Approximate transfer functions for multivariable systems

In this paper, a higher-order integrator approach is proposed to obtain an approximate discrete-time transfer function for uncertain continuous systems having interval uncertainties. Because of the simple algebraic operations of this approach, the resulting discrete model is a rational function of the uncertain parameters. The problem of non-linearly coupled coefficients with exponential nature occurring in the exact discretetime transfer function is therefore circumvented. Furthermore, the interval structure of the uncertain continuous-time system is preserved in the resulting discrete model by using this approach. Formulae to obtain the lower and upper bounds for the coefficients of the discrete interval system are derived, so that digital simulation and design for the uncertain continuous systems can be performed by using the available robustness results in the discrete-time domain.

Transfer function estimation of turboalternator from practical operating data by spectral analysis

The problem of estimating the transfer function of a linear system, together with the spectral density of an additive disturbance, is considered. The set of models used consists of linear rational transfer functions and the spectral densities are estimated from a finite-order autoregressive disturbance description. The true system and disturbance spectrum are, however, not necessarily of finite order. We investigate the properties of the estimates obtained as the number of observations tends to ∞ at the same time as the model order employed tends to ∞. It is shown that the estimates are strongly consistent and asymptotically normal, and an expression for the asymptotic variances is also given. The variance of the transfer function estimate at a certain frequency is related to the signal/noise ratio at that frequency and the model orders used, as well as the number of observations. The variance of the noise spectral estimate relates in a similar way to the squared value of the true spectrum.

Experimental investigation of model-based IMC control of severe slugging

The approximation of a fractional order PIλDμ-controller transfer function using a chain fraction theory is considered. Analytical expressions for the approximation of s±α components of the transfer functions of PIλDμ-controllers were obtained through the application of the chain fraction theory. Graphs of transition functions and frequency characteristics of Dμ (α = μ = 0.5) and Iλ (α = λ = −0.5) parts for five different decomposition orders were obtained and analyzed. The results showed the possibility of applying the approximation of the PIλDμ-controller transfer function by the method of chain fractions with different valuesof λ and μ. For comparison, the transfer functions with the same order polynomials, obtained by the methods of Oustaloup transformation and chain fractions, were approximated for α = ±0.5. The analysis proved the advantages of using the chain fraction method to approximate the transfer function of the PIλDμ-controller. The performed approximation opens up the possibility of developing engineering methods for the technical implementation of PIλDμ-controllers. The accuracy of the same order transfer function approximation is higher when the method of chain fractions is used. It has been established that the adequacy of the frequency characteristics of the transfer functions obtained by the chain fraction method also depends on the approximation order.

I investigate the optical transfer function of three-dimensional display systems. Moreover, I obtain an average sampled modulation transfer function describing discrete, sampled display systems and show that in the proper limit of geometrical optics it is equivalent to the shift-invariant optical transfer function. I apply the theory to describe holographic stereograms and discuss the effects of amplitude and phase filters on the optical resolution.

The notion of the transfer function of the discrete-time nonlinear control system is defined. The definition is based on a non-commutative twisted polynomial ring, which can be by the Ore condition extended into its quotient ring (field of fractions). Some properties of the transfer function, related to accessibility and observability of the system, are studied and the transfer functions of different composite systems (series, parallel, and feedback connections) are given. The resulting theory is, in principle, similar to that in the linear case, except that the polynomial description relates now the differentials of inputs and outputs, and the resulting polynomial ring is non-commutative.

The load parameter, Q, and the ratio of the switching frequency to the resonant frequency, Fs/Fo, characterize the operation of resonant converters. An accurate do analysis of the series and parallel resonant converters is given in terms of these parameters whereby the conversion ratio, peak stresses, and diode conduction time are determined. An exact and systematic method of small-signal analysis is given whereby the control-to-output transfer function, audio susceptibility, and input impedance are determined at a given operating point. In addition, simple and approximate transfer functions are obtained under high-Q assumption.

We extend the approximate transfer function calculus of "underspread" linear time-varying (LTV) systems introduced by W. Kozek (1992). Our extension is based on a new, generalized definition of underspread LTV systems that does not assume finite support of the systems' spreading function. We establish explicit bounds on various error quantities associated with the transfer function approximation. Our results yield a simple and convenient transfer function calculus for a significantly wider and practically more relevant class of LTV systems than that previously considered.

