An Interactive System SDI on Microcomputer

SDI is an interactive system,based on PASCAL,for Symbolic Differentiation and Integrationcompulation.It runs on an IBM-PC.Both input and output are symbolic mathematical expressions.It canmanipulate symbolic differentiation,symbolic integration,and algebraic simplification,etc.The languageand implementation of SDI will be presented in this paper.     

Symbolic image indexing and retrieval by spatial similarity: An approach based on B-tree

In this paper, the problem of indexing symbolic images based on spatial similarity is addressed. A model based on modified triangular spatial relationship (TSR) and B-tree is proposed. The model preserves TSR among the components in a symbolic image by the use of quadruples. A Symbolic Image Database (SID) is created through the construction of B-tree, an efficient multilevel indexing structure. A methodology to retrieve similar symbolic images for a given query image is also presented. The presented retrieval model has logarithmic search time complexity. The study made in this work reveals that the model bears various advantages when compared to other existing models and it could be extended towards dynamic databases. An extensive experimentation is conducted on various symbolic images and also on the ORL and YALE face databases. The results of the experimentation conducted have revealed that the proposed scheme outperforms the existing algorithms and is of practical relevance.     

Recursive Implementation of LoG Filtering

LoG filters have been widely used as a second derivative filtering function. One problem with LoG filtering is that it is very time consuming, especially with a large size filter. We use an analytical method to obtain the z-transform of LoG function in a rational function form and develop a recursive implementation. The structure of the recursive filters is defined by the order of rational functions. The algorithm gives a constant computation complexity per pixel. The computational complexity of recursive filtering depends on the number of poles and zeros of the transfer function, i.e., on the structure of the recursive filter. It is independent of the size of the filter, and thus has a substantial saving in computation. A general method of designing high order recursive filters is also given. Recursive functions can be implemented in a number of shifting registers in hardware. The methodology will contribute to real-time image processing and robot vision.     

Analysis and design of minimum-phase zeros of sampled systems

Criteria are presented to ensure that all zeros of the equivalent discrete transfer function of a continuous-time plant with a sampler and a zero-order hold are stable. An algorithm is proposed which is more efficient than methods based on the Nyquist curve, and works with transfer function poles of any multiplicity. A method has been developed to modify the location of the zeros of the discretized system which is based on the addition of an analogue first-order lag-lead filter between the computer DA converter and the plant.     

SIMO和MISO系统绝对稳定性问题的一个猜想和几个推论

首先分析了具有多个非线性特性的 SIMO 和 MISO 系统的绝对稳定性问题, 指出应用已知的频域判据来解决上述问题很难奏效. 然后, 基于所有孤立部分传递函数都正实的充分必要条件给出了上述系统为稳定的一个猜想, 当传递函数的零极点都位于虚轴上时, 由这一猜想得到了一个已知的结论; 当传递函数的零极点都位于实轴上时, 由这一猜想得到了一个新的结论, 本文证明该结论是正确的; 最后, 根据这一猜想, 给出了传递函数极点位于复平面的一个例子, 它涉及到一类系数矩阵为时变正定矩阵的振动方程的稳定性问题, 值得去深入研究.     

Properties of modulated and demodulated systems with implications to feedback limitations

It is well known that the poles, zeros and delay of a system play an important role in determining the associated feedback performance limitations. In this paper, we first derive an approximate transfer function for a modulated and demodulated system of a particular form. We next analyse the behaviour of the poles, zeros and delay of this transfer function when the modulation frequency is varied. Some implications of these results are also briefly discussed.     

Cascade decomposition and realization of multivariable systems via block-pole and block-zero placement

A technique is presented for state-feedback and state-feedforward block decomposition of a class of multivariable systems into a block-cascaded form structure having the assigned block poles and block zeros. A state-space technique is also presented for minimal realization of a multivariable compensator, represented by a voltage transfer function matrix, using the decoupled RC cascaded networks and summers.     

Parametric system identification on logarithmic frequency responsedata

Gradient search methods that fit the parameters of a user-defined transfer function to experimental logarithmic frequency response data are presented. The methods match a model based on physically significant parameters, including natural frequencies of poles and zeros and damping ratios of complex poles and zeros. The algorithms construct and utilize their own analytical gradient descent functions, based on the desired model. One method attempts to fit both log magnitude and phase, while another identifies a minimum phase transfer function model from only log magnitude frequency response data. The log magnitude algorithm is shown to be superior to traditional methods using nonlogarithmic frequency response data, including those used in commercially available frequency response analyzers. The algorithms are shown to perform well, especially for systems with lightly-damped dynamics     

Graph theoretic modeling and analysis of multibody planarmechanical systems

A methodology of modeling and analysis of planar mechanical systems is developed based on graph theoretic methods, with improvements in component models. The system model based on cutset and circuit topologies is used to derive a new hybrid cutset-circuit method of formulation of the equations of motion for planar systems. Computer-aided formulation is based on analysis of the substitution procedure mandated by the hybrid cutset-circuit formulation. A new graphical representation of the formulation process is introduced: substitution graphs. No special programming is needed for computer-aided formulation which can be achieved in a symbolic form using the off the shelf Maple symbolic mathematics system. Symbolic formulation requires only inputting the systems equations in an order and form as derived from the analysis of the hybrid formulation. An algorithm for symbolic formulation using Maple is given. A compact set of differential-algebraic equations results, which can be solved numerically. Some simple systems will result in closed-form solutions. A number of examples are given to illustrate the modeling and formulation. Numerical solutions are also given to demonstrate the effectiveness and correctness of the formulation procedure     

