A theory for decoupling lossless coupled tapered lines with applications to directional couplers

A simple theory is presented for decoupling a pair of lossless coupled nonuniform transmission lines (CNUTL), with a common return and supporting TEM waves, into two lossless nonuniform transmission lines (NUTL). This theory is independent of the port terminations, symmetry conditions, etc. The method directly relates the line parameters of the lossless CNUTL's to those of the decoupled lines and vice versa; further, the matrix parameters of the CNUTL's as a four-port are explicitly expressed in terms of those of the decoupled lines as two-ports. This theory is then utilized to study the applications of CNUTL's as directional couplers.It is shown that for CNUTL's to behave as a codirectional coupler, each of the decoupled lines should be a proportional line, while for contradirectional coupler action, the two decoupled lines have to be duals of each other. The coupling response of the codirectional coupler is found to be periodic, while the phase shift between coupled and transmitted signals varies linearly with frequency. The coupling response of various contradirectional couplers with smooth transition at one of the ends, for which the decoupled lines are “basic NUTL's with hyperbolic solutions”, are studied in detail. It is shown that all these couplers have a high-pass response and that the CNUTL's with “hyperbolic cosine squared lines” as decoupled lines have the best response of all the CNUTL's considered.     

二阶系统数值解耦方法的研究

数值代数领域通过保持Lancaster结构来研究二阶系统的解耦问题,但寻找解耦变换涉及到了非线性方程组求解问题,难以实现. 提出了一种二阶系统数值解耦的新方法. 根据系统解耦前后的同谱信息确定解耦后的系统,将寻找解耦变换的非线性问题转化为齐次Sylvester方程求解问题; 并利用矩阵的Kronecker积理论求解二阶系统的解耦变换. 数值试验证明了该方法的可行性,为二阶系统的数值解耦找到了更便易的实现途径.     

State feedback uniform decoupling problem of linear time-varying analytic systems

A new approach to the input-output uniform decoupling problem of linear time-varying analytic systems via proportional state feedback is presented. A major feature of the proposed approach is that it reduces the solution of the uniform decoupling problem to that of solving a linear algebraic system of equations. This system of equations greatly facilitates the solution of the three major aspects of the decoupling problem: the necessary and sufficient conditions, the general analytical expressions for the controller matrices, and the structure of the uniformly decoupled closed-loop system.     

A floquet theory of the linear synchronous machine

The differential equation describing the three-phase linear synchronous machine containing an arbitrary stator MMF distribution is reformulated and solved as a perturbation theory problem. The solution algorithm presented also produces a transformation capable of reducing to constant coefficient form the differential equation describing the machine. The theory is illustrated by applying it to a simple two pole machine.     

A general modulation theory for single-phase Thyristor systems

Amplitude Modulation (AM) and Phase Modulation (PM) processes of discrete form have been discussed in a previous associated paper. This present paper discusses discrete Frequency Modulation (FM) in power frequency circuits, highlighting their advantages compared with amplitude and phase modulations. Mixed modulation systems of both PM and FM nature are introduced to solve the disadvantages and undesirable features associated with pure FM modulation. A generalised equation of modulation is introduced to represent the various forms of power frequency modulation.     

Stabilization of coupled linear plant and reaction-diffusion process

Boundary control to stabilize a system of coupled linear plant and reaction-diffusion process is considered. Backstepping transformations with a kernel function and a vector-valued function are introduced to design control laws. For the situation without heat resource, the kernel function and the vector-valued function of the transformation are obtained, and an explicit control law is established, and simulation results are presented through figures. For the general situation with heat resource, the existence of the kernel and the vector-valued function of the transformations is shown, and an control law is derived. Stability of the closed loops is achieved for both the situations.     

A new method for linear system reduction

A simple and flexible algorithm is presented to find stable reduced models, provided the original system has a set of dominant poles. The proposed technique applies to the multi- variable case as well and provides a parameter to control the approximation for small and large t.     

Topological formulation of general linear network functions

This paper first discusses the corrections of the errors which Jong and Zobrist made in Ref. (1) and next describes the sign determination suitable forthese topological formulas. The technique for sign determination is based on the node partitioning algorithm which is also presented.     

A method to obtain the semi-canonical Morse's form of a linear multivariable system

A method is presented in this paper to obtain an element of a transformation group, which takes a state space representation of a linear multivariable system to its semi-canonical Morse's form. The system under consideration is supposed to be right invertible, controllable and with no invariant zeros. The element of the transformation group involves state feedback, permutation of outputs and change of basis in states and inputs.     

Stabilization for a coupled PDE–ODE control system

A control system of an ODE and a diffusion PDE is discussed in this paper. The novelty lies in that the system is coupled. The method of PDE backstepping as well as some special skills is resorted in stabilizing the coupled PDE–ODE control system, which is transformed into an exponentially stable PDE–ODE cascade with an invertible integral transformation. And a state feedback boundary controller is designed. Moreover, an exponentially convergent observer for anti-collocated setup is proposed, and the output feedback boundary control problem is solved. For both the state and output feedback boundary controllers, exponential stability analyses in the sense of the corresponding norms for the resulting closed-loop systems are given through rigid proofs.     

Output formation-containment of coupled heterogeneous linear systems under intermittent communication

This paper investigates the output formation-containment problem of the coupled heterogeneous linear systems under intermittent communication. The systems considered in this paper are more general in the sense that each system, whether a leader or a follower, has different dimension and different dynamic. Besides, each system only communicates with its neighbors intermittently. Based on the intermittent information, both the state-feedback and the output-feedback distributed control protocols are designed and a criterion is derived to calculate the lower bound of the communication ratio. Furthermore, a heuristic algorithm based on the Fireworks Algorithm is developed to obtain an optimized communication ratio, which greatly reduces the communication burden. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical results.     

