Showing papers on "Transfer function published in 1970"

Decoupling and Pole Assignment in Linear Multivariable Systems: A Geometric Approach

Abstract: Decoupling and pole assignments in linear multivariable control systems using geometric method

Return-difference and return-ratio matrices and their use in analysis and design of multivariable feedback control systems

Abstract: Bode's concepts of return difference and return ratio are shown to play a fundamental role in the analysis of multivariable feedback control systems. Matrix transfer functions are regarded as operators on linear vector spaces over the field of rational functions in the complex variable s. The eigenvalues of such operators are identified as characteristic transfer functions. The corresponding characteristic frequency responses provide a simple and natural link between classical single-loop design techniques and multivariable-system feedback theory. These concepts then serve as a unifying thread in a coherent and systematic discussion of multivariable-feedback-system design techniques.

A Low-Pass Prototype Network for Microwave Linear Phase Filters

Abstract: A new approximation theory is presented for a low-pass prototype filter which simultaneously optimizes both the passband amplitude and phase response of the scattering transfer coefficient over the same finite band. This closed form solution is expressed in terms of single polynomial, which is readily generated through a simple recurrence formula, and has been termed the equidistant linear phase polynomial since its phase deviation from linearity vanishes at equidistant points along the real frequency axis. A synthesis procedure is presented for the realization of this transfer function using a resistively terminated, symmetrical, lossless, two-port network where extensive use is made of the immittance inverter concept. The even-mode admittance, which defines the network, possesses a simple closed form representation in terms of the equidistant linear phase polynomial and its derivative, and consequently, the entire theory is derived in an analytic form. Typical performance characteristics are graphically presented for networks of up to 14th degree, illustrating the superiority of this new approach over any other known form of approximation theory for selective linear phase filters.

Distributed system simulation using infinite product expansions

Abstract: Linear distributed dynamic system simulation using infinite product expansions for transcendental terms in transfer functions

An improved technique for transfer function synthesis from frequency response data

Abstract: An improved curve fitting technique, based on modification of work by Levy and Sanathanan and Koerner, incorporating known physical constraints is described. A comparison with experimental results on high-order systems shows that there is a much better guarantee of obtaining stable transfer functions and of predicting responses in other domains.

Calculation of transfer functions in grid-controlled convertor systems. With special reference to h.v. d.c. transmissions

Abstract: In high-power grid-controlled convertor systems large parallel capacitor batteries are usually installed and connected to the a.c. busbar at the same point as the convertor. They can be used either for filtering harmonics, e.g. as parts of tuned filters, or for the generation of reactive power, or both. The capacitive components introduced complicate the dynamic behaviour of the convertors considerably, and thus the system cannot be described by simple convertor theory. In the paper, the frequency response of such a system is deduced, using the concept of ‘conversion functions’ introduced to systematise and simplify the calculations. The frequency response for the current-control loop is deduced with reference to h.v. d.c. transmissions, but the results are applicable to any kind of rectifier load. The numerical calculations are laborious and require the use of a digital computer. The comparison between calculated and simulator-measured frequency responses for two practical h.v. d.c. transmissions shows satisfactory agreement. The calculated transfer functions are useful for the synthesis of the current-control system and allow an inexpensive study of the effects of system changes on the achievable speed of response.

Improved convergence and increased flexibility in the design of model reference adaptive control systems

Abstract: A modified Liapunov design technique for model reference adaptive control system is shown to result in improved system convergence. An adaptive rule, derived on the basis of a new Liapunov function, is compared to the previous rule. A local stability analysis applied to the modified design shows that the error response is more rapidly convergent. Furthermore, system simulations show that the transient response for the adjustable parameters is also improved. A second result presented is a design technique for a class of plants whose parameters cannot be adjusted directly. This design leads to a system with a set of prefilter and feedback adjustable gains as the adaptive parameters and physically realizable linear time-invariant filter networks in both the feedback and prefilter paths. It eliminates the problem of nonunique adaptive laws previously encountered and requires only n - m - 1 derivative networks for its implementation (nth order plant with m zeros); hence, if m = n - 1, no derivative networks are required for implementation. In order to maintain a bounded plant input signal, the zeros of the plant transfer function must be restricted to the open left-half plane.

Adaptive echo canceller for nonlinear systems

Abstract: Operation of a closed-loop echo cancellation system for use in a two-way communication circuit is improved by employing a multidimensional network capable of approximating a large class of nonlinear transfer functions, and a control circuit arrangement for automatically adjusting parameters of the network. Signals incoming to a four-wire to two-wire junction are supplied to the network which, supplied with an error signal derived from signals in the outgoing path, develops a replica of an undesired echo. The replica signal is subtracted from outgoing signals and the differential is used for the derivation of a new error signal.

