Showing papers on "Transfer function published in 1992"

System identification and control using genetic algorithms

Abstract: It is shown how genetic algorithms can be applied for system identification of both continuous and discrete time systems. It is shown that they are effective in both domains and are able to directly identify physical parameters or poles and zeros. This can be useful because changing one physical parameter might affect every parameter of a system transfer function. The estimates of poles and zeros are then used to design a discrete time pole placement adaptive controller. Simulations for minimum and nonminimum phase systems and a system with unmodeled dynamics are presented. >

Applications of hysteresis switching in parameter adaptive control

Abstract: The hysteresis switching algorithm of R.H. Middleton et al. (ibid., vol.33, no.1, p.50-8, Jan. 1988) is reexamined in a broader context. To demonstrate its utility, the algorithm is applied to various families of identifier-based parameterized controllers of both the direct and indirect control types. Application to the direct control type results in a model reference adaptive controller capable of stabilizing, without excitation, any SISO process which can be modeled by a minimum phase linear system whose transfer function has relative and McMillan degrees not exceeding prescribing integers m and n, respectively. It is shown that such processes can also be adaptively stabilized with indirect adaptive controllers and hysteresis switching. A simple numerical example involving a non-minimum-phase process model is used to illustrate how hysteresis switching might be applied to implicitly tuned parameterized controllers to realize an adaptive controller with capabilities which might prove very difficult, if not impossible, to achieve without hysteresis switching or some other form of discontinuous control. >

Adaptive Control of Plants with Unknown Dead-zones

Abstract: Model reference adaptive controllers are designed for plants with unknown dead-zones. Several control strategies are investigated in which two sets of adjustable parameters, one belonging to a dead-zone inverse and the other to a linear controller, are either kept fixed or adaptively updated. The developed adaptive control schemes ensure boundedness of all closed-loop signals and reduce the tracking error.

Analog reconstruction circuit and bar code reading apparatus employing same

Abstract: A bar code detection circuit accepts as input the discretized analog output of a CCD array, and performs piecewise linear reconstruction to produces a continuous polylinear output signal. In the region of a bar/space transition, the output signal is a close approximation of the reflectance function of a bar code symbol convolved with the system transfer function of the bar code reader. Linear interpolation is performed in order to determine the offset of a given threshold value from an edge of the CCD analog output.

Hard frequency-domain model error bounds from least-squares like identification techniques

Abstract: The problem of deriving so-called hard-error bounds for estimated transfer functions is addressed. A hard bound is one that is sure to be satisfied, i.e. the true system Nyquist plot will be confined with certainty to a given region, provided that the underlying assumptions are satisfied. By blending a priori knowledge and information obtained from measured data, it is shown how the uncertainty of transfer function estimates can be quantified. The emphasis is on errors due to model mismatch. The effects of unmodeled dynamics can be considered as bounded disturbances. Hence, techniques from set membership identification can be applied to this problem. The approach taken corresponds to weighted least-squares estimation, and provides hard frequency-domain transfer function error bounds. The main assumptions used in the current contribution are: that the measurement errors are bounded, that the true system is indeed linear with a certain degree of stability, and that there is some knowledge about the shape of the true frequency response. >

Transfer Functions of One-Dimensional Distributed Parameter Systems

Abstract: Distributed parameter systems describe many important physical processes. The transfer function of a distributed parameter system contains all information required to predict the system spectrum, the system response under any initial and external disturbances, and the stability of the system response. This paper presents a new method for evaluating transfer functions for a class of one-dimensional distributed parameter systems. The system equations are cast into a matrix form in the Laplace transform domain. Through determination of a fundamental matrix, the system transfer function is precisely evaluated in closed form. The method proposed is valid for both self-adjoint and non-self-adjoint systems, and is extremely convenient in computer coding. The method is applied to a damped, axially moving beam with different boundary conditions.

