On Time-Constant Robust Tuning of Fractional Order [Proportional Derivative] Controllers

This paper deals with analyzing a newly introduced method for tuning of fractional order [proportional derivative] (FO[PD]) controllers to be used in motion control. By using this tuning method, not only the phase margin and gain crossover frequency are adjustable, but also robustness to variations in the plant time-constant is guaranteed. Conditions on the values of control specifications (desired phase margin and gain crossover frequency) for solution existence in this tuning method are found. Also, the number of solutions is analytically determined in this study. Moreover, experimental verifications are presented to indicate the applicability of the obtained results.      

PI控制下开环不稳定对象可行稳定裕度范围的研究

针对一阶不稳定加延迟对象, 基于传统稳定裕度定义的PI控制整定方法缺乏对幅值裕度下边界的考虑, 使得结果与实际有一定偏差. 通过对延迟环节的逼近, 得到更精细的可达稳定裕度区域. 利用多项式方程数值求解算法, 同时获得了另一种以幅值裕度下边界为基准的控制参数整定方法. 所得结果显示, 按照严格稳定裕度定义所得到的可达区域明显减小. 数值实例验证了本文方法的有效性.     

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.     

A PI/PID controller for time delay systems with desired closed loop time response and guaranteed gain and phase margins

In this article we present a graphical tuning method of PI/PID controller for first order and second order plus time delay systems using dominant pole placement approach with guaranteed gain margin (GM) and phase margin (PM). The stability equation method and gain phase margin tester have been used to portray constant GM and PM boundaries. The PID controller parameters have been obtained for different dominant poles and plotted graphically in the parameters plane of controller within the specified GM and PM regions. To demonstrate the effectiveness and confirm the validity of the proposed methodology, three examples with numerical simulations are presented.     

基于改进IMC的开环不稳定时滞过程控制

针对开环不稳定对象,在传统内模控制结构中增加了一个预稳定控制器,提出了改进的内模控制结构,给出了闭环系统内稳定判定定理;更重要的是提出一个综合闭环性能和相角裕度的指标函数,将该指标函数最大化,可获得在不同归一化时滞情况下的优化预稳定控制器整定参数,并拟合出公式．最后,与国际上最新发表的控制方法进行了对比,显示了该方法的优越性．     

A Novel Boundary Control Solution for Unstable Heat Conduction Systems Based on Active Disturbance Rejection Control

In this study, a new boundary control scheme is proposed for a class of unstable heat conduction systems based on active disturbance rejection control and frequency domain analysis methods. The unstable heat conduction systems studied here corresponds to a thin rod with surface heat loss and internal heat generation. An active disturbance rejection boundary controller is designed to stabilize the unstable heat conduction systems. Using the frequency domain analysis method, the Nyquist stability criterion for distributed parameter systems, the relative stability indices (gain margin, phase margin, and exponential stability speed) can be obtained for performance evaluation, and a constructive parameter‐tuning method for controller is proposed. Finally, it is proved that an active disturbance rejection boundary controller can stabilize the unstable heat conduction systems with one unstable pole, and the simulation results demonstrate that the temperature profile of the whole rod has good convergence properties under both Dirichlet and Neumann boundary control.     

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.     

飞机鲁棒稳定裕度的频域试验分析方法

提出一种结合频率试验的MIMO系统稳定裕度分析方法,通过对图解方法的分析,提出了逆Nyquist阵对角占优的解析判别式,简化了多变量频率域鲁棒性分析和设计,给出一种在线数值计算方法,使计算量大大减少,同时给出了MIM0飞行控制系统鲁棒稳定裕度的飞行试验方案,飞行控制的应用表明,该方法可以得到令人满意的结果。     

QFT bounds for robust stability specifications defined on the open‐loop function

In the framework of quantitative feedback theory, this paper develops a new method to compute robust stability bounds. This is of special interest when stability is defined directly on the open‐loop function. Thus, ignorance of the plant gain and phase shift can be specifically and independently considered. Furthermore, upper and lower stability margins for both gain and phase can be chosen. However, classical quantitative feedback theory stability specifications are defined as constraining the peak magnitude of closed‐loop functions, which lack the said flexibility. Once the upper tolerance has been defined, all stability margins are determined. Moreover, confining the most restrictive stability margin may result in other excessive margins. However, the stability bounds of the new approach guard just the required distance from the open‐loop frequency response to the critical point. This allows maximization of the available feedback in the functional bandwidth and minimization of the cost of feedback beyond the crossover frequency, provided that the open‐loop frequency response is shaped to closely follow the stability bounds. It should be noted that the new bound computation algorithm performs few and simple arithmetic operations. This makes it far more efficient than traditional methods. The flight altitude control of an unmanned aerial vehicle is proposed as a practical example to show the new method's potential benefits.     

混合控制系统的稳定裕度分析与计算

数字控制与连续对象组成的混合系统是常见的控制形式，而通过有效的计算方法得到混合系统的稳定裕度是衡量控制系统性能指标的重要工作。通过一个具体的数字实例，对于目前常用的几种混合系统的稳定裕度计算方法进行了比较，明确了正确的计算步骤和方法，即只有对于整个开环传递函数进行整体ZOH离散化才能够得到真实结果，并指出通过Matlab中的相应函数可以得到精确的数值解。最后给出了混合系统设计的指导性意见。     

一阶时滞系统的智慧PI控制

针对一阶时滞系统的控制问题,提出了一种不依赖于受控对象模型和属性的智慧比例–积分(WPI)控制方法. WPI控制方法通过速度因子将比例和积分环节紧密联系在一起形成一个协同控制核心.理论分析表明,由WPI控制器构成的闭环控制系统是全局渐近稳定的.数值仿真实验表明了WPI控制方法不仅响应速度快、控制精度高,而且还具有良好的抗扰动鲁棒性,因而是一种有效的控制方法,在时滞系统控制领域具有广泛的应用价值.     

