Synthesis of a Class of Non-linear Systems†

A problem in the practical application of the Volterra series to nonlinear theory is the synthesis of systems with a given set of Volterra kernels. In this article we present a method of determining whether a given Volterra kernel can be synthesized exactly by using only a finite number of multipliers. A method for the synthesis of such kernels is also presented. The use of the techniques discussed here is illustrated by examples.     

Parameter Estimation in the Presence of Measurement Noise†

The parameter estimation problem is formulated for the situation in which the measurement of every variable is subject to noise. The method of maximum likelihood is shown to produce estimators for which the amount of computation is prohibitive but these estimators fire used as a standard against which the accuracy of more easily computed methods may be judged, A number of alternative methods are introduced, a form of weighted least squares being shown to require the least computation and to approximate the accuracy of the maximum likelihood estimators. An example of the appli-cation of this method is given.     

Stability of a Hysteretic System with Random Signal Inputs†

The stability of a feedback system with a hysteretie relay controller, when forced by a Gaussian signal, is analysed by applying the quasi-linearization approach.A method for computing the sinusoidal and random signal gains of a non-linear element, based on the evaluation of the input—output cross power of the clement, is first explained. Knowledge of these two gains for an ideal relay is then used to find the corresponding gains for a hysteretic relay. These gains are finally used for analysing the effects of both high-frequency and low-frequency random signals on the auto-oscillations of a second-order system with the hysteretic relay. Results of simulator studies are also presented.     

Decomposition of a Finite Quantum System into Subsystems: Symbolic–Numerical Approach

Programming and Computer Software - Any Hilbert space with composite dimension can be represented as a tensor product of Hilbert spaces of lower dimensions. This factorization makes it possible to...     

On modifying the prediction control of a second-order plant†

The switching behaviour of a second-order plant under the combined influence of system non-linearities such as Coulomb friction, stiction, backlash, dead zone, hysteresis and switching delay is analytically examined in this paper.

In the first instance, the mathematical model which characterizes the system dynamics is formulated on a more realistic basis by considering the effect of these non-linearities as integrated parameters rather than isolated phenomena. This is then followed by the derivation of the modified switching equation which, upon careful mathematical manipulation, may be expressed in terms of a power series as a function of the system velocity. Such an approach not only leads to a better understanding of the general switching behaviour during the change over of forward to reversed drive, but also provides a more practical solution for the bang-bang control problem     

On the controllability of systems with a time-varying delay†

This paper is concerned with the controllability of a system with a time-varying delay. The system to be considered here is described by a linear differential-difference equation of a retarded type, where a time-varying delay is a certain class of a time-varying function. First, the concepts of controllability for linear differential-difference systems with a constant delay, introduced by Weiss (1987), are developed to the system with a time-varying delay. Second, necessary and sufficient conditions for controllability are obtained. Finally, the controllability of a stationary system with a constant delay is treated, including the results of Chyung and Lee (1966).     

More on the phase-plane analysis of a relay control system†

The transcendental equation relating the parameters of a closed trajectory of a relay system containing a symmetrical two-position element, a dead element and a rational part of the second order has two solutions. It will be shown that only one of these solutions supplies the self-oscillation of the system.

The phase-plane method is developed for systems containing a relay element with hysteresis. The effect of varying any parameter of the system on the period and amplitude of the self-oscillation can be predicted from the transcendental equation.     

Analysis of a class of non-linear discrete-time systems by the Volterra series†

The discrete form of the Volterra series is used to evaluate the response of a class of non-linear discrete-time systems described by an ordinary nonlinear difference equation with zero initial conditions. Recurrence relations for the Volterra kernels are developed in the time domain and in the transform domain as well.     

Study of Electromagnetic Disturbance Turntable Measurement System Based on a New Predictive Control Algorithm

1 IntroductionElectromagnetic disturbance is the phenomenon ofdegrading the device, equipment or system' s functionand doing harm to life or lifeless matter. It can transmitby radiating and conducting, and the measurement ofradiated disturbances must consider its repeatability, e-conomy, accuracy, anti- disturbing capacity and rapiddetermination. Figure 1 show the concept of measure-ments made on an open area test site.In order to obtain the maximum reading of EUT e-mission, the turntable sh…     

Counting Near-Perfect Matchings on Cm × Cn Tori of Odd Order in the Maple System

Programming and Computer Software - In the Maple computer algebra system, a set of recurrence relations and associated generating functions is derived for the number of near-perfect matchings on...     