Pulse Shaping for Nuclear Pulse Amplifiers

Abstract: The emphasis of this paper, in which a systematic approach to nuclear pulse shaping is presented, is on the power, versatility, and practicability of lumped-element transfer functions and their associated networks. The approach consists of first determining a suitable theoretical, but realizable, lumped-element transfer function for the problem at hand -- pulse height analysis is the example used in this paper -- and of then synthesizing this transfer function in a way that minimizes the sensitivity of the final output-pulse shape to network element variations. Finally, the network is built and tested using elements having tolerances determined by a sensitivity analysis of the chosen circuits. The unipolar transfer functions and networks discussed in this paper have better signal-to-noise ratios than any other published lumped-element transfer functions or networks. One unipolar pulse function has a signal-to-noise ratio that is only 0.5% worse than that of the delayline-produced triangular pulse. Since the bipolar pulses discussed in this paper are more symmetrical about the base line than those of any other published lumped-element network, spectral peaks at high count rates obtained with these networks will be more symmetrical than those obtained with any other lumped-element network. Furthermore, these symmetrical pulses will produce smaller countrate-dependent base-line shifts than will less-symmetrical equal-area pulses. Although the networks that are discussed in this paper are extremely useful for pulse height analysis, the systematic approach that is presented is more important because of its obvious extensions to other pulse shaping problems in nuclear physics.

Rational approximation to transfer-function matrix of distributed system

Abstract: A solution is given to the problem of finding a matrix of rational functions which is an approximation to the transfer-function matrix of a multivariable system described by a mixed set of partial and ordinary differential equations.

Predicting servomechanism dynamic performance variation from limited production test data

Abstract: A probabilistic model describing the considerable variation in dynamic performance of a large family of electro-hydraulic servomechanisms is presented. Two fundamentally different techniques are employed to obtain the parameters of the model, both techniques giving very similar results. A third-order dominant transfer function (derived from the production test data) together with high frequency complex poles and a high frequency lag (both factors derived from field testing) form a sixth-order system. Variable parameters for the sixth-order system form the probabilistic model and are presented as a table for use in Monte Carlo simulation. The model is then used to derive experimentally verified production test limits in a new test domain, equivalent to the original frequency domain gates, showing how the use of a novel filtering technique, recently described elsewhere, may be employed to simplify the setting of test limits. The model is also shown to be of use in the prediction of dynamic errors in many domains (whilst only requiring data in one domain) and the initial production test data are shown to predict accurately the dynamic error variation for the complete family.

Transfer Equivalence of Linear Dynamical Systems

Abstract: The concepts of weak and strong transfer equivalence of constant (time-invariant) linear dynamical systems are defined and analyzed. The analysis leads to a simple new algorithm for constructing minimal realizations of transfer function matrices. In addition, it provides new information on the significance of the polynomial invariants which appear in the Smith–McMillan canonical form.

On the phase-plane analysis of relay control system with dead time†

Abstract: An exact method of analysis of non-linear systems containing a two-position relay element and a dead-time element is given using the phase-plane concept. Equations of the switching lines for both unsymmetrical and symmetrical relay characteristics are obtained under consideration of the dead time. Expressions to evaluate the period and amplitude of the self-oscillation of the system are derived from the stable limit cycle in the phase plane. This method is developed for a second-order system with a zero in its transfer function. For such a system it is indicated with a help of an example that approximation methods as the describing function yield large errors because the low-pass condition is not satisfied. The phase-plane method will be developed for other relay characteristics.

A New Model Performance Index for Engineering Design of Flight Control Systems

Abstract: The theory and application of a new performance index, the Model PI, that brings engineering design specifications into the analytical design process is presented. A parameter optimization design procedure is established that starts with practical engineering specifications and uses the Model PI as a synthesis tool to obtain a satisfactory design. The Model PI represents a new criterion for approximating one dynamical system by another, based on a novel geometrical representation of linear autonomous systems. It is shown to be an effective performance index in designing practical systems and to be substantially more efficient to use than a comparable model-referenced integral squared error performance index. The design procedure is demonstrated by designing a lateral-directional stability augmentation system for the X-15 aircraft. Nomenclature a = system extended coefficient vector di = system characteristic polynomial coefficient of sl bi = system transfer function numerator polynomial coefficient of s* I = order of model m = number of system zeros n = order of system Q = Model PI weighting matrix, a«Vll«ll2 r = pseudo initial condition weighting factor u = input variable W = extended pseudo initial condition weighting matrix x = system transient response variable x = system extended state vector or trajectory y = output variable OL = model extended coefficient vector in system's extended state space Subscripts m = model 0 = initial time Special notation ( )(») = rith derivative of the variable ( ) ( )' = transpose of ( ) ||v|| = (v'v) which is the length of v |Hk2 = v'Mv

Theory of distributed systems.

