基于H∞优化设计分数阶PDμ控制器

本文针对分数阶时滞系统,利用H∞优化理论,设计分数阶PDμ控制器.首先,给定微分阶次μ,利用图解稳定性准则确定并画出分数阶时滞系统的PDμ控制器在（Kp,Kd）参数平面上的稳定域.然后,在稳定域内计算出满足补灵敏度函数的H∞范数约束的控制器比t例增益和微分增益,并确定H∞边界曲线.最后,通过改变H∞控制器的微分阶次,能得到H∞曲线与分数阶次μ之间的关系.     

基于窗口H∞范数的PID控制器优化设计

针对有限频段提出了窗口 H∞ 范数的新概念, 然后给出了有限频段的界实定理及其对偶形式. 按照模型匹配原则, 将 PID 控制器的设计问题转化为窗口 H∞ 范数优化问题, 通过求解 LMI 得到 PID 控制器参数. 仿真结果验证了设计方法的有效性.     

非线性变参数系统的混合 H2/H∞控制

本文研究了一类非线性变参数系统的混合 H2/H∞ 保性能控制问题. 基于Lyapunov稳定性理论, 建立了状态反馈混合 H2/H∞ 保性能控制的可解性条件. 该条件是依赖于状态和参数的线性矩阵不等式, 显式地体现了系统的时变和非线性特性, 通过多项式平方和方法, 可以转化为优化问题. 特别地, 本文构造一种新颖的控制器和Lyapounov范数. 在此基础上, 研究了基于多项式平方技术的不确定非线性变参数系统混合 H2/H∞ 保性能控制问题. 最后, 通过倾转旋翼飞行器实例和数值仿真均验证本文方法的可行性和有效性.     

基于观测器具有不确定性的鲁棒保性能控制

在鲁棒性控制问题的研究中,针对系统状态不可测的具有范数有界不确定性和外界干扰的线性系统,其求解过程繁琐,某些参数选取不当.为了保证闭环系统的稳定性,提出一种基于观测器的鲁棒 H∞保性能控制方法.根据李亚普诺夫原理和H∞理论,获得鲁棒H∞保性能控制器存在的一个充分性条件,用矩阵奇异值分解方法,将控制器和观测器存在条件转化为求解一个线性矩阵不等式的可行性.通过凸优化方法,获得最优的线性二次型性能指标和 H∞性能指标.进行仿真的结果表明,上述方法求解简单,稳定性好,验证了所提方法的有效性.     

具有时延的参数不确定主动悬架广义H2/H∞控制

提出了一种新的综合考虑系统的输入时延和参数不确定性的广义H2/H∞混合控制器设计方法,并将其用于车辆主动悬架设计.假定作动器时延是一个已知其边界但不确定的恒定的量,且系统的小确定参数是范数有界的.针对悬架设计需求,分别用H∞和广义H2性能评价指标反映车身加速度和机械结构设计约束.通过定义一个李亚普诺夫函数来同时满足闭环系统的两个性能指标,将广义H2/H∞混合控制器设计转化为线性矩阵不等式的求解.用两自由度1/4车悬架模型进行仿真,结果表明:不论是否存在有界时延和车身参数变异,控制器始终能给出很好的控制效果.     

基于粒子群优化算法的永磁同步电机H2/H∞混合控制

为了提高永磁同步电机(PMSM)控制系统的控制性能,设计了一种混合H2/H∞控制器。通过混合灵敏度方法设计系统的H∞次优控制器,采用粒子群优化(PSO)算法选取H2性能指标最小的控制器,从而得到混合H2/H∞控制器。采用仿真对所设计控制器的性能与比例积分(PI)控制器进行了对比测试,测试结果证明了混合H2/H∞控制器具有比PI控制器更好的控制效果,同时也表明采用PSO算法进行控制器设计是有效、可行的。     