Charge control: modeling, analysis and design

Abstract: There are many ways to use the inductor current of a PWM converter as part of its feedback control mechanism. A simple and widely used method is peak current-mode control which uses the instantaneous inductor current as part of the control signals. Charge control is a special type of current-mode control. It uses the integration of the on-time inductor current as the feedback control signal. The characteristics of charge control are studied. A complete small-signal analysis is performed for the control scheme. Subharmonic oscillation similar to that of peak current-mode control is found, and the relationship between subharmonic oscillation and the line/load condition of charge control is defined. Based on the analysis, design guidelines which guarantee the stability of the control system under given line and load ranges are proposed. The small-signal model was confirmed experimentally. >

Small-signal modeling of series and parallel resonant converters

Abstract: A small-signal modeling technique based on the extended describing function concept is applied to series-resonant converters (SRCs) and parallel-resonant converters (PRCs). The models developed include both frequency control and phase-shift control. The small-signal equivalent circuit models are also derived and implemented in PSPICE. The models are in good agreement with measurement data. The high-frequency dynamics of resonant converters around the beat frequency can be accurately modeled. These simple analytical models can be employed in the control loop design of resonant converters. >

Extended Bandwidth Zero Phase Error Tracking Control of Nonminimal Phase Systems

Abstract: This paper describes a new feedforward algorithm for accurate tracking control of nonminimal phase systems. Accurate feedforward calculation involves a prefilter design using the inverse system model. Nonminimal phase systems cause problems with this prefilter design, because unstable zeros become unstable poles in the inverse model. The zero phase error tracking control algorithm (ZPETC) consists of a substitution scheme, which removes the unstable zeros

Asymptotic Properties of the Least Squares Method for Estimating Transfer Functions and Disturbance Spectra

Abstract: 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.

H ∞ optimal sampled-data control in continuous time systems

Abstract: We consider the design of H ∞ optimal discrete-time (digital) controllers in continuous-time systems. An apparent difficulty, especially in utilizing modern transform-domain analysis in this context, stems from the absence of an appropriate (transfer function) model for the hybrid-time (discrete and continuous) closed-loop system. This difficulty is overcome through the introduction of an equivalent difference-equation model for the continuous-time system, with distributed inputs and outputs; equivalence being in the sense that the continuous-and discrete-time inputs and outputs are essentially identical. Using the interplay between the discrete and the continuous time models, solutions of the well-known purely continuous-time and purely discrete-time standard problems extend to solutions of the problem at hand. They comprise Riccati equation characterizations of feasible combinations of sampling rates and bounds on the closed-loop induced input-output norm, and parameterization of compensators. We consid...

Acoustic transfer function simulating method and simulator using the same

Abstract: A plurality of acoustic transfer functions for a plurality of sets of different positions of a loudspeaker and a microphone in an acoustic system are measured by an acoustic transfer function measuring part. The plurality of measured acoustic transfer functions are used to estimate poles of the acoustic system by a pole estimation part, and a fixed AR filter is provided with the estimated poles as fixed values. A variable MA filter is connected in series to the fixed AR filter and the acoustic transfer function of the acoustic system is simulated by the two filters. The filter coefficients of the variable MA filter are modified with a change in the acoustic transfer function of the acoustic system.

Frequency Domain Optimal Control of Wind‐Excited Buildings

Abstract: An optimal frequency‐domain approach to active control of wind‐excited buildings is proposed in which the H2 norm of the transfer function from the external disturbance to the regulated output is minimized. A wind‐excitation model established by factorizing the cross‐spectral density matrix of the wind fluctuation is included in the control design. The control of a 60‐story building under an along‐wind excitation by one mass damper, two mass dampers, and active tendon mechanisms is presented in the numerical examples. As an improvement over previous results in civil‐engineering structural control studies, measurement and minimization of building accelerations is achieved. The effects of using constant and frequency‐dependent weighting functions in the control design are also shown. In this case, the frequency‐dependent weighting functions are designed based on the frequency domain response characteristics of the building. The frequency‐domain‐based‐design approach is shown to be both flexible and powerful.