The gradient of a sampled function†

One of the applications of digital computers in processing sampled data is in determining the gradient of a sampled function. In this paper an algorithm is found for determining the gradient in N dimensions of an N-dimensional wave-number-limited function from its samples. The gradient is found at the sampling points. An upper bound to the truncation error is calculated. The dependence of this error on the pitch of the sampling lattice, the number of samples and the maximum exeursion is found for a cardinal reconstruction function.     

Closed-loop control of a class of non-linear systems†

A technique is described for the closed-loop control of a class of non-linear systems iii a potentially large neighbourhood of a nominal trajectory. By the introduction of extra states it is shown how to reduce non-linear differential equations to a related canonical linear form. Since the linear form is not readily amenable to standard design techniques a new synthesis procedure is proposed for the construction of a closed-loop control. The proposed technique relies heavily on computer computation. The computation for the closed-loop control of a lifting body, a system not completely controllable, is given in detail to illustrate the applicability of the method.     

Root-locus Equations of the Fourth Degree†

The paper is a study of the geometrical properties of root-loci for higher-order systems. Properties of general higher-plane algebraic curves are invoked to provide the broad framework of reference for systematic investigation of root-locus properties. Such an approach affords better integrated and more comprehensive understanding of the nature of the root-paths for higher-order systems.

The discussion is a composite one, encompassing all T(N,M) systems of the order N + M Δ h = 5 and 6, whose equations involve fourth-degree powers in ω: N and M denote the number of poles and zeros, respectively, of the open-loop function G(S) where, S = σ + jω.

The examples cited are illustrative of all significant features of higher-plane algebraic curves as manifest in root-locus shapes. Conditions for existence of such features in root-loci are examined and procedures for their identification and location established.     

On the stability of interconnected systems†

This paper investigates the stability of systems which can be regarded as composed of interconnected subsystems. A sufficient condition for inputs-output L ^p stability, in terms of the L ^p gains of the subsystems and their interconnections is derived. For the case of L ² stability, it is compared with other criteria for asymptotic stability, obtained by Lyapunov techniques, and shown to give better results for a certain class of systems.     

Stabilization of a class of linear time-delay systems†

Sufficient conditions for memoryless feedback stabilization of linear time-invariant delay systems are derived. Conditions for this class of system to be stabilized with any desired stability degree are also determined.     

On the asymptotic stability of a particular class of distributed parameter feedback control systems†

In this paper the stability problem for a particular class of non-linear feedback control systems governed by a parabolic partial differential equation is considered. A sufficient condition for global asymptotic stability of the null equilibrium state is derived by the method of comparison functions.     

A method of obtaining the dual-input describing functions for a periodic input†

A combined analytic and graphic procedure is described for obtaining the dual-input describing functions for a class of non-linear elements subjected to a periodic input. The procedure is illustrated by considering the non-linearity to be a simple contactor involving hysteresis and the describing functions obtained for the element are presented.     

On the Optimal Control Problem of a Nonlinear Elliptic Population System

The optimal control problem for a nonlinear elliptic population system is considered. First, under certain hypotheses, the existence and uniqueness of coexistence state solutions are shown. Then the existence of the optimal control is given and the optimality system is established.     

A Parallel System of the Personification Control System On the Basis of Biology Functions

1 Biology and system science of hu-man bodyLooked from the modern system science viewpoint,the human body is precisely a complex great system.The biology research has already divided into the humanbody many levels, like system(Breath, digestion, bloodcirculation, nerve, uropoiesis, reproduction, movementand so on) tissue( connective tissue, fat tissue, epitheli-um tissue, muscular tissue, the nerve and so on)Cell(Cy-tobiology, cytochemistry, cytophysiology, cytogeneticsand so on)、molecule (M…     

On attempts to reduce the sensitivity of the optimal linear regulator to a parameter change†

One suggested method is to adjoin a quadratic form in the sensitivity vector to the integrand of the cost functional and to find the feedback, linear in the state and sensitivity vectors, which minimizes the augmented cost functional.

Several authors have incorrectly assumed that the augmented system can be treated as another optimal regulator problem. In this paper it is shown that the problem, when correctly formulated, has no solution in the sense that there can be no finite state-independent feedback matrices which will satisfy the necessary conditions for an optimum.