectively. The (robust) stability of the resulting closed‐loop control system is investigated by indirect Lyapunov method. It is shown that the composite model reference adaptive control can achieve better performance on output tracking than that of model reference adaptive control. Finally, the effectiveness and applicability of the proposed control scheme are demonstrated in 3 numerical examples.     

主汽温系统模糊自适应内模控制

基于内模控制理论,针对火电厂主汽温被控对象的大惯性、大迟延、时变、多干扰的特点,设计了内模-比例串级控制系统,并将量子遗传算法应用于滤波器参数的寻优。并在此基础上结合T-S模糊建模和自适应控制技术,提出了模糊自适应内模控制(fuzzy adaptive internal model control,FAIMC)策略。该方案实现简单,对工况变化具有优良的适应性。对某超临界600 MW直流锅炉主汽温系统4种典型工况进行仿真控制,其过渡过程时间短,超调量小,适用于大惯性、大迟延过程的控制,控制效果明显优于串级PID控制。为克服负荷变化对主汽温系统性能的影响,采用模糊自适应内模控制策略分别进行了升降负荷实验。仿真结果表明：提出的控制系统能较好的适应对象动态模型的大幅度变化,保持较优的调节性能。     

Fractional adaptive systems in the presence of bounded disturbances and parameter variations

This paper presents the analysis of fractional adaptive systems in the presence of bounded disturbances and parameter variations. Fractional adaptive systems are analyzed using the error model approach, to give generality to the results. Modified fractional adaptive laws are proposed to make the adaptive systems robust against bounded disturbances and parameter variations. The boundedness of the signals is analytically proved using Lyapunov functions. A simulation example is included to show the effectiveness of the proposed solutions.     

双神经网络交流传动自适应规划控制

将Hopfield神经网络应用于交流传动系统的自适应控制，通过神经网络来规划交流调速系统的速度控制器动态输出；并将Hopfield神经网络控制器代替矢量控制系统中的转速调节器，使速度控制器具有对某些参数变化良好的鲁棒性。对于不可控的负载转矩分量，加入神经网络负载转矩在线跟踪控制器，形成参数自动跟踪神经网络，构成具有参数在线跟踪功能的交流传动双神经网络自适应规划控制模式，进一步提高了系统的性能．仿真结果证明了该控制方案的有效性．     

规则自适应模糊控制在同步发电机励磁系统中的应用

对于像电力系统这样的典型非线性系统,采用常规PID控制器很难保证系统在不同工作状态下均取得良好的控制效果.采用模糊参数自适应PID励磁控制器对解决小干扰下的励磁控制问题具有较好的控制效果.当系统工作状态变化较大以及遇到较强的干扰时,系统控制性能将趋于恶化.为解决此问题,提出了同步发电机励磁系统的规则自适应模糊控制方案.主要讨论在模糊集Ai、Bi 的比例因子K1、K2、K3给定的条件下,通过调整 di 的取值来实现控制规则的自适应问题, 该规则自适应机构由两组关于控制规则自生成与自校正的元规则组成.仿真结果表明,所提出的方案正确可行并具有良好的性能.     

Indirect model reference adaptive control with dynamic adjustment of parameters

The paper discusses in detail a new method for indirect model reference adaptive control (MRAC) of linear time-invariant continuous-time plants with unknown parameters. The method involves not only dynamic adjustment of plant parameter estimates but also those of the controller parameters. Hence the overall system can be described by a set of non-linear differential equations as in the case of direct control. Many of the difficulties encountered in the conventional indirect approach, where an algebraic equation is solved to determine the control parameters, are consequently bypassed in this method. The proof of stability of the equilibrium state of the overall system is found to be different from that used in direct control. Using Lyapunov's theory, it is first shown that the parameter errors between the parameter estimates of the identifier and the true parameters of the plant, as well as those between the actual parameters of the controller and their desired values, are bounded. Following this, using growth rates of signals in the adaptive loop as well as order arguments, it is shown that the error equations are globally uniformly stable and that the tracking (control) error tends to zero asymptotically. This in turn establishes the fact that both direct and indirect model reference adaptive schemes require the same amount of prior information to achieve stable adaptive control.     

基于预测模型双模糊分数阶PID的BLDCM调速系统优化控制

无刷直流电机（BLDCM）具有复杂的非线性系统,强耦合、变量多等特点,传统的PID控制无法获得满意的控制效果。为此,在模糊控制、分数阶微积分及模型预测相关理论的基础上,提出了预测模型双模糊分数阶PID控制器。分数阶控制为系统提供更多的控制余度,并采用一种间接算法（Oustaloup算法）完成整数阶PID控制的延伸和扩展,模糊控制实现分数阶PID控制参数的在线调整;建立预测模型,并引入模糊控制动态调整预测模型系数K值,实现更加精确的控制。针对模糊分数阶PID控制器中参数选择,又提出了一种改进的万有引力算法进行参数优化,增强控制器的自适应能力。仿真结果表明:基于改进万有引力算法的预测模型双模糊分数阶PID控制的BLDCM调速系统较传统的PID控制具有更快的响应速度、更小的超调量及抗负载扰动能力强等优良的动、静态性能指标。     

Composite learning fuzzy synchronization for incommensurate fractional‐order chaotic systems with time‐varying delays

This paper presents a composite learning fuzzy control to synchronize two different uncertain incommensurate fractional‐order time‐varying delayed chaotic systems with unknown external disturbances and mismatched parametric uncertainties via the Takagi‐Sugeno fuzzy method. An adaptive controller together with fractional‐order composite learning laws is designed based on both a parallel distributed compensation technology and a fractional Lyapunov criterion. The boundedness of all variables in the closed‐loop system and the Mittag‐Leffler stability of tracking error can be guaranteed. T‐S fuzzy systems are provided to tackle unknown nonlinear functions. The distinctive features of the proposed approach consist in the following: (1) a supervisory control law is designed to compensate the lumped disturbances; (2) both the prediction error and the tracking error are used to estimate the unknown fuzzy system parameters; (3) parameter convergence can be ensured by an interval excitation condition. Finally, the feasibility of the proposed control strategy is demonstrated throughout an illustrative example.