饱和时滞非线性系统的间接线性矩阵不等式抗饱和设计

当时滞非线性系统具有执行器饱和时,其稳定性无法得到保证.为了寻找饱和时滞非线性系统的稳定控制器,本文阐述了一种间接线性矩阵不等式(LMI)一步抗饱和设计方法.首先,利用Takagi-Sugeno (T–S)模糊模型将一类饱和时滞非线性系统精确重构,引入输出反馈并行分布补偿系统得到闭环控制系统.然后,运用李雅普诺夫稳定性理论,导出闭环系统的稳定条件,利用一个矩阵不等式的等价引理,将闭环系统稳定条件间接的转化为两个LMIs条件,进而得到间接LMI抗饱和补偿算法,同时给出了吸引域估计及其优化模型.最后给出了应用此方案的一个仿真实例.     

一类非线性系统的模糊可靠H2/H∞混合控制器设计的LMI方法

基于T-S模糊模型,利用线性矩阵不等式(LMI)方法,研究一类非线性系统的模糊可靠H2/H∞混合控制器设计问题.首先,分别以LMI形式给出了系统模糊可靠H2及H∞控制器存在的充分条件和控制器设计方法;然后.给出系统混合H2/H∞性能的可靠控制器设计方法,所设计的控制器使得故障闭环系统二次稳定,同时满足H∞性能,且优化系统的H2性能指标,最后,通过数值例子验证了结论的正确性和控制器设计方法的有效性.     

一类具有执行器饱和的非线性系统抗饱和方法研究

针对一类具有执行器饱和的非线性控制系统, 提出了一种双环路的动态抗饱和补偿方案, 为执行器输出受限的非线性系统提供了新思路. 与现有结果相比, 所提方案能更好地改善闭环系统控制性能. 考虑执行器饱和约束, 通过优化执行器饱和发生前后控制器的状态误差的积分性能指标, 综合设计一类同时包含传统抗饱和及延迟抗饱和补偿器两个环路的改进抗饱和补偿器, 这类补偿器有效地抑制了饱和现象对控制器的影响, 从而降低了执行器饱和对控制系统性能的影响. 当系统存在高饱和度现象时, 利用该双环路抗饱和补偿器, 可以最大程度弱化饱和对系统性能的影响. 最后, 利用输入状态稳定 (Input state stability, ISS) 定理分析和证明了该闭环系统全局一致有界稳定. 并通过舵机执行器受约束的舵减横摇系统的仿真试验, 验证了该方案的有效性及优越性.     

基于扩张状态观测器的动态抗饱和补偿器设计方法

针对一类受外界扰动以及执行器饱和影响的不确定非线性系统,提出一种基于扩张状态观测器的动态抗饱和补偿器设计方法.首先通过将系统的不确定项以及外部扰动作为扩张状态,设计线性扩张状态观测器(ESO)对系统的总扰动进行估计;然后,在控制器中引入对扩张状态的估计值,对系统的总扰动进行补偿,设计了动态抗饱和补偿器,将控制器、观测器以及动态抗饱和补偿器的参数求解问题转化为基于LMI不等式组约束的优化问题,确保系统具有尽可能大的收敛域;最后通过数值仿真验证所提出设计方法的有效性.     

基于系统输出的嵌套饱和系统抗饱和补偿器设计

针对嵌套输入饱和系统的吸引域扩大问题,本文提出了一种基于系统输出的抗饱和补偿器激发策略,将被控系统输出信号经性能补偿器馈入到抗饱和补偿器激发环节中,形成蕴含系统实时性能信息的抗饱和激发新机制,克服了传统抗饱和激发机制无法直接反映系统性能的缺点.基于上述抗饱和控制新框架,本文建立了抗饱和补偿器及性能补偿器存在的充分条件,并依此构建了优化问题求解最优补偿器增益以实现扩大闭环系统吸引域的目的.仿真结果表明本文方法的有效性.     

采用条件技术设计AIMC结构的抗饱和控制器

AIMC(Anti-windup IMC)结构是内模控制与扰动观测器相结合的抗饱和控制结构,为了有效地解决AIMC结构中的抗饱和控制器的设计问题,提出了采用条件技术设计AIMC结构中的抗饱和控制器的方法。分析了AIMC结构是一种二自由度的新型IMC结构,能够同时解决扰动及饱和问题。通过引入条件技术的可行性参考输入的概念,给出了抗饱和控制器的设计方法。给出了运用该方法的一个仿真实例,仿真结果表明所设计的系统具有良好的抗饱和性能及抗扰动性能。采用条件技术设计AIMC结构中的抗饱和控制器,计算简便,在没有引入新的不确定参数的条件下改善了系统的整体性能。该方法是一种很有实际价值的抗饱和控制器的设计方法。     

一类饱和不确定非线性系统静态抗饱和控制设计

研究一类执行器幅值与速率饱和的不确定非线性系统静态抗饱和控制问题.采用线性微分包含的方法处理系统模型中的非线性项.给出了抗饱和补偿器设计方法,该方法能同时保证闭环鲁棒稳定及鲁棒性能.给出了此类非线性系统代数环良定的充要条件,从而将抗饱和补偿器设计问题转化为线性矩阵不等式约束的凸优化问题.最后通过仿真算例说明了所提出方法的有效性.     

