Fractional-order unstable pole-zero cancellation in linear feedback systems

As a very well-known classical fact, non-minimum phase zeros of the process put some limitations on the performance of the feedback system. The source of these limitations is that non-minimum phase zeros cannot be cancelled by unstable poles of the controller since such a cancellation leads to internal instability. The aim of this paper is to propose a method for fractional-order cancellation of non-minimum phase zeros of the process and studying its properties. It is specially shown that the proposed cancellation strategy increases the phase and gain margin without leading to internal instability. Since the systems with higher gain and phase margin are easier to control, the proposed method can be used to arrive at more effective controls, which is also verified by the simulation results.     

Finite-dimensional control of a flexible space structure: A new view based on input-output space

How to design a simple, finite-dimensional controller for complex, infinite-dimensional Flexible Space Structures (FSSs) with uncertain physical parameters is the main topic of this paper. The research shows that a simple controller that makes the controlled FSS system of high stable degree can be obtained by using only the input-output property instead of the poles-zeros property of the FSS system, which is a new result in the control of uncertain FSS systems. The main idea can be summarized as: (1) it is difficult, even impossible, to obtain convergent poles and zeros estimation for an uncertain FSS system, which is different from that in a finite-dimensional system; (2) there is an inherent relation between the input-output property and the poles-zeros property for the FSS system, which means that modelling and controlling, based on the input-output property, may guarantee the high authority control of the FSS system; (3) in the H sense and based on input-output space to make the model error as small as possible and the controller tolerate a model error as large as possible, will result in a very low dimensional controller.     

Partial fraction expansion and root locus method

Partial fraction expansion is a computationally simple method to obtain the angles of exit from poles or entry into zeros as well as angles and point of intersection of asymptotes of the root loci. Under certain assumptions partial fraction expansion can also be used to get a simple approximation for the coalescent points on the real axis.     

A low profile miniaturized widely‐spaced triband bandpass FSS using coupled resonance

In this article, a triband highly selective widely‐spaced bandpass frequency‐selective surface (FSS) is presented. The proposed FSS is consisted of five metal layers that are separated from each other by four dielectric substrates. Using coupled resonance between layers, three passbands operating at 11.0, 17.4, and 31.9 GHz are achieved. Meanwhile, the dimension of the unit cell of the FSS can be achieved in 0.139λ₀ × 0.139λ₀ (λ₀ is the wavelength of the first resonant frequency in the free‐space), and the overall thickness can be 0.057λ₀, exhibiting miniaturization and low profile characteristics. Due to the proposed FSS can provide multitransmission zeros between two adjacent passbands, the relative bandwidth of the spacing between the second passband and the third passband can reach 58.8% from 17.4 to 31.9 GHz. Thus, a widely spaced response is achieved. In practical, the proposed FSS has an important role in the radio cross‐sectional reduction of some military systems, such as homing head, which can simultaneously detecting mid‐range and long‐range targets. Furthermore, the FSS shows the stable response of angles for both TE and TM polarizations. The equivalent circuit model (ECM) is provided to analysis its operating principle. Finally, a prototype of the proposed FSS is simulated, fabricated and measured. The measured results are in good agreement with the simulation ones.     

The asymptotic behaviour,the angles of departure,and the angles of approach,of the characteristic frequency loci

In algebraic function theory, there is a well established method which uses ‘Newton's diagram’ to find the series expansions of an algebraic function q(x) in the neighbourhood of a point x₀ . In this paper it is shown how, for a linear, time-invariant, multi-variable feedback system, this method can be used to find :

(i) the asymptotic behaviour of the characteristic frequency loci (multivariable root loci) ;

(ii) the angles of departure of the characteristic frequency loci from the open-loop poles ; and

(iii) the angles of approach of the characteristic frequency loci to the finite zeros of such a system.     

A Suboptimal Shifting Based Zero-pole Placement Method for Systems with Delays

An appropriate setting of eventual controller parameters for a derived controller structure represents an integral part of many control design approaches for dynamical systems. This contribution is aimed at a practically applicable and uncomplicated controller tuning method for linear time-invariant time delay systems (LTI-TDSs). It is based on placing the dominant poles as well as zeros of the given infinite-dimensional feedback control system by matching them with the desired ones given by known dynamical properties of a simple fixed finite-dimensional model. The desired placing is done successively by applying the Quasi-Continuous Shifting Algorithm (QCSA) first such that poles and zeros are forced to be as close as possible to those of the model. Concurrently, rests of both system spectra are shifted to the left as far as possible to minimize the spectral abscissa. The obtained results are then enhanced by a non-convex optimization technique applied to a selected objective function reflecting the distance of desired model roots from the eventual system ones and the spectral abscissae. Retarded LTI-TDS are primarily considered; however, systems with neutral delays are touched as well. The efficiency of the proposed method is proved via numerical examples in Matlab/Simulink environment. Some drawbacks and possible improvements or extensions of the algorithm for the future research are also concisely suggested to the reader.     

