Lambda整定方法的频域分析及工程应用

Lambda是针对自衡对象有效的PID控制器工程整定方法。在频域上针对使用该整定方法的闭环控制系统进行分析,给出了相位裕度和幅值裕度的计算公式,并对λ选择进行了分析。当λ=τ相位裕度和幅值裕度分别达到61.4°和π,这两个参数都非常接近工程推荐的最佳裕度。当被控对象是高阶过程时,可以采用基于响应曲线的控制模型辨识工程方法获得控制模型的等效模型增益、等效时间常数和等效纯滞后时间,然后用Lambda整定公式进行PID整定。仿真结果展示了获得模型的过程和整定方法的有效性。     

一阶时滞过程PID控制器优化准则

对单回路控制系统,期望得到控制器的统一优化准则.以误差积分性能指标描述系统时间响应,以环路函数的频域约束表示系统稳定裕度,从而建立一种综合的鲁棒性能(RP)指标,即系统的稳定裕度和积分性能的指数加权指标.针对比例积分微分( PID)控制器串联一阶时滞过程(FOPDT)的系统,通过计算机数值运算,选择出RP的合理加权因子范围为1～2.以加权因子取1.5的RP作为控制器优化准则,对时滞比从0到∞的FOPDT过程获得了最优PID控制.仿真表明,该法对鲁棒性和积分性能的折中是合适的,对一般工业过程的控制器参数优化有较大的借鉴意义.     

飞行器滚转通道地面半实物仿真系统研究

为了验证飞行器滚转稳定控制系统,搭建了滚转通道地面半实物仿真平台。根据相关分析法,采用扫频技术,测量系统开环和闭环频率响应,验证利用开环频率特性计算闭环频率特性的正确性。考虑飞行器实际飞行条件,选择-15℃的低温弹道作为典型弹道,在与滚转稳定控制系统相关的滚转阻尼与副翼舵偏效率分别变化20%的最坏情况下,测试飞行器滚转稳定控制系统的频域和时域特性。实验结果表明,该半实物仿真系统能够准确有效地测试飞行器滚转稳定控制系统的各种性能。     

基于Maclaurin展开的时间绝对误差积分次优时滞系统设计

根据经典时间绝对误差积分（ITAE）最优系统标准型,给出了ITAE最优时滞系统的期望模型;利用Maclaurin展开技术,讨论了ITAE次优时滞系统的设计方法,并就ITAE次优和最优的三阶系统进行了频域和时域比较.论文最后给出了基于ITAE次优时滞系统的PID和超前滞后补偿器设计实例.阶跃响应、负载扰动以及参数鲁棒性方面的比较研究表明,本文方法能够获得十分满意的性能指标.     

基于多点频率特性辨识的自整定 PID控制器的研究

利用改进的双通道继电反馈测试,获取0～π范围的任意点频率特性,基于多点频率特性设计满足期望的系统闭环频率特性的方法整定PID控制器的参数。仿真表明系统获得了满意的控制性能,是实现自动型工业控制器简单、有效的方法。     

PID控制器增益的稳定范围研究

基于逆Nyquist曲线,提出了一种线性系统在PID控制下确定增益稳定范围的方法,为PID控制器增益的稳定提供了一条快速而有效的途径。由逆Nyquist曲线上的实部为极值的点,将PID增益分割成若干区间。再运用广义的Her—mite-Biehler定理得出一个推理和二个条件,通过纵向直线与逆Nyquist曲线的交点数,可获得系统在PID控制下增益稳定的区间。仿真实例验证了该方法的有效性。该方法应用简便,能有效解决PID控制下增益的稳定范围。     

PID控制器增益的稳定范围研究

基于逆Nyquist曲线,提出了一种线性系统在PID控制下确定增益稳定范围的方法,为PID控制器增益的稳定提供了一条快速而有效的途径。由逆Nyquist曲线上的实部为极值的点,将PID增益分割成若干区间。再运用广义的Her—mite-Biehler定理得出一个推理和二个条件,通过纵向直线与逆Nyquist曲线的交点数,可获得系统在PID控制下增益稳定的区间。仿真实例验证了该方法的有效性。该方法应用简便,能有效解决PID控制下增益的稳定范围。     

