控制系统的脆弱性分析

脆弱性是指一闭环系统的稳定性对参数摄动极端敏感.这类系统的开环频率特性经过距临界点(-1,j0)的近旁,这种与(-1,j0)点之间脆弱的相对关系遇到任何可能的摄动就会遭到破坏.文中分析指出,控制系统的脆弱性可以用Bode积分来进行定量分析.对于一个非最小相位的不稳定对象的控制来说,控制器的不稳定极点与对象的不稳定极点加到一起会大大增加系统灵敏度函数的峰值.故这类系统的设计必然是脆弱的.对于不稳定的多变量对象的控制来说,如果其中一个等价的输出反馈回路中有一个较大的不稳定极点,那么其灵敏度函数也会出现大的峰值,会导致脆弱性,而利用Bode积分则可以避免设计的脆弱性.     

一种基于预稳定区域的∞控制器参数优化方法

基于控制理论, 提出了一种具有预期闭环极点区域的H_∞ 控制器参数优化设计方法, 该方法设计中既考虑了H_∞ 性能指标又兼顾了动态性能指标, 克服了常规H_∞ 设计方法中不稳定控制器的问题等不足. 实验结果表明, 该方法具有计算简便、可实现性好、鲁棒性和动态品质良好、对模型参数变化的敏感性低等优点.     

基于高阶干扰观测器的极点配置控制器及应用

本文设计了一种可以对外部干扰进行估计的高阶干扰观测器,并针对一类具有外部干扰的单输入单输出离散时间线性系统,提出了一种基于高阶干扰观测器的极点配置控制方法.该方法由常规极点配置控制器和高阶干扰观测器组成.常规极点配置控制器用来保证闭环系统稳定,并将闭环系统的极点配置到理想位置,高阶干扰观测器用来补偿外部干扰对闭环系统的影响.理论分析以及仿真和水箱液位系统中的实验结果表明了所提方法的有效性和优越性.     

非自衡时滞对象的改进内模控制

针对化工生产中常见的具有积分和时滞特性的过程对象，采用一种改进的两自由度内模控制方案．其中一个新增的控制器用于设定值跟踪响应的期望极点配置，利用直接合成法设计设定值跟踪控制器；另一个新增的控制器用于稳定对象和抑制扰动，并采用期望闭环余灵敏度法确定控制器．设定值跟踪控制器和扰动抑制控制器可通过性能参数独立调节，并保证系统具有较好的鲁棒稳定性．最后，通过仿真实例验证了控制方案的有效性．     

Model-reference robust tuning of 2DoF PI controllers for first- and second-order plus dead-time controlled processes

The aim of this paper is to present a robust tuning method for two-degree-of-freedom (2DoF) proportional integral (PI) controllers. This is based on the use of a model reference optimization procedure with servo and regulatory target closed-loop transfer functions for first- and second-order plus dead-time (FOPDT, SOPDT) controlled process models. The designer is allowed to deal with the performance/robustness trade-off of the closed-loop control system by specifying the desired robustness level by selecting a maximum sensitivity in the range from 1.4 to 2.0. In addition, a smooth servo/regulatory performance combination is obtained by forcing both closed-loop transfer functions to perform as closely as possible to non-oscillatory dynamic targets. A unified set of controller tuning equations is provided for FOPDT and SOPDT models with normalized dead-times from 0.1 to 2.0 that guarantees the achievement of the design robustness level. The robustness of the control system is analyzed as well as the robustness–fragility and performance–fragility of the optimized controllers. Comparative examples show the effectiveness of the proposed tuning method. The exact achievement of the control system robustness target for all the controlled process models considered (first- and second-order) is one of the distinctive characteristics of the proposed model reference robust tuning (MoReRT) method.     

高超声速飞行器非线性鲁棒控制律设计

高超声速飞行器具有模型非线性程度高、耦合程度强、参数不确定性大、抗干扰能力弱等特点,其自主控制具有较大的挑战.论文提出了一种基于鲁棒补偿技术和反馈线性化方法的非线性鲁棒控制方法.文中首先采用反馈线性化的方法对纵向模型进行输入输出线性化,实现速度和高度通道的解耦和非线性模型的线性化.针对得到的线性模型,设计包括标称控制器和鲁棒补偿器的线性控制器.基于极点配置原理,设计标称控制器使标称线性系统具有期望的输入输出特性,利用鲁棒补偿器来抑制参数不确定性和外界扰动对于闭环控制系统的影响.基于小增益定理,证明了闭环控制系统的鲁棒稳定性和鲁棒跟踪性能.相比于非线性回路成形控制方法,仿真结果表明了所设计非线性鲁棒控制算法的有效性和优越性.     