一类非线性系统的模糊可靠H2/H∞混合控制器设计的LMI方法

基于T-S模糊模型,利用线性矩阵不等式(LMI)方法,研究一类非线性系统的模糊可靠 H2/H∞混合控制器设计问题.首先,分别以LMI形式给出了系统模糊可靠H2及 H∞ 控制器存在的充分条件和控制器设计方法;然后,给出系统混合 H2/H∞性能的可靠控制器设计方法,所设计的控制器使得故障闭环系统二次稳定,同时满足 H∞ 性能,且优化系统的H2性能指标;最后,通过数值例子验证了结论的正确性和控制器设计方法的有效性.

     

具有反馈增益不确定的Delta算子系统H∞控制

基于线性矩阵不等式（LMI）方法，研究Delta算子系统状态反馈增益具有加性不确定时的H∞非脆弱控制器的设计问题．给出既能保证闭环Delta算子系统稳定，又有一定H∞性能的充分必要条件．利用相关引理把该充分必要条件转化为LMI形式．数值算例表明。所提出的设计方法是有效的．     

一类饱和不确定非线性系统静态抗饱和控制设计

研究一类执行器幅值与速率饱和的不确定非线性系统静态抗饱和控制问题.采用线性微分包含的方法处理系统模型中的非线性项.给出了抗饱和补偿器设计方法,该方法能同时保证闭环鲁棒稳定及鲁棒性能.给出了此类非线性系统代数环良定的充要条件,从而将抗饱和补偿器设计问题转化为线性矩阵不等式约束的凸优化问题.最后通过仿真算例说明了所提出方法的有效性.

     

Incorporating anti-windup gain in improving stability of actuator constrained linear multiple state delays systems

This paper proposes the design of anti-windup compensator gain for improving stability of actuator input constrained linear multiple state delays systems. The system state delays are classified into mixed delay-dependent/delay-independent analysis and described by delay-differential equations. The real scalar delays are assumed to be fixed and unknown, but with known coefficient matrices. It is shown that the closed-loop system containing the controller plus the anti-windup gain can be modeled as a linear system with dead-zone nonlinearity. The formulation of anti-windup compensator gain is based on convex optimization using linear matrix inequalities (LMI) that ensure closed-loop asymptotic stability of the system while accounting upper-bound delays. The devised LMIs based on Lyapunov-Krasovskii functionals prove significantly less conservative in giving higher upper bounds delays in the formulation of anti-windup gain besides ensuring closed-loop asymptotic stability.     

基于观测器的发动机怠速控制

针对发动机怠速控制系统时滞、不确定性等特点,提出一种基于状态观测的状态反馈控制方法。根据发动机力学原理建立发动机数学模型,并给出Luenberger型状态估计;基于Lyapunov泛函理论,给出闭环系统鲁棒渐近稳定的充分条件。进一步,运用矩阵奇异值分解（SVD）和线性矩阵不等式（LMI）方法,获得观测-状态反馈控制器参数的求解方法。所得结果以LMI形式给出,可以方便地利用Matlab工具箱求解。通过数值仿真,表明该方法的有效性。     

Active Disturbance Rejection Control for Uncertain Nonlinear Systems With Sporadic Measurements

This paper deals with the problem of active disturbance rejection control (ADRC) design for a class of uncertain nonlinear systems with sporadic measurements. A novel extended state observer (ESO) is designed in a cascade form consisting of a continuous time estimator, a continuous observation error predictor, and a reset compensator. The proposed ESO estimates not only the system state but also the total uncertainty, which may include the effects of the external perturbation, the parametric uncertainty, and the unknown nonlinear dynamics. Such a reset compensator, whose state is reset to zero whenever a new measurement arrives, is used to calibrate the predictor. Due to the cascade structure, the resulting error dynamics system is presented in a non-hybrid form, and accordingly, analyzed in a general sampled-data system framework. Based on the output of the ESO, a continuous ADRC law is then developed. The convergence of the resulting closed-loop system is proved under given conditions. Two numerical simulations demonstrate the effectiveness of the proposed control method.      