一类非最小相位过程内模控制系统设计

非最小相位过程是较难控制的一类过程。针对一类自衡二阶非最小相位过程 ,采用内模控制系统结构 ,使系统具有良好的抗扰性和鲁棒性。给出了在希望的幅值和相角裕量下控制器参数的计算方法。设计例子与仿真结果表明 ,根据该方法设计的系统有比较理想的稳定性和鲁棒性     

由回差阵奇异值求稳定裕度的退化算法

本文研宄使用回差阵奇异值求多输入多输出(MIMO)线性定常系统稳定裕度的方法.首先对此方法进行退化分析,得到求解单输入单输出(SISO)线性定常系统稳定裕度的算法步骤.在此基础上,讨论退化所得算法与传统稳定裕度的关系;进一步地,详细分析此退化算法相比传统稳定裕度的优势,进而指出当系统的增益和相位同时变化时,系统Nyquist曲线g(jω)到临界点(-1,j0)的最短距离min|1+g(jω)|可作为一种更加合理的稳定裕度指标.最后,通过对实例进行数值仿真,说明本文所提退化算法可以克服传统稳定裕度局限性,同时与传统稳定裕度结合得到比较完整的SISO线性系统稳定裕度衡量体系.     

直升机强跟踪自适应变稳控制器设计

变稳控制是直升机飞行模拟的关键技术之一, 气动参数的不确定性是其设计的困难所在. 对此, 提出了利用双目标直升机模型构造原型直升机的强跟踪自适应变稳控制器, 它将强跟踪的反馈补偿机构和自适应控制参数设计相分离, 简化了控制设计, 同时实现了提高自适应参数修正过程的系统稳定裕度和显著降低跟踪误差的目的. 仿真实验结果验证了所提出方法的有效性和可行性.     

Simple Tuning Rules for Integrating Processes with Large Time Delay

In the present article, controllers of the modified Smith predictor are designed for pure integrating, integrating plus first order and double integrating processes with large time delays. The direct synthesis approach is used to tune the set point tracking controller. Suitable values of the desired closed loop time constant that satisfies both robust stability and robust performance conditions are provided based on extensive simulation studies. The PD controller, which is used for load disturbance rejection, is designed so as to achieve a specified slope (ψ) of the Nyquist curve at the gain crossover frequency. The gain crossover frequency that corresponds to a phase margin of 45 degrees is suggested for all three considered integrating processes. Furthermore, ψ is recommended as 45 degrees for double integrating processes and 90 degrees for pure integrating and integrating plus first order process models. Two simulation examples are considered to illustrate the usefulness of the proposed tuning rules.     

改进PID的无人机飞行姿态角控制消颤算法

无人机在整个纵平面飞行过程中,由于飞行姿态角的大幅度变化以及气流的作用,导致机身颤抖,影响飞行稳定性.提出一种基于PID变结构控制的无人机飞行姿态角控制消颤算法,首先进行了无人机飞行姿态角控制系统的被控对象参量分析,构建无人机在姿态角变化剧烈、大迎角飞行时的三通道模型,采用变结构控制方法进行控制器设计.结合小扰动原理和Lyapunov稳定性原理进行扰动抑制和稳定性证明,采用梯度算法调整权值进行飞行姿态角控制的消颤处理,采用自适应算法在线调整权值实现PID变结构控制改进.仿真结果表明:采用该算法进行无人机飞行姿态角控制和消颤处理,大幅度提高无人机飞行定姿的精度,横滚角、俯仰角和航向角的控制精度有较大提高,稳定性和收敛性较好,确保了无人机飞行稳定性.     

PI‐PD controller design for time delay systems via the weighted geometrical center method

In this study, a PI‐PD controller tuning method is presented using the weighted geometrical center method, which is based on the calculation of the weighted geometric center of the stability region obtained by the stability boundary locus method. The proposed method for tuning of PI‐PD controller parameters (k_d,k_f,k_p and k_i ) is performed in three steps. In the first step, the (k_d,k_f) parameter region for the inner loop with PD controller is obtained, and then the weighted geometric center of this region is calculated. In the second step, the inner PD loop is reduced to a single block using the numerical values of (k_d,k_f) that are obtained in the first step. Then, the (k_p,k_i) values of the external loop with PI controller are determined by the same procedure. This tuning method has some advantages over other tuning methods in terms of simplicity and robustness. The simulation examples show that a PI‐PD controller designed using the proposed method provides good performance results when compared to other tuning methods presented in the literature.     

小型无人机姿态系统的变论域模糊控制

无人机飞行姿态控制过程具有较强的时变特征,且存在随机扰动,因而常规的定参数控制方法往往不能满足要求;同时,由于小型无人机体积小、系统配置简单,也不宜建立太过复杂的控制系统。为此,设计了变论域模糊自整定飞行姿态智能PID控制器,建立了相应的控制策略,使无人机在飞行过程中能有效克服环境扰动的影响,沿预定航线稳定飞行。仿真结果表明了该方法的有效性。     

直升机自动过渡悬停系统方案设计

为了实现直升机自动过渡悬停功能,首先运用模糊建模方法建立全包线飞机特性的T-S模型;然后基于增稳控制系统,实现飞机姿态角的稳定;在此基础上引入“多普勒”地速与无线电高度信号,设计高度和速度控制器,使飞机实际输出跟踪指令信号;最后提出了两种合理的高度速度指令设计方案,使得飞机能快速平稳地悬停到预定高度.仿真结果表明,该设计方法有效可行.     

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。