区域技术创新体系动态演进一般性规律分析——基于三螺旋理论的视角

区域技术创新体系是区域创新活动的基础体系,其中结构以制度基础和产业基础为支撑,并包含技术创新主体、资源结构和经济要素结构等三个结构维度.在其演化过程中,三个结构维度呈现出不同的演进规律,而制度基础和产业基础又制约着三个结构维度的演进,并规范着它们的演进方向和路径.发现区域技术创新体系呈现三维结构螺旋发展的形式从低水平向高水平演进,这其中制度基础与演进过程相适应.     

Fixed-time stabilization of general linear systems with input delay

In this paper, the fixed-time stabilization control problem for general linear systems with input delay is addressed. In addition to the Artstein–Kwon–Pearson reduction transformation, a pre-compensation control structure is established first to convert the original system into a single input delay-free linear system. Then, we show that the origin of the transformed system is fixed-time stabilizable by an additional homogeneous control design if the original system is controllable. Finally, an example is used to validate the proposed method via simulation results.     

Modeling of a novel fish passage-way using coupled spatially varied flow

An innovative hydraulic structure was proposed for passage of fish in surface water. The structure consisted of identical ‘cells’ throughout its length and was designed to create coupled spatially varied flow for optimization of depth and velocity of water. The objective of this paper was to simulate the hydraulics of a single cell of this fish passage structure. A numerical model was developed to simulate the water surface profiles and longitudinal variation of 1-D velocity through one cell. The transition in the water surface profile between longitudinally adjacent cells (chamber) was also investigated. It was found that numerical convergence was usually achieved after three iterations with 2% discretization. The difference in depth arising from cell vs. chamber analysis was found to be small. The experimental results indicated turbulence in the water surface. The water surface profile matched the results obtained from numerical results. However, there were errors observed in estimation of flow rate. It is concluded that the mathematical approach used for the numerical simulation is reliable and can be used to analyze coupled spatially varied flow for any hydraulic structures aimed at controlling depth and velocity of water. Innovative approach to the interface between can potentially be used to achieve hydraulic goal of any structure.     

Simplification of large linear systems using a two-step iterative method

A simple iterative technique, which is free of certain shortcomings of the previous methods, is proposed for the approximation of large linear systems by a lower- order model. Here, the measure of the goodness of the approximate model is taken to be the value of the integral-square error between the step responses of the exact and the simplified systems. The proposed technique consists of a two-step iterative scheme. In the first step, the optimum residues are obtained by the minimization of the objective function, while the poles (or eigenvalues) are kept constant. In the second step, the poles are optimized while the residues remain fixed. This procedure is continued cyclically until the objective function is satisfactorily minimized. The necessary and sufficient conditions for existence of an optimum are satisfied in each step. The residues, poles and objective functions converge monotonically. The resulting reduced-order model obtained by this method is stable if the original system is stable. The method can also be applied to systems with repeated poles and to multivariable systems. The results are superior to those obtained previously in the steady-state, the point-by-point transient response, and the value of the integral-square error. Illustrative examples are presented.     

Information and communication: An outline of a possible general theory of sign information

All live systems acquire and use knowledge to ensure appropriate efficiency in the mutual intercourse with the surrounding environment. Knowledge can be communicated only when the subject's internal model of the object of reality is objectified by means of a certain set of physical signs. Such an externalized model, a communicate, is to be accepted, adequately understood and evaluated by other relevant live systems. The information value of a communicate is therefore a function not only of the communicate itself but of the needs, aims, expectations and possibilities of relevant live systems as well. The information value of the same communicate can vary within a set of those systems. The determination of regularities in the relations between the information value of communicates, their content similarity and distinctive features of live systems producing and using them is a problem for experimental and empirical studies.     

Distributed optimization of general linear multi-agent systems with external disturbance

In this paper, we consider the distributed optimization problems with linear coupling constraint of general homogeneous and heterogeneous linear multi-agent systems under weighted-balanced and strongly connected digraphs. In order to control all agents converge to the optimal output, we propose distributed control laws, therein, the optimal output can make the global cost function reach minimum. Then we guarantee the convergence of the proposed algorithms by the properties of Laplacian matrix and Lyapunov stability theorem. Furthermore, we extend the result of heterogeneous linear multi-agent system to the case that dynamics of agents are subject to external disturbances, and prove that the algorithm designed by internal model principle can make all agents reach the optimal output exactly. Finally, we provide examples to illustrate the effectiveness of the proposed distributed algorithms.     

Observer-based event-triggered tracking consensus of non-ideal general linear multi-agent systems

In this paper, the leader-following consensus problem of general linear multi-agent systems without direct access to real-time state is investigated. A novel observer-based event-triggered tracking consensus control scheme is proposed. In the control scheme, a distributed observer is designed to estimate the relative full states, which are used in tracking consensus protocol to achieve overall consensus. And an event-triggered mechanism with estimated state-dependent event condition is adopted to update the control signals so as to reduce unnecessary data communication. Based on the Lyapunov theorem and graph theory, the proposed event-triggered control scheme is proved to implement the tracking consensus when real-time state cannot direct obtain. Moreover, such scheme can exclude Zeno-behavior. Finally, numerical simulations illustrate the effectiveness of the theoretical results.