The fundamental role of general orthonormal bases in systemidentification

The purpose of this paper is threefold. Firstly, it is to establish that contrary to what might be expected, the accuracy of well-known and frequently used asymptotic variance results can depend on choices of fixed poles or zeros in the model structure. Secondly, it is to derive new variance expressions that can provide greatly improved accuracy while also making explicit the influence of any fixed poles or zeros. This is achieved by employing certain new results on generalized Fourier series and the asymptotic properties of Toeplitz-like matrices in such a way that the new variance expressions presented here encompass pre-existing ones as special cases. Via this latter analysis a new perspective emerges on recent work pertaining to the use of orthonormal basis structures in system identification. Namely, that orthonormal bases are much more than an implementational option offering improved numerical properties. In fact, they are an intrinsic part of estimation since, as shown here, orthonormal bases quantify the asymptotic variability of the estimates whether or not they are actually employed in calculating them     

Equations for the angles of arrival and departure for multivariable root loci using frequency-domain methods

Frequency-domain methods are used to study the angles of arrival and departure for multivariable root loci. Explicit equations are obtained. For a special class of poles and zeros, some simpler equations that are generalizations of the single-input-single-output equations are presented.     

Variance-error quantification for identified poles and zeros

This paper deals with quantification of noise induced errors in identified discrete-time models of causal linear time-invariant systems, where the model error is described by the asymptotic (in data length) variance of the estimated poles and zeros. The main conclusion is that there is a fundamental difference in the accuracy of the estimates depending on whether the zeros and poles lie inside or outside the unit circle. As the model order goes to infinity, the asymptotic variance approaches a finite limit for estimates of zeros and poles having magnitude larger than one, but for zeros and poles strictly inside the unit circle the asymptotic variance grows exponentially with the model order. We analyze how the variance of poles and zeros is affected by model order, model structure and input excitation. We treat general black-box model structures including ARMAX and Box–Jenkins models.     

纯量反馈系统稳定零极近似相消的积分约束

导出了单输入单输出反馈控制系统误差响应基于名义系统稳定的零、极点近似相消的时间域积分约束，此积分约束是任何反馈控制系统均应满足的．这一约束给出了单输入单输出反馈系统固有折中的新的观点．名义系统稳定的零、极点近似相消的存在导致反馈控制系统的调节时间延长或者误差响应的无穷范数变大．因此，在反馈控制系统设计中，尽量避免补偿器的零、极点与名义系统的极、零点近似相消(即使这些零、极点是稳定的)．     

Simple criterion for testing non-minimum-phase systems

Simple sufficient conditions for non-minimum-phase systems are derived using the fundamental theorem of algebra. It is shown that the unstable poles or zeros of a control system can be tested directly from the coefficients of the characteristic polynomials without any calculation. This criterion is useful for the computer-aided design of control systems.     

Model reduction of systems with zeros interlacing the poles

The problem of reducing a system with zeros interlacing the poles (ZIP) on the real axis is considered. It is proved that many model reduction methods, such as the balanced truncation, balanced residualization, suboptimal and optimal Hankel approximations, inherit the ZIP property. Properties of the Hankel singular values of ZIP systems are also listed.     

Simultaneous Stabilization and Constant Reference Tracking of LTI,MIMO Systems

It is shown that any finite number of plants that belong to certain classes of multi‐input multi‐output systems with no zeros in the region of instability can be simultaneously stabilized using linear, time‐invariant integral‐action controllers. These plants may be stable or unstable and their poles are not restricted; they may also have any number of zeros in the stable region of the complex plane. The classes of systems under consideration include plants with blocking or transmission zeros at infinity. The common controller achieves asymptotic tracking of step‐input references with zero steady‐state error and has a low order transfer‐function. Systematic synthesis methods are presented, and a parametrization of all simultaneously stabilizing controllers with integral‐action is also provided.     

Input-output stability degrees for undamped constant coefficients linear partial differential equations

It is an established fact that systems which have transfer matrices with poles converging to the imaginary axis cannot have exponentially stable time responses. Recently it was proved that for a class of partial differential equations with such a structure of poles it is possible to have a fast decay in time, uniformly in space, as arbitrary polynomials if the initial conditions are smooth enough and with an appropriate decay at infinity. The non-homogeneous version of this result which we present here can be summarized as follows: 'arbitrary regularity in space of the input function leads to arbitrary polynomial convergence in time towards the steady state'. The relation between the properties of the input function and the rate of convergence of the poles to the imaginary axis is quantitative and we indicate methods for computing this rate. We also provide conditions for exponential stability in this context. Due to some limitations in exponential stabilization by feedback a natural alternative to stability enhancement is this polynomial one. Therefore it is useful to investigate when it can be recovered in more practical situations (bounded space, boundary control, etc). Possible applications include the control of distributed oscillatory phenomena (e.g. in large flexible structures, plates), and more recently the control of some advanced materials.     