Order estimation for linear time-invariant systems using frequencydomain identification methods

A two-step coarse-fine order estimation technique is proposed to determine the order of the numerator and the denominator polynomials of rational transfer function models for single-input/single-output (SISO) linear time-invariant systems. The coarse order estimation is based on rank detection by verification of the stochastic significance of the singular values of a linearized problem. The fine order estimation is based on a statistical analysis of the maximum likelihood cost function. The method is tested on measurements of low-(4 zeros, 6 poles) and high- (58 poles, 58 zeros) order systems     

Pole and zero assignment by state vector feedback

A procedure is described which enables specified poles and zeros of a scalar transfer function of a controllable, observable, linear system to be obtained by using state vector feedback to two inputs. The number of zeros is equal to the number of zeros in the transfer function, before feedback is applied, from one input or the other, whichever is the greater. Those zeros which can be changed, and those which cannot, are identified. The former can be made equal to, or arbitrarily close to, any assigned values, and the poles can be assigned arbitrarily.     

Closed form ℒ 2/ℋ2-optimising of zeros for model reduction of linear continuous time systems

Closed form expressions of transfer function responses are applied in this article to model reduction of nth order continuous time systems with respect to the location of zeros for a given location of poles. Explicit closed form formulae are derived for the numerator coefficients in the transfer function of the reduced system that minimise the integrated square deviation from the original system with respect to the impulse response or higher order responses, i.e. effective ?₂ or ?₂-optimisation. The relative degree of the reduced model can be selected freely, e.g. as the original model's one, by selecting the number of numerator coefficients. Constraints are dealt with by introducing a vector of Lagrange multipliers corresponding to the response order. The formulae are also related to solutions of Lyapunov and Sylvester equations based on the companion matrices of the original and reduced systems. The formulae derived can be used to enhance the results obtained from other reduction techniques such as those based on balanced Grammian reduction and singular value decomposition for mid-sized systems. Two examples, demonstrating this, are presented. The formulae can also be used as a basis for a more general optimisation approach, where the optimisation with respect to the numerator coefficients or the zeros, resulting in the solution of a linear system of equations, is combined with non-linear optimisation with respect to the denominator coefficients or the poles.     

用时域法分析增加零极点对控制系统性能的影响

主要用时域法分析增加零极点对系统性能的影响。给出原系统的阶跃响应曲线和主要性能指标,然后在原系统闭环传递函数的基础上增加一个零点,或者增加一个极点,并不断改变零极点的位置来分析,从而得出增加零极点后对系统的性能有哪些影响。     

Routh approximations for reducing order of linear, time-invariant systems

A new method of approximating the transfer function of a high-order linear system by one of lower order is proposed. Called the "Routh approximation method" because it is based on an expansion that uses the Routh table of the original transfer function, the method has a number of useful properties: if the original transfer function is stable, then all approximants are stable; the sequence of approximants converge monotonically to the original in terms of "impulse response" energy; the approximants are partial Padé approximants in the sense that the firstkcoefficients of the power series expansions of thekth-order approximant and of the original are equal; the poles and zeros of the approximants move toward the poles and zeros of the original as the order of the approximation is increased. A numerical example is given for the calculation of the Routh approximants of a fourth-order transfer function and for illustration of some of the properties.     

Symbolic pattern manipulation of Karnaugh-Veitch maps for pneumatic circuits

Pneumatics continue to play a vital role in low-cost automation. The designing of pneumatic control circuits has to date been a slow manual process. This paper describes the computational symbolic manipulation of the Karnaugh-Veitch (KV) map which is the heart of the prototype expert system called PNEUMAES. The symbolic manipulation of a KV map is governed by two sets of generic rules for signal flow plotting and for logic equation minimisation applicable for complex pneumatic circuits. As the complexity of the circuit increases, the symbolic manipulation of a KV map leads to the combinatorial explosion problem. Because of this problem, PNEUMAES can only automatically generate pure pneumatic circuit design equations which will yield minimised circuit configuration for up to four cylinders with auxiliary control valves. A case study is included and issues and problems relating to the implementation of the KV map are discussed. Symbolic and sub-symbolic learning approaches are suggested as a means by which the search space of the symbolic patterns of the KV map can be pruned.     

Controllable and Uncontrollable Poles and Zeros of nD Systems

 We use the behavioural approach to define and characterize controllable and uncontrollable poles and zeros of multidimensional (nD) linear systems. We show a strong relationship between controllable poles and zeros and properties of the transfer function matrix, and we give characterizations of uncontrollable poles and zeros, in particular demonstrating that these have an input decoupling property. Date received: December 13, 1999. Date revised: October 9, 2000.     

Symbolic sensitivity analysis of IIR digital filters using MATLAB

This paper presents a MATLAB-based symbolic sensitivity analysis of second-order IIR digital filters. The sensitivity matrix of the pole displacement is derived in a symbolic form using the Symbolic Toolbox of MATLAB, and the symbolic expressions for various structures are presented. From the sensitivity matrix the variations of pole radius and angle are derived as a function of changes of the parameters of the denominator polynomial and the filter coefficients. In addition, a new second-order structure has been introduced and its pole sensitivities are compared with that of other known structures using the proposed sensitivity analysis.     

区域搜索法自动绘制根轨迹和补根轨迹

本文用一维直接搜索法在给定的区域内能准确地搜索出根轨迹点或补根轨迹点.它可 适用于零极点或分式多项式且均带有纯时间迟延的开环传递函数,原则上不受阶次的限制.本 法的程序在袖珍机PC-1500上已满意地做出了大量的实例,高至十阶.