基于周期控制的有限集输入通道任意增益/相角裕度调节方法

针对有限多输入多输出(MIMO)线性时不变(LTI)对象集,提出了一种调节输入通道增益/相角裕度的方法,采用离散线性二次调节器(LQR)理论和周期控制方法设计一个针对有限对象集的线性周期控制器.该控制器可使有限对象集的所有反馈控制回路在输入通道同时实现任意大的增益裕度和直到90°的相角裕度.仿真结果表明了该方法的有效性.     

一种解析的模糊PI自整定方法

针对模糊PID控制器缺乏系统的整定方法的问题,提出了一种解析的基于增益裕度和相位裕度的模糊PI控制器的参数自整定方法。首先推导出模糊PI控制器的解析模型,该解析模型包括线性控制器和非线性补偿控制器2个部分。参数整定时,将非线性补偿控制器看作过程的扰动,由线性控制器和被控对象的一阶纯时滞模型,基于系统的增益裕度和相位裕度,导出模糊PI控制器的参数。仿真结果表明,对于时变高阶系统,和传统的PI控制器相比,模糊PI控制器具有鲁棒性强,超调小,调整时间短等优点。     

基于继电反馈自整定PID控制器研究及应用

研究控制器优化问题,提出了一种改进型的继电反馈自整定PID,用来控制自衡过程.改进型的继电环节是由一个标准的继电环节串联一个比例积分控制器组成,比例积分控制器的比例系数设定为单位增益,积分时间由保持最小相角裕度为π/6来确定.自整定PID控制器的参数是根据改进型的继电环节产生的极限环的输出数据确定的,微分时间常数需保持上述提到的相角裕度.积分时间常数等于改进型继电环节中的比例积分控制器的积分时间,进行仿真.结果PID控制器可用到造纸机的热泵供汽控制中,并收到了明显效果.     

连续时间多胞线性变参数系统变增益H∞/H2输出反馈控制

针对一类同时具有参数不确定性和外界干扰的非线性系统,提出了一种连续时间多胞线性变参数(LPV)系统变增益H_∞/H_2输出反馈控制方法.首先,对连续时间多胞LPV系统的变增益混合目标(H_∞/H_2指标和区域极点约束)输出反馈控制器综合方法进行了数学描述;其次,引入新的结构化松弛矩阵变量和参数依赖Lyapunov函数,将满足期望性能的混合目标鲁棒动态输出反馈控制问题转化为线性矩阵不等式框架内的有限维凸优化问题,进一步降低了所设计LPV控制器的保守性.最后,以四分之一车辆模型主动悬架系统为研究对象进行仿真,仿真结果验证了本文控制器的有效性.     

线性连续时间时滞系统的有限时间有界跟踪控制

研究一类线性连续时间时滞系统的有限时间有界跟踪控制问题.首先,采用预见控制理论中求导的方法构造带有时滞的误差系统,把误差信号的信息包含在误差系统的状态向量中,再将其作为误差系统的输出向量;其次,通过为误差系统设计一个有记忆的状态反馈控制器,把问题转化为研究带有时滞的误差系统的闭环系统输入-输出有限时间稳定问题;再次,借鉴输入-输出有限时间稳定的研究方法和线性矩阵不等式的方法, 通过构造Lyapunov-Krasovskii函数,给出由一组线性矩阵不等式表征的控制器增益矩阵的设计方法,由此得到原系统的一个有限时间有界跟踪控制器;最后,通过一个数值实例验证所设计的控制器的有效性和优越性.     

基于自适应滑模观测器的不匹配非线性系统执行器故障重构

针对一类含有未知干扰的不匹配非线性Lipschitz系统,提出了基于自适应滑模观测器的执行器故障重构方法.首先引入辅助输出矩阵,使得辅助输出系统的观测器匹配条件得以满足,同时设计了高增益观测器实现对未知辅助输出的精确估计;然后针对辅助输出系统建立故障重构滑模观测器,设计了自适应律在线修正滑模控制器增益,考虑故障上界未知的前提下,提出了观测器状态估计误差稳定的存在定理,运用Schur补引理将观测器反馈增益矩阵设计方法转化为求解线性矩阵不等式约束优化问题,同时引入线性变换矩阵,在故障上界未知的前提下设计了滑模控制增益,使得输出估计误差收敛稳定,确保了滑模运动在有限时间内发生,在此基础上利用等效控制输出误差注入原理实现了执行器故障重构;最后通过仿真算例验证了本文方法的有效性.     