基于INA设计方法的多变量PID控制器设计方法的深入研究

基于增大求解方法选择性的目的,本文给出了一种从系统开环传递函数入手求解极限增益和极限频率的计算方法,并以TITO系统为例,给出了详细的推导过程;此外,在详细研究设计方法的基础上,本文以两个典型对象作为研究对象对设置点位置与逆Nyquist阵列（INA）设计方法的多变量PID控制器设计方法的设计性能之间的规律性进行了系列仿真实验研究,并得出：系统开环传递函数矩阵的逆的行Gershgorin带与负实轴的交点（离原点最近的交点）与点（-1,j0）之间的距离越远,系统闭环响应曲线的震荡性越弱,系统的稳定裕量越大。     

基于时-频域指标的控制系统演化校正

针对控制系统校正器参数适应系统时-频域特定性能要求的问题,提出一种基于自适应粒子群算法的控制系统校正方法。它以系统的时域误差积分指标为目标函数,以系统的幅值裕度、相角裕度等频域指标为约束条件建立优化模型。再利用罚函数,将该带约束的目标函数转化无约束的目标函数。之后,在Matlab环境下,将自适应粒子群算法与Simulink仿真技术相结合,优化控制系统校正器参数,从而实现控制系统校正。仿真结果表明,这种方法简单、高效,所设计的校正器性能优异,十分适合于工程应用。     

基于新的误差积分准则的PID控制器优化

用PID控制器控制有共轭极点和负实零点的二阶模型对象,当对象时滞比很小时,用现有准则如ITAE进行优化,很难保证幅值稳定裕度。在广义平方误差积分准则(GISE)的基础上,用对象响应特征时间来平衡准则中误差项与误差变化率项的数量级。并用一个恒大于1的时间函数作为误差项的权。从而提出了一种新的误差积分准则一改进的广义平方误差积分准则(RGISE)。仿真结果表明,新准则能够获得较大的幅值稳定裕度和较好的响应曲线。     

Optimal-tuning PID controller design in the frequency domain with application to a rotary hydraulic system

In this paper a new PID controller design scheme that uses optimisation in the frequency domain is proposed for industrial process control. An optimal-tuning PID controller is designed to satisfy a set of frequency-domain performance requirements: gain margin, phase margin, crossover frequency and steady-state error. Using an estimated process frequency response, the method can provide optimal PID parameters even in cases where the process dynamics are time variant. This scheme is demonstrated through its application to a rotary hydraulic system and its performance is compared with six alternative PID tuning rules.     

Robust IMC–PID tuning for cascade control systems with gain and phase margin specifications

In this article, an internal model control plus proportional-integral-derivative (IMC–PID) tuning procedure for cascade control systems is proposed based on the gain and phase margin specifications of the inner and outer loop. The internal model control parameters are adjusted according to the desired frequency response of each loop with a minimum interaction between the inner and outer PID controllers, obtaining a fine tuning and the desired gain and phase margins specifications due to an appropriate selection of the PID controller gains and constants. Given the design specifications for the inner and outer loop, this tuning procedure adjusts the IMC parameter of each controller independently, with no interference between the inner and outer loop obtaining a robust method for cascade controllers with better performance than sequential tuning or other frequency domain-based methods. This technique is accurate and simple, providing a convenient technique for the PID tuning of cascade control systems in different applications such as mechanical, electrical or chemical systems. The proposed tuning method explained in this article provides a flexible tuning procedure in comparison with other tuning procedures because each loop is tuned simultaneously without modifying the robustness characteristics of the inner and outer loop. Several experiments are shown to compare and validate the effectiveness of the proposed tuning procedure over other sequential or cascade tuning methods; some experiments under different conditions are done to test the performance of the proposed tuning technique. For these reasons, a robustness analysis based on sensitivity is shown in this article to analyze the disturbance rejection properties and the relations of the IMC parameters.     

Tuning of PID controllers based on simplified single parameter optimisation

A simple method to design PID controllers in the frequency domain based on a simplified constrained optimisation is proposed. The method is based on the use of a single tuning parameter, defined as the quotient between the final crossover frequency and the zero of the controller. The tuning procedure is based on the maximisation of the controller gain subject to an equality constraint in the phase margin and an inequality constraint in the gain margin. The main advantage of the proposed method is that, even though the maximisation of the controller gain is straightforward, since there is only one parameter to be tuned, the solution is close to the optimal tuning obtained with direct numerical optimisation methods. Moreover the method is applicable to any linear model structure, including dead time and non-minimum phase systems.     