Abstract: Physical networks with lumped components and hydraulic, pneumatic, electric, thermal and elastic lines of transfer matrices

A New Sine-Squared Pulse and Bar Shaping Network

Abstract: The Fourier method for time domain synthesis is applied to find the transfer functions of five-, seven-, and nine-pole networks that have an impulse response approximating a sine-squared pulse to an increasing degree of accuracy. Results are compared to a seven-pole Thomson network. Where the departures of the impulse response from the sine-squared curve reach 2 percent of the peak amplitude in a seven-pole Thomson network, the new seven-pole network does not exceed 1.3 percent, whereas the nine-pole network is within 0.7 percent. Practical networks are synthesized from the transfer functions, both of the single-and double-terminated ated type.

Signal design for efficient detection in dispersive channels

Abstract: Signal design for maximizing the efficiency of the Neyman-Pearson detection procedure in randomly dispersive media is investigated. The medium is modeled as a randomly time-varying linear filter; by viewing the filter transfer function as a homogeneous random field on the time-frequency plane, a second-order theory results that relates various second-order measures of the time and frequency structures of input and output processes. A signal design strategy is developed that dictates transmitting signals that produce output processes with degrees of freedom possessing a signal-to-noise ratio (SNR) in the vicinity of 2. A distribution of signal energy in the output time-frequency plane that achieves the proper SNR for each degree of freedom is deduced and is used to infer constraints on input ambiguity functions that maximize detection efficiency. The general structure of efficient input signals for both high and low SNR is briefly discussed.

Design of dominant-type control systems with large parameter variations†

Abstract: Optimum design of dominant type adaptive control systems with large parameter variations, using fourth order approximation

A new method of solving optimal servo problems reducible to regulator problems

Abstract: A new method of solving linear single-input single-output optimal servo problems reducible to regulator problems is presented. The starting point for the design procedure is the description of the plant in state-variable equations, and there is no need to compute the transfer function of the plant. A numerical example is also worked out to illustrate the procedure.

Combinational arithmetic systems for the approximation of functions

Abstract: The concepts of arithmetic building blocks (ABB) and combinational arithmetic (CA) nets as well as their applications have been previously reported in References 3, 4, and 5 The unique ABB, resulting from the efforts of minimizing the set of building blocks in Reference 3, is designed at the arithmetic level, employing the redundant signed-digit number system, and is to be implemented as one package by LSI techniques The ABB performs arithmetic operations on individual digits of radix r > 2 and its main transfer functions are: the sum (symbol +) and product (symbol) of two digits, the multiple sum of m digits (m ≤ r + 1), (symbol ≠), and the reconversion to a non-redundant form (symbol RS)

Determination of a Behavioural Transfer Function by Frequency Analysis

Abstract: TRANSFER functions are used by engineers as a means of describing, in a single equation, the relationship between the input and output of a system. Frequency analysis is a classic method of determining transfer functions in physical systems, and has also been used for quasi-behavioural systems, such as those controlling optokinetic responses1 and the pupillary light reflex2. In the behavioural context, a transfer function describes the stimulus–response relationship in all possible stimulus conditions. It also makes it possible to compare biological and physical systems directly. In other words, it offers an explanation of behaviour that is independent of the “hardware” involved. In this preliminary report, frequency analysis is applied to behaviour, with the eventual aim of accounting for motivational phenomena rigorously and quantitatively.

System frequency response using p-n binary waveforms

Abstract: A method is presented by which the frequency response of a system may be obtained directly from the response to a pseudorandom binary sequence without recourse to the calculation of the cross correlation function and its subsequent Fourier transformation. The technique is ideally suited to digital computer processing but could also be carried out by equipment having a combination of features available in present day transfer function analyzers and noise generators.

Modified time domain comb filters

Abstract: A delay line type comb filter is adapted to produce a response in which a selected portion of the comb characteristic is modified. This is accomplished by attenuating the signal through the delay line in a predetermined manner over a selected frequency range and inversely modifying the nondelayed transmission in that range. These two functions are provided by applying the input signal to a filter element having a transfer function appropriate to the desired modification and combining the filtered output with the input signal in two combiners (one additive and one subtractive). The differential resultant signal is applied to the delay line to produce the prescribed attenuation and the additive resultant signal (enhanced inversely to the differential resultant) is added to the output of the delay line producing the desired modified comb transmission characteristic.