积分二次约束线性系统的H∞控制器设计:一种LMI方法

基于动态耗散理论, 给出了具有积分二次约束线性系统稳定和具有L₂有限增益的充分条件. 导出了积分二次约束线性系统H_∞ 状态反馈和动态输出反馈降阶控制器的设计方法, 并转化为多个线性矩阵不等式, 利用LMI工具箱求解.     

有限频域线性重复过程的动态迭代学习控制

针对不同相对度的离散线性重复过程,研究有限频域范围的动态迭代学习控制问题.对于零相对度和高相对度的控制对象,结合二维(2D)系统理论,分别设计有限频域的动态迭代学习控制器;然后,运用广义Kalman-Yakubovich-Popov (KYP)引理,以线性矩阵不等式(LMI)的形式给出控制器存在的充分条件以及控制器的增益矩阵;最后,在弹簧阻尼系统和桁架机器人模型的仿真中,与静态迭代学习控制算法进行比较,验证所提算法的优越性和可行性.     

基于可视化的PI控制器参数整定方法

在控制器优化设计问题的研究中,PI控制器的参数通常采用归一参数法和试凑法来整定,很难得到最优的整定参数.为解决上述问题,提出了一种快速且有效的四维数据可视化算法的PI控制器参数整定方法.采用可视化方法将伯德图图形簇体现在四维可视化幅频特性图和相频特性图里,可直接观察kp,ki与幅频特性和相频特性的关系,并可间接地将幅值裕度和相角裕度表现在频域特性里,通过观察频域特性的变化来达到整定的目的.仿真实例表明,提出的方法适用于低阶或高阶被控对象,得到了满意的效果,为控制器优化设计提供了依据.     

机器人多胞变增益输出反馈H∞控制

针对n类关节的刚性机器人,提出一种设计包含极点配置的多胞变增益输出反馈H_∞控制器的新方法.利用平衡族附近的线性化,机器人系统可化为一关于平衡族的连续线性变参数系统,通过引入滤波器得到易于设计变增益控制器的增广对象,并将其凸分解为多胞表示,基于二次D 稳定和二次H_∞性能概念,利用多胞特性将整个控制器设计转化为对胞体顶点控制器的设计,然后利用LMI方法,对多胞的各顶点分别设计满足H_∞∞性能和动态特性的输出反馈控制器,最后综合顶点控制器得到具有同     

Robust compensation of time delayed plant by continuous‐time high frequency periodic controller with negligible output ripples

The present work addresses the problem of ensuring robust stability to time delayed plants, compensated with continuous‐time high frequency periodic controller. An efficient design methodology is proposed to synthesize the periodic controller for robust compensation of time delayed linear time‐invariant plants. The periodic controller, by virtue of its loop zero‐placement capability, is shown to achieve superior gain as well as phase/delay margin compensation, especially for non‐minimum phase plants having right half plane poles and zeros in close vicinity to each other. The periodic controller is considered in the observable canonical form which results in realizable bounded control input as well as ensuring insignificant periodic oscillations in the plant output. As a consequence, this paper, furthermore, establishes the fact that the periodic controller designed and synthesized with the proposed methodology can be implemented in real‐time with an assurance of model matching and robust zero‐error tracking. Simulation and experimental results are illustrated to establish the veracity of the claims. The closed‐loop system comprising of time‐delayed linear time‐invariant plant with the periodic controller is analyzed employing the averaging principle and presented here explicitly in a meticulous approach. Copyright © 2015 John Wiley & Sons, Ltd.     

Fixed-time output regulation of linear delay systems by smooth time-varying control

This article investigates the fixed-time output regulation problem (FxTORP) for linear systems in the presence of input delay. A linear controller consisting of the linear periodic delayed feedback (PDF) gain and the feedforward gain obtained by solving regulator equations is designed, such that FxTORP is addressed. If only the measurable output can be used for feedback, a linear observer with periodic coefficient and artificial delay is designed so that its state converges to the state of the augmented system at a prescribed finite time. Based on the estimated state, the output regulation problem can also be solved by using observer-based output feedback. The most significant advantages of this article are that the PDF gain can be taken as smooth and the output regulation problem is achieved within a prespecified regulation time. Finally, a simulation example is given to substantiate the validity of the proposed approaches.     