考虑参数不确定性的主动悬架鲁棒H2/H∞混合控制

基于线性矩阵不等式方法,提出了一种新的考虑参数不确定性的鲁棒H2／H∞控制器设计方法,并用于车辆主动悬架设计．假定系统不确定参数是范数有界的,通过引入同一个Lyapunov矩阵来同时满足闭环系统的也和H∞性能条件,把鲁棒H2／H∞控制器设计转化为具有线性矩阵不等式约束的凸优化问题,进而应用内点法等凸优化技术进行求解．以四分之一车辆模型主动悬架设计为例,进行了数值仿真．结果表明,无论车辆簧上质量是否存在变异,鲁棒H2／H∞控制器均能给出很好的控制效果．     

基于 LMI 的广义系统混合H2/ H∞优化控制

研究了广义线性系统的混合H2／H∞状态反馈优化控制问题。设计一个混合H2／H∞状态反馈控制器，在满足闭环系统的容许性及H∞范数界的同时使得H2范数极小。利用线性矩阵不等式(LMI)方法得到该控制器存在的一个充分条件，并且给出闭环系统H2范数的极小上界。     

不确定离散系统具有H∞性能界的鲁棒LQG状态反馈控制

研究了含有范数有界参数不确定线性离散系统具有H∞性能界的鲁棒LQG状态反 馈控制问题,考虑了有限时域时变及无限时域时不变两种情形.所得的控制器对于所有可容 许的参数不确定都能满足给定的H∞性能界,且为最坏情形H∞性能指标提供了一个最优上 界.对于无限时域时不变情形,该控制器还能保证闭环系统渐近稳定.结果仅需求解一含有 一个尺度参数的Riccati方程.     

线性时变参数系统的混合鲁棒H2/H∞控制

研究具有模型参数不确定性和外部扰动的一类系统，即线性变参数系统（LPV）。考虑参数在多胞内变化，系统状态方程可以由多胞矩阵描述，利用H2／H∞范数条件与系统状态空间实现的线性矩阵不等式（LMI）之间的等价性，来求出H2／H∞。设计问题的解，同时设计含有极点配置的多胞状态反馈控制器，使闭环系统具有所期望的混合H2／H∞性能和动态特性。给出一个弹簧阻尼器算例进行分析求解，仿真说明了系统的鲁棒稳定性和对脉冲干扰的抑制作用，验证了设计方案的有效性。     

Stabilizing sets of PI/PID controllers for unstable second order delay system

In this paper, the problem of stabilizing an unstable second order delay system using classical proportional-integralderivative(PID) controller is considered. An extension of the Hermite-Biehler theorem, which is applicable to quasi-polynomials, is used to seek the set of complete stabilizing proportional-integral/proportional-integral-derivative(PI/PID) parameters. The range of admissible proportional gains is determined in closed form. For each proportional gain, the stabilizing set in the space of the integral and derivative gains is shown to be a triangle.     

New results on the synthesis of PID controllers

This paper considers the problem of stabilizing a first-order plant with dead time using a proportional-integral-derivative (PID) controller. Using a version of the Hermite-Biehler theorem that is applicable to quasi-polynomials, the complete set of stabilizing PID parameters is determined for both open-loop stable and unstable plants. The range of admissible proportional gains is first determined in closed form. For each proportional gain in this range, the stabilizing set in the space of the integral and derivative gains is shown to be either a trapezoid, a triangle or a quadrilateral. For the case of an open-loop unstable plant, a necessary and sufficient condition on the time delay is determined for the existence of stabilizing PID controllers     

基于稳定参数空间的PID 调节器遗传优化设计

提出一种满足平方误差积分（ＩＳＥ）最小的闭环反馈稳定ＰＩＤ调节器遗传优设计方法,运用增广Ｈｅｒｍｉｔｅ－Ｂｉｅｎｌｅｒ定理,解析地给出了使任意给定（稳定或不稳定）被控对象闭环稳定的调节器参数取值范围。在该取值范围内动用遗传优化自救得到了满足指定性能指标（ＩＳＥ）最小撮佳调节器参数值。仿真例子验证了该方法的有效性。     