A fast raw signal simulation method based on the equivalent scatterer and subaperture processing for the one-stationary bistatic synthetic aperture radar (OS-BSAR) is presented. It considers the radar's motion error to simulate the more accuracy raw signal. First, the OS-BSAR geometry is built in elliptical polar coordinate, and then the scene is divided into several equidistant elliptical rings. Based on the equivalent scatterer, the approximate SAR system transfer function is derived, thus each pulse's raw signal is calculated by the convolution of the transmitted signal and transfer function, using the fast Fourier transform (FFT). To further improve the simulation speed, the subaperture and subscene processing are used. The transfer function for the same subaperture's pulses is calculated by the weighted sum of all the subscenes' equivalent scattering coefficient in the same equidistant elliptical ring, using the nonuniform FFT (NUFFT). This method involves NUFFT, FFT and complex multiplication, which means the easier operation and higher speed. Implementation of the proposed method is discussed. Simulation is given to prove the validity of the proposed method.

Significant arterio-venous differences in nicotine concentrations have been observed during and after cigarette smoking, nicotine nasal spray, and intravenous nicotine administration. In this paper we describe a novel mathematical method for estimating arterial blood levels from venous blood level data. The model allows to quantify: (i) the influence of the microcirculation in the hands and forearm on the distribution of nicotine, and (ii) the influence of disregarding the venous to arterial circulation in the estimate of systemic inputs. We also (iii) propose a general method to predict arterial concentrations and inputs given venous data. The basic model we adopt is based on the relationship Cv = T * Ca, where Cv and Ca are the concentration in the venous and arterial site, respectively, T is the arterio-venous transfer function and * indicates convolution. We use empirical data to estimate T. We then compare estimates of systemic inputs to the venous site obtained taking into account the transfer function or, as usually done, disregarding it. The relationship we use to compare estimated inputs are: Cv = T * ka * A (where Ka is the arterial disposition function and A the systemic input), and Cv = Kv * A (where Kv is the venous disposition function), respectively. Finally, the estimated transfer function allows to estimate (average) Ca or A given arbitrary venous data. (i) Our analysis suggests that a bi-exponential T is needed to describe observed arterial-venous differences. The estimated transfer function indicates that no elimination of nicotine is involved in the forearm. (ii) Disregarding T, as usually done, erroneously obtains too complex venous input functions (because these input functions incorporate T). (iii) Disregarding T erroneously estimates significantly higher total inputs. (iv) Using the proposed model and previously published venous nicotine level data we predict substantial arterial-venous differences in blood nicotine levels for smokeless tobacco and nicotine gum. The use of disposition functions obtained from venous data may lead to erroneous estimation of the rates of entry into the circulation and systemic bioavailability for many drugs.

An iterative method for simplification of discrete systems

On the Estimation of Transfer Functions

This paper proposes robust proportional -integral-derivative (PID) control for a proton exchange membrane fuel cell (PEMFC) system. We model a PEMFC as a multivariable system, and apply identification techniques to obtain the system's transfer function matrices, where system variations and disturbances are regarded as system uncertainties. In previous studies, robust control has been successfully applied to improve the stability, performance, and efficiency of a PEMFC system. However, the resulting robust controllers can be complicated. On the other hand, PID control has been widely applicable to engineering practices because of its simple structure, though it lacks stability analysis for systems with uncertainties. Therefore, combining the merits of robust control and PID control, we design robust PID controllers to regulate hydrogen and air flow rates of a PEMFC system. From the discussion of stability, performance, and efficiency, the proposed robust PID controllers are shown to be effective.

Statistical estimation theory is applied to derive effective techniques for measurement of the pulse transfer function of a linear system from normal operating records obscured by additive noise. It is shown that the problem is equivalent to that of fitting a hyperplane to a set of observed points with random errors in certain coordinates. A method of Koopmans is applied to obtain generalized least squares estimates which are also maximum likelihood estimates when the noise is white and Gaussian. The estimates of the coefficients are obtained as the components of the eigenvector corresponding to the smallest eigenvalue of a matrix equation involving the sample auto- and cross-correlation functions of the input and output records and the covariance matrix of the corresponding noise components. Expressions for the sampling variances and biases are given. The properties of the simpler standard least squares estimates are also considered. The appropriate modifications for nonwhite noise are described.