A broadband miniaturized ultra‐thin tri‐band bandpass FSS with triangular layout

A tri‐band broadband ultra‐thin miniaturized highly selective bandpass frequency‐selective surface (FSS) has been proposed by using coupled resonance. The proposed FSS is a three‐layer periodic arrays consisting of three metal layers that are separated from each other by two dielectric substrates. Two exterior layers are composed of gridded‐double hexagonal loops (G‐DHLs), while the middle layer is composed of double hexagonal loops (DHLs) structure. The second passband has a relative bandwidth of more than 20%, exhibiting broadband characteristics. Due to the superior bandwidth of the hexagon loop, the design FSS can achieve both broadband and low insertion loss characteristics. The FSS show stable incident angles response and wide out‐of‐band rejection performance over a wide range of incidence angle of 60° for both TE and TM polarizations. The wide and sharp out‐of‐band rejection behavior is caused by multi‐transmission zeros on both sides of each passband. The equivalent circuit model of the FSS is provided to analyze its operating principle. The prototype of this FSS is simulated, fabricated, and measured. The measured results show a good agreement with its theoretical analysis and simulation.     

Limit results for sampled systems

Properties of discrete time systems obtained by sampling continuous time systems are described. By introducing prefilters, we can treat different ways of sampling within one framework. Results on the convergence of poles and zeros of transfer functions and noise filters as the sampling interval tends to zero are given. These results are generalizations of the results of Åström, Hagander and Sternby (1984) on the convergence of poles and zeros for zero-order hold sampled transfer functions. Sampled noise models are also analysed. Knowledge of these properties is very important in, for example, discrete time simulations of continuous time systems, and identification of continuous time models based on discrete time measurements.     

自动控制系统动态校正的计算机辅助设计

本文叙述了基于频率法的线性定常系统动态校正的计算机辅助设计方法,该设计适用于 控制对象具有不同原极点(0型至2型)、实零、极点和复数极点的控制系统的校正;在给定的 性能指标下,能实现超前、滞后和超前-滞后校正;计算机运算后能打印出校正参数的设计结 果;可根据设计者的需要,通过计算机分析打印出原系统及已校正系统的时间响应曲线和性能 指标.经对多种实例的设计,均获得较满意的结果.     

Logarithmic integrals, interpolation bounds, and performancelimitations in MIMO feedback systems

We study performance limitation issues found in linear multivariable feedback systems. Our main contributions include Bode and Poisson type integral inequalities and performance limits for the sensitivity and complementary sensitivity functions. These results characterize and quantify explicitly how open-loop unstable poles and nonminimum phase zeros may impose inherent limitations on feedback design and fundamental limits on the best achievable performance. The role of time delay is also studied in this context. Most notably, we show that the performance and design limitations in multivariable systems intrinsically depend on the locations as well as directions of unstable poles and nonminimum phase zeros, and in particular, on how pole and zero directions are aligned. The latter is characterized by angles measuring the mutual orientation between zero and pole directions, and it is shown to play a crucial role in multivariable system design     

用零极点动态控制波形图显示的Java小程序实现方法

用Java小程序实现了通过拉普拉斯逆变换和z逆变换中s域或z域的零极点动态控制波形图显示的过程。为了增强人机界面的交互性和稳定性,程序采用了Java语言中的鼠标事件来捕获零极点坐标从而动态控制波形图显示,并且也应用了双缓冲技术来消除擦旧画新过程所引起的画面闪烁。实际应用表明,用户通过此程序可以更加方便直观地理解诸如系统稳定性等一系列问题,达到传统教学系统所没有的效果。     

Zeros and Poles of Linear Continuous-Time Periodic Systems: Definitions and Properties

The paper deals with definitions of zeros and poles and their features in finite-dimensional linear continuous-time periodic (FDLCP) systems under a harmonic framework. More precisely, system and transfer zeros and poles in the harmonic wave-to-wave sense are defined on what we call the regularized harmonic system operators and the harmonic transfer operators of FDLCP systems by means of regularized determinants; then their composition and properties related to system structures are examined via the Floquet theory and controllability/observability decompositions of FDLCP systems. The study shows that under mild assumptions, the harmonic transfer operators of FDLCP systems are analytic and meromorphic, on which zeros and poles are well-defined. Basic zero/pole relationships are established, which are similar to their linear time-invariant counterparts and in particular explicate some interesting harmonic wave-to-wave behaviors of FDLCP systems. The results are significant in analysis and synthesis of FDLCP systems when the harmonic approach is adopted.