Pseudorandom signals to estimate apparent transfer and coherence functions of nonlinear systems: applications to respiratory mechanics

Abstract: For pseudorandom (PRN) input stimuli, general expressions are derived for the apparent transfer (Z) and coherence ( gamma /sup 2/) functions of nonlinear systems that can be represented by a Volterra series. To avoid the problems that are shown here to be associated with harmonic distortions and to minimize the influence of crosstalk, a family of pseudorandom signals which are especially suited for the estimation of Z and gamma /sup 2/ in mechanical measurement of physiological systems at low frequencies is proposed. The components in the signals cannot be reproduced as linear combinations of two or more frequency components of the input. In a second-order system, this completely eliminates the bias, while in higher order but not strongly nonlinear systems, the interactions among the components are reduced to such a level that the response can be considered as if it were measured with independent sine waves of an equivalent amplitude. It is also shown that the values of gamma /sup 2/ are not appropriate for assessing linearity of the system. The theory is supported by simulation results and experimental examples. >

Small-signal modeling of average current-mode control

Abstract: A recently proposed average current-mode control is analyzed. A complete small-signal model for the control scheme is developed. The model is accurate up to half the switching frequency. By closing the current loop, a flat control-to-inductor current transfer function, up to half the switching frequency, can be achieved. This control scheme enables the converter to behave as an ideal current source. The subharmonic oscillation, as frequently reported in peak current-mode control, also exists in this control. This subharmonic oscillation can be eliminated by choosing a proper gain of the compensation network in the current loop. Model predictions are confirmed experimentally. >

Optimal controllers for finite wordlength implementation

Abstract: When a controller is implemented by a digital computer with A/D and D/A conversion, numerical errors can severely affect the performance of the control system. There exist realizations of a given controller transfer function exhibiting arbitrarily large effects from computational errors. Assuming sufficient excitation of the system, the problem of designing an optimal controller in the presence of both external disturbances and internal roundoff errors is solved. The results reduce to the standard LQG controller when infinite-precision computation is used. For finite precision, however, the separation principle does not hold. A penalty is also added to the cost function to penalize the sum of the wordlengths used to compute the fractional part of each state variable of the controller. This sum can be used to represent the lower bound on computer memory needed for controller synthesis. It measures controller complexity and is minimized (penalized) here. >

Frequency domain analysis of an optical FM discriminator

Abstract: Measurement of optical phase and frequency deviations using a frequency-domain network analysis approach is described. The frequency domain transfer functions are given which relate the conversion of optical phase, frequency, and intensity modulation into photodetector current after passing through a quadrature biased Mach-Zehnder interferometer. It is shown that the error term in the phase and frequency transfer functions depends only to second order on any accompanying intensity modulation. Experimental data are given illustrating the analytical results. >

Frequency domain diagnostics for linear smoothers

Abstract: Frequency domain analysis is used to examine estimates from linear smoothers operating on realizations of random fields over space and/or time. The estimates are expressed in terms of the Fourier transforms of the dependent variable and of the smoother weights. The latter is referred to as the equivalent transfer function. The data do not need to be evenly spaced to perform this analysis. The modulus of the equivalent transfer function characterizes the spectral content of an estimate and may reveal subtle sampling properties of the design. Frequency domain bias calculations are useful for comparing different smoothers and for assessing the resolution capabilities of a data set. These methods are used to compare six one-dimensional smoothers and analyze a complex three-dimensional example using data from a satellite altimeter.

State space models for current programmed pulse width modulated converters

Abstract: State space models are derived for pulse-width-modulated power converters operating at constant switching frequency under current programmed control. One model neglects the sample and hold effect of the current loop and is therefore representative of the traditional approach taken to modeling current programmed converters. The order of the model is the same as that of the power stage. A second state space model which incorporates the sample and hold effect is derived. The order of this model is two higher than that of the power stage. A comparison of the two models clearly demonstrates the superiority of the second modeling approach. As the models are in state space form they may be quite readily used in a computer-aided-design package for general power converter analysis and design, to determine all transfer functions and associated pole/zero locations of interest. >

Asymptotic properties of the least-squares method for estimating transfer functions and

Abstract: 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