Long-range predictive control - closed-loop system analysis

Analysis of the closed-loop system consisting of a long-range predictive controller and a scalar process, described by the ARMAX model, is presented. A criterion for the stability of the closed-loop system is derived. The influence of the controller parameters on the closed-loop system pole location and performance can be easily examined.     

基于D分解的分数阶PID控制器的图形化参数整定

针对二自由度分数阶PID控制器设计的参数多,结构复杂等复杂问题,提出了一种基于D分解法和主导极点配置的新型参数整定方法。其基本原理首先基于动态响应指标约束进行主导极点配置,在确保闭环系统的响应特性良好的条件下确定系统超调量和调节时间,由此经过转换得到未知参数之间的函数关系。其次,使用D分解法,将未知参数在不影响的控制性能的条件下由多减少,再由相关参数取得系统性能稳定的参数域中优化,最后以差分进化算法为导向,以两种方法取得的相关约束条件为指标取得最优控制器参数,在确保所选极点的优势下使所设计的控制器达到理想的控制性能。最终,将所设计的控制器通过应用在整数阶和分数阶被控对象上,使用仿真验证新方法的鲁棒性和快速性,同时也表现了新方法的有效性和实用性。     

Accurate two-degree-of-freedom discrete-time current controller design for PMSM using complex vectors

Properties of the current controller are essential for permanent magnet synchronous machine (PMSM) drives, but the conventional continuous-time current controller cannot fully decouple the cross-coupling terms when applied in the digital processor. Its performance is related closely to the rotational speed. To improve the performance of the current loop, the direct design method in the discrete-time domain is adopted using the accurate discrete-time complex vector model. An integrated accurate hold-equivalent discrete model for PMSM is derived considering the difference between the output of the voltage source inverter and the back electro-motive force. Then an accurate two-degree-of-freedom (2DOF) current controller with a third-order closed-loop transfer function is designed. The 2DOF controller has more freedom in pole placement, and two schemes with a different cancelled pole-zero pair are investigated. Analysis is conducted by the robust root locus method via the complex vector root locus and sensitivity functions, showing properties in disturbance rejection and sensitivity to parameter variation of two schemes. Both schemes have their own advantages. Finally, the dynamic performance and flexibility of the proposed current controller is verified on a 2.5-kW PMSM test bench.     

基于极点配置控制的风机叶片颤振控制研究

针对风力机叶片的颤振会严重影响风力机的发电效率和运行安全问题,设计了一种基于极点配置的振动控制器在抑制叶片颤振的同时可以取得良好的闭环控制特性,并且能够有效抑制来自阵风的干扰.重点研究了利用Diophantine方程求解极点配置(PPC) PID控制器的方法,并选取有效的系统输出信号来设计反馈控制器,达到抑制叶片颤振的目的.Matlab/Simulink仿真结果表明,在叶片颤振控制系统中极点配置PPC-PID控制器比传统PID控制器具有更好的抗干扰性和动态特性.     

Two approaches based on pole sensitivity and stability radius measures for finite precision digital controller realizations

This paper compares the two approaches based on pole sensitivity and the complex stability radius measures, respectively, for optimizing the closed-loop stability robustness of digital controllers with respect to finite word length (FWL) errors in fixed-point implementation. Design details and related optimization procedures are derived for the two methods. The two measures, although derived from different motivations, can both be regarded as lower-bound measures of a true but computationally intractable FWL stability measure in some senses. An example is used to verify the theoretical analysis and to illustrate the two designs for determining optimal FWL controller realizations.     

Youla-Kučera design of decoupled control systems

A multivariable linear controller based upon pole placement design is developed from the family of all stabilizing controllers. In addition, decoupling behaviour is achieved. The decoupling conditions are established and guarantee the existence of a stabilizing controller that will give rise to a closed-loop transfer function matrix which is non-singular and diagonal. Further requirements may be imposed on the controller - here we discuss H 2 norm minimization.     