Satisfactory control of discrete-time linear periodic systems

In this paper satisfactory control for discrete-time linear periodic systems is studied. Based on a suitable time-invariant state sampled reformulation, periodic state feedback controller has been designed such that desired requirements of steady state covariance, H-infinity rejection bound and regional pole assignment for the periodic system are met simultaneously. By using satisfactory control theory, the problem of satisfactory periodic controller can be transformed into a linear programming problem subject to a set of linear matrix inequalities （LMIs）, and a feasible designing approach is presented via LMI technique. Numeric example validates the obtained conclusion.     

Disc margins of the discrete-time LQR and its application to consensus problem

This article presents a complex gain margin of discrete-time linear quadratic regulator (DLQR) and its application to a consensus problem of multi-agent higher order linear systems. Since the consensus problem can be converted into a robust control problem with perturbation expressed by complex numbers, and since the classical gain and phase margins are not enough to handle the current case, we study the so-called ‘disc margin’ which is somehow a combination of gain and phase margins. We first compute the disc margin of DLQR controller based on a Lyapunov argument, which is simple but yields a relaxed result over those previously reported in the literature. Then, it is shown that the disc margin can be enlarged arbitrarily when the system is asymptotically null controllable with bounded controls and when a low-gain feedback is employed. Based on this fact, the discrete-time consensus problem is solved by a DLQR-based consensus controller. Simulation study shows that the DLQR-based consensus controller has better robustness property against model uncertainties in the input channel.     

Adaptive learning control of linear systems by output error feedback

This paper addresses the problem of designing an output error feedback tracking control for single-input, single-output uncertain linear systems when the reference output signal is smooth and periodic with known period T. The considered systems are required to be observable, minimum phase, with known relative degree and known high frequency gain sign. By developing in Fourier series expansion a suitable unknown periodic input reference signal, an output error feedback adaptive learning control is designed which ‘learns’ the input reference signal by identifying its Fourier coefficients: bounded closed-loop signals and global exponential tracking of both the input and the output reference signals are obtained when the Fourier series expansion is finite, while global exponential convergence of the input and output tracking errors into arbitrarily small residual sets is achieved otherwise. The structure of the proposed controller depends only on the relative degree, the reference signal period, the high frequency gain sign and the number of estimated Fourier coefficients.     

Frequency-domain design of pid controllers for stable and unstable systems with time delay

An approach for tuning PID-type controllers is developed for single input single-output, linear time-invariant systems, based on an extension to the method of D-partition. This method permits design for simultaneous minimum gain and phase margin requirements. It also allows design for specified maximum gain and phase cross-over frequencies of the controlled system. The technique can be applied to systems with stable or unstable plants as well as to irrational systems with significant time delay. Another advantage of the method is that it can be used for various controller configurations including derivative in the feedback path. Three examples illustrate the tuning method.     

H∞ Output Feedback Control of Linear Time-invariant Fractional-order Systems over Finite Frequency Range

This paper focuses on the H_∞ output feedback control problem of linear time-invariant fractional-order systems over finite frequency range. Based on the generalized Kalman-Yakubovic-Popov (KYP) Lemma and a key projection lemma, a necessary and sufficient condition is established to ensure the existence of the H_∞ output feedback controller over finite frequency range, a desirable property in control engineering practice. By using the matrix congruence transformation, the feedback control gain matrix is decoupled and further parameterized by a scalar matrix. Two iterative linear matrix inequality algorithms are developed to solve this problem. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.      

Control of the INFANTE AUV using gain scheduled static output feedback

The paper describes the design and experimental testing of a control system for the INFANTE AUV in the horizontal plane. The methodology adopted for controller design is nonlinear gain scheduling control, whereby a set of linear finite static output feedback controllers are designed using linear matrix inequality (LMI)-based techniques and scheduled on the vehicle's forward speed. The paper summarizes the basic controller design steps, describes a technique for practical implementation of the nonlinear control system derived, and presents experimental results obtained with the AUV during tests at sea.     

基于灰色预测可变裕度PID网络自适应算法

为了综合控制拥塞链路的队列长度,提高AQM系统对动态网络环境的自适应能力,提出了一种基于灰色预测和考虑可变裕度PID控制的自适应TCP网络主动队列管理。首先,建立相角和幅值裕度与网络参数相关的PID自适应主动队列(TCP/AQM)控制论模型,该模型可以根据网络参数的变化而动态改变控制参数,以提高AQM网络动态自适应能力,及系统的鲁棒性;其次,将灰色预测引入该模型,实现路由器队列长度的超前预测,补偿带有PID反馈模块的AQM算法给队列造成的时滞影响。与其他算法的仿真结果相比较,该设计算法能够使信息流在较短的时间内稳定在期望队列长度阈值附近。