A frequency domain design of PID controller for an AVR system

We propose a new proportional-integral-derivative （PID） controller design method for an automatic voltage regula- tion （AVR） system based on approximate model matching in the frequency domain. The parameters of the PID controller are obtained by approximate frequency response matching between the closed-loop control system and a reference model with the desired specifications. Two low frequency points are required for matching the frequency response, and the design method yields linear algebraic equations, solution of which gives the controller parameters. The effectiveness of the proposed method is demonstrated through examples taken from the literature and comparison with some popular methods.     

Relay feedback tuning of robust PID controllers with iso-damping property.

A new tuning method for proportional-integral-derivative (PID) controller design is proposed for a class of unknown, stable, and minimum phase plants. We are able to design a PID controller to ensure that the phase Bode plot is flat, i.e., the phase derivative w.r.t. the frequency is zero, at a given frequency called the "tangent frequency" so that the closed-loop system is robust to gain variations and the step responses exhibit an iso-damping property. At the "tangent frequency," the Nyquist curve tangentially touches the sensitivity circle. Several relay feedback tests are used to identify the plant gain and phase at the tangent frequency in an iterative way. The identified plant gain and phase at the desired tangent frequency are used to estimate the derivatives of amplitude and phase of the plant with respect to frequency at the same frequency point by Bode's integral relationship. Then, these derivatives are used to design a PID controller for slope adjustment of the Nyquist plot to achieve the robustness of the system to gain variations. No plant model is assumed during the PID controller design. Only several relay tests are needed. Simulation examples illustrate the effectiveness and the simplicity of the proposed method for robust PID controller design with an iso-damping property.     

基于幅值裕度和相位裕度的PID参数最优整定方法

给出一种基于幅值裕度和相位裕度的PID参数最优整定方法.首先,基于改进的D–分割法确定满足幅值裕度和相位裕度要求的控制参数稳定域,然后根据最大灵敏度函数、超调和调节时间定义控制器设计的目标函数,在所得到的控制参数稳定域中计算出一组最优的控制参数值.仿真结果表明,该整定方法能够保证闭环系统具有强鲁棒性、良好的跟踪性能和抗干扰性能.它不仅适用于稳定时滞对象,而且还适用不稳定时滞对象.     

Design of a digital PID stand-alone single-loop controller

A digital PID algorithm is proposed for the control of a wide class of processes that may be characterized by steady-state gain, time constant, and transport lag. The grapho-analytical pole-placement procedure proposed enables the designer to make rapid and straightforward adjustments to the controller parameters with respect to the desired system accuracy, speed of continuous time response, and stability margin. A sensitivity analysis procedure is developed for investigating the effects of transport lag on the system dynamic behaviour in the sampled-data control system considered     

一种拟Laguerre控制器设计

拉盖尔(Laguerre)级数是一类L2空间上的正交级数,具有很好的函数逼近能力,目前在自动控制领域用于连续动态过程建模以及数字控制器设计;为了拓展拉盖尔级数在连续控制器设计方面的应用范围,文章将0型拉盖尔级数型传递函数模型,改进为1型拟拉盖尔级数型传递函数模型,提出了一种具有积分行为的拟拉盖尔控制器;比较了拟拉盖尔控制器与工业常用PID控制器的频域特点;通过将拟拉盖尔控制系统模型和期望模型的麦克劳林(Maclaurin)展开,给出了拟拉盖尔控制器参数的整定规则;在三类不同被控对象的仿真实验中,将拟拉盖尔控制器和PID控制器的系统逼近性能以及抗扰性能进行了对比研究;结果表明,拟拉盖尔控制器只需要三阶展开项,即可获得高于PID控制器的系统逼近能力和抗扰能力,具有较好的应用前景.     

Bode 理想传递函数在分数阶控制中的应用

本文将Bode 理想传递函数应用于分数阶控制器的设计和分数阶PID 控制器参数整定中．所得控制器 可以在满足系统要求的截止频率和相角裕度的前提下,使补偿后系统Bode 图的相频特性曲线在截止频率附近有一 个水平区域,即闭环系统对增益的变化具有鲁棒性．它不仅适合于分数阶对象,也适用于整数阶对象,并能够提高 系统的控制品质．仿真结果证明了上述方法的有效性．     

用直接综合法设计的微分先行鲁棒PID控制器

针对积分时滞系统应用直接综合方法设计了一种微分先行鲁棒PID控制器.这种方法基于比较积分时滞系统与后置超前滞后滤波器的微分先行PID控制器组成的闭环系统的特征方程和期望特征方程.期望特征方程由多个位于同一期望位置的极点组成.所设计的控制器的参数以实现期望鲁棒性的方式获得.通过选择不同的调优参数获取相应的Ms值,进而在参...