汽车主动悬架系统H∞控制器的降阶

基于整车模型设计的主动悬架控制系统,控制器阶数往往较高.在保证主动悬架闭环系统性能的情况下如何尽可能地降低控制器的阶数,是有待解决的问题.本文首先建立汽车7自由度整车悬架模型.针对人体敏感的振动频率范围,设计汽车主动悬架H_∞控制器.在此基础上采用Hankel范数最优降阶法对所设计的高阶控制器进行降阶研究,与模态截取法、均衡截取法进行比较,结果显示Hankel范数最优降阶法能获得更好的降阶效果.对采用降阶和全阶控制器的主动悬架系统进行仿真的结果表明,Hankel范数最优降阶法在较大程度地降低控制器阶数的同时,闭环系统频域和时域特性没有明显降低且汽车乘坐舒适性良好.     

一类线性系统区域极点配置静态输出反馈可靠控制

考虑连续线性系统,在连续增益故障模型的前提下,提出带有执行器故障的圆形区域极点配置的静态输出反馈的可靠控制问题。本文利用线性矩阵不等式(LMI) 在考虑执行器故障模型的基础上,给出圆形区域极点配置的静态输出反馈的可靠控制器存在的充分条件。通过成果的仿真,并进一步说明当系统发生故障时,正常控制的闭环系极点可能离开所给定的圆形区域,而可靠控制的闭环系统仍然会保持极点在给定的圆形区域内。从而看出对系统进行极点配置的静态输出反馈的可靠控制的必要性。     

基于Delta算子的永磁直线同步电机非脆弱保性能速度控制器设计

利用Delta算子离散化系统采样周期是显式参数的特点,基于Delta算子方法对永磁直线同步电机(PMLSM)不同采样周期下的非脆弱保性能速度控制器的统一化设计问题进行研究.以线性矩阵不等式(LMI)给出该控制器的存在条件.通过对PMLSM闭环系统极点的分析,表明所设计的非脆弱保性能速度控制器不但能保证PMLSM在其对象参数和控制器参数同时发生范数有界摄动时闭环系统仍保持渐近稳定,而且系统的二次型性能指标上界的数学期望值不超过某个给定的上界,而不考虑控制器参数摄动情况所设计的控制器在其参数摄动时闭环系统将无法保持稳定.     

Robust, fragile, or optimal?

We show by examples that optimum and robust controllers, designed by using the H₂, H_∞, l¹, and μ formulations, can produce extremely fragile controllers, in the sense that vanishingly small perturbations of the coefficients of the designed controller destabilize the closed-loop control system. The examples show that this fragility usually manifests itself as extremely poor gain and phase margins of the closed-loop system. The calculations given here should raise a cautionary note and draw attention to the larger issue of controller sensitivity which may be important in other nonoptimal design techniques as well     

具有方差和极点约束的不确定系统鲁棒H∞输出反馈控制

针对一类具有范数有界不确定性的连续系统和二次矩阵不等式区域,考虑系统具有方差和区域极点约束的输出反馈控制器设计问题．为此首先导出闭环系统区域稳定的充分必要条件．然后用线性矩阵不等式方法给出输出反馈控制器存在的一个充分条件．在此充分条件下闭环系统是鲁棒区域稳定的且具有H∞性能以及当干扰为白噪声信号时其稳态状态方差有限．接下来用矩阵分解方法给出输出反馈控制器增益矩阵的求解过程．最后通过一个仿真实例说明本文所提出的控制器设计方法的有效性．     

带传输滞后的离散系统的观测器及输出动态反馈

针对带输出传输滞后的线性离散系统,讨论了其状态观测器设计问题.利用滞后输出信息,给出了状态观测器的设计方法,并得到状态观测器存在的充要条件,进而设计出基于观测器的输出动态反馈控制器,证明了闭环系统满足极点分离原理.数值仿真验证了所提出方法的有效性.     

An auto-pole-placement self-tuning controller†

An explicit self-tuning controller is described that incorporates closed-loop pole location as the principal design criterion for the objective function of Clarke and Gawthrop. The algorithm includes several minor extensions to improve robustness : a variable dead-time compensator to deal with unknown or time-varying delay, and a method of treating steady-state offset that avoids retaining an integrator in the loop continuously. A new technique has been developed and included in the algorithm that enables the controller to be auto-tuning in the sense that the closed-loop pole(s) and sampling period can be determined on-line so as to optimize the system set-point step response, leaving the system designer to specify only internal model orders and noise characteristics on which to initiate retuning. The resulting controller is quite robust and can easily handle unstable, non-minimum phase systems in a single-loop configuration, as is demonstrated by several simulations including a non-linear model of a fixed-bed autothermal reactor operating over such a large range that auto-tuning of the poles is a necessity.