Synthesis of PID controllers for integral processes with time delay

This article deals with the problem of determination of the stabilizing parameter sets of Proportional‐Integral‐Derivative (PID) controllers for first‐order and second‐order integral processes with time‐delay. First, the admissible stabilizing range of proportional‐gain is determined analytically in terms of a version of the Hermite–Biehler Theorem applicable to quasi‐polynomials. Then, based on a graphical stability condition developed in parameter space, the complete stabilizing regions in an integral‐derivative plane are drawn and identified graphically, not calculated mathematically, by sweeping over the admissible range of proportional‐gain. An actual algorithm for finding the stabilizing parameter sets of PID controllers is also proposed. Simulations show that the stabilizing regions in integral‐derivative space are either triangles or quadrilaterals. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Synthesis of H∞ PID controllers: A parametric approach

This paper considers the problem of synthesizing proportional-integral-derivative (PID) controllers for which the closed-loop system is internally stable and the H_∞-norm of a related transfer function is less than a prescribed level for a given single-input single-output plant. It is shown that the problem to be solved can be translated into simultaneous stabilization of the closed-loop characteristic polynomial and a family of complex polynomials. It calls for a generalization of the Hermite-Biehler theorem applicable to complex polynomials. It is shown that the earlier PID stabilization results are a special case of the results developed here. Then a linear programming characterization of all admissible H_∞ PID controllers for a given plant is obtained. This characterization besides being computationally efficient reveals important structural properties of H_∞ PID controllers. For example, it is shown that for a fixed proportional gain, the set of admissible integral and derivative gains lie in a union of convex sets.     

A new approach to digital PID controller design

In this note, we present a new approach to the problem of designing a digital proportional-integral-derivative (PID) controller for a given but arbitrary linear time invariant plant. By using the Tchebyshev representation of a discrete-time transfer function and some new results on root counting with respect to the unit circle, we show how the digital PID stabilizing gains can be determined by solving sets of linear inequalities in two unknowns for a fixed value of the third parameter. By sweeping or gridding over this parameter, the entire set of stabilizing gains can be recovered. The precise admissible range of this parameter can be predetermined. This solution is attractive because it answers the question of whether there exists a stabilizing solution or not and in case stabilization is possible the entire set of gains is determined constructively. Using this characterization of the stabilizing set we present solutions to two design problems: 1) maximally deadbeat design, where we determine for the given plant, the smallest circle within the unit circle wherein the closed loop system characteristic roots may be placed by PID control and 2) maximal delay tolerance, where we determine, for the given plant the maximal-loop delay that can be tolerated under PID control. In each case, the set of controllers attaining the specifications is calculated. Illustrative examples are included.     

二阶加纯滞后过程的非脆弱PID稳定化控制器设计

根据Hermite-Biehler定理在准多项式稳定性问题上的推广，研究用PID控制器镇定二阶加纯滞后过程的问题，给出了使闭环系统稳定的PID参数区域，并以稳定的PID参数区域内切圆半径为目标函数，寻优得到非脆弱PID控制器参数，最后通过线性规划给出了非脆弱PID稳定化控制器的设计方法。     

参数不确定时滞系统的鲁棒P ID 控制

提出一种简单而有效的参数不确定时滞系统鲁棒PID控制器设计方法．通过在kp-ki平面上绘制稳定边界线,确定稳定的PID控制器参数区域;推导了一阶不稳定时滞系统PI控制器和PID控制器的存在性条件;基于推广到时滞系统的棱边定理,确定所有鲁棒PID控制器参数集．仿真实例表明了该方法的优越性．     

Robust non-fragile fractional order PID controller for linear time invariant fractional delay systems

A fractional order PID controller is designed to stabilize fractional delay systems with commensurate orders and multiple commensurate delays, where the time delays in the system may belong to several distinct intervals. Moreover, the controller parameters should belong to given intervals. In order to stabilize the system, the D-subdivision method is employed to choose the stabilizing set of the controller parameters from their available values. Furthermore, the nearest values of the obtained stabilizing set to their mean values are selected as the controller parameters so that a non-fragile controller is concluded. Two numerical examples evaluate the proposed control design method.     

基于HQ混合灵敏度控制的船用舵机位置伺服系统研究

建立了船用舵机位置伺服系统的数学模型,设计了HQ混合灵敏度控制器,并利用MATLAB／Simulink进行了计算机仿真,研究了其控制特性。结果表明,HQ混合灵敏度控制比常规PID控制具有更好的鲁棒性,可以很好的满足船用舵机位置伺服系统的控制要求,具有很强的实用性。