内模强化学习型模型预测控制及其在人工胰脏上的应用

在学习型模型预测控制的框架里,迭代学习控制器被用来更新模型预测控制器的设定点.在已经发表的研究成果里,学习型模型预测控制用到的是比例型的学习率,这种学习率的学习能力有限,而且怎样设计学习增益仍然是一个开放性问题.在本文中,基于内模控制理论提出的PID型的迭代学习控制器被用来更新模型预测控制器的设定点.为了方便起见,本文提出的结合算法可称为内模强化学习型模型预测控制.本文提出的算法应用在(1)型糖尿病人的人工胰脏闭环控制上.仿真结果显示,本算法对比于比例学习型模型预测控制可以达到更好的收敛性能,而且对非重复干扰有很好的鲁棒性.     

Data-based Fault Tolerant Control for Affine Nonlinear Systems Through Particle Swarm Optimized Neural Networks

In this paper, a data-based fault tolerant control (FTC) scheme is investigated for unknown continuous-time (CT) affine nonlinear systems with actuator faults. First, a neural network (NN) identifier based on particle swarm optimization (PSO) is constructed to model the unknown system dynamics. By utilizing the estimated system states, the particle swarm optimized critic neural network (PSOCNN) is employed to solve the Hamilton-Jacobi-Bellman equation (HJBE) more efficiently. Then, a data-based FTC scheme, which consists of the NN identifier and the fault compensator, is proposed to achieve actuator fault tolerance. The stability of the closed-loop system under actuator faults is guaranteed by the Lyapunov stability theorem. Finally, simulations are provided to demonstrate the effectiveness of the developed method.      

不确定线性系统迭代学习控制器的设计

推导出采用闭环动态迭代学习律的不确定线性系统收敛充分条件, 把它转化为系统输出反馈H_∞控制问题, 然后用线性矩阵不等式 (LMI)方法系统设计迭代学习控制器, 控制器具有鲁棒性较强、阶次较低等优点. 最后仿真结果表明该设计方法的有效性.     

Static output feedback control design for linear MIMO systems with actuator dynamics governed by diffusion PDEs

This paper deals with the problem of static output feedback (SOF) control design for a class of diffusion partial differential equation (PDE) and ordinary differential equation (ODE) cascades, where the ODE model is used to describe the dynamics of the multi-input and multi-output (MIMO) plant and the diffusion PDE model is employed to represent the dynamics of actuators. The objective of this paper is to develop a simple as well as effective SOF controller via the Lyapunov's direct method such that the resulting closed-loop system is globally exponentially stable. By constructing a quadratic Lyapunov function, the sufficient condition on the globally exponential stability of the closed-loop cascaded system is presented in terms of linear matrix inequality (LMI). Then, an LMI-based design method of the SOF controller is developed on the basis of the obtained stability analysis result. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed design method.     

Controller synthesis for uncertain fuzzy systems with integrating multiple time-varying delays

This article mainly investigates the controller synthesis for uncertain fuzzy systems with integrating multiple time-varying delays, which can describe a much larger class of nonlinear systems or uncertain time-delay systems. First, a sufficient stability condition for the unforced Takagi–Sugeno (T-S) fuzzy models with multiple time-varying delays and uncertainties are derived. By involving the parallel distributed compensator (PDC), some design conditions for the resulting closed-loop fuzzy systems are further presented. These proposed conditions are all expressed in terms of linear matrix inequalities (LMIs), and we can readily perform the PDC synthesis from current LMI solvers. Numerical examples are given to demonstrate the validity and superiority of the proposed approach.     

T-S模糊系统的二次稳定

应用LMI(线性矩阵不等式)方法,研究了T-S模糊系统二次稳定性及控制器设计问题.首先,通过考虑模糊系统隶属函数的性质,将原系统进行变换,给出了T-S模糊系统二次稳定的新条件,并提出了基于LMI的控制器设计方法.与现有结果相比,该方法不仅考虑了各子系统间的关系,还考虑到隶属函数的性质,计算量和保守性较小.仿真算例验证了其有效性.     

Tuning algorithms for fractional order internal model controllers for time delay processes

This paper presents two tuning algorithms for fractional-order internal model control (IMC) controllers for time delay processes. The two tuning algorithms are based on two specific closed-loop control configurations: the IMC control structure and the Smith predictor structure. In the latter, the equivalency between IMC and Smith predictor control structures is used to tune a fractional-order IMC controller as the primary controller of the Smith predictor structure. Fractional-order IMC controllers are designed in both cases in order to enhance the closed-loop performance and robustness of classical integer order IMC controllers. The tuning procedures are exemplified for both single-input-single-output as well as multivariable processes, described by first-order and second-order transfer functions with time delays. Different numerical examples are provided, including a general multivariable time delay process. Integer order IMC controllers are designed in each case, as well as fractional-order IMC controllers. The simulation results show that the proposed fractional-order IMC controller ensures an increased robustness to modelling uncertainties. Experimental results are also provided, for the design of a multivariable fractional-order IMC controller in a Smith predictor structure for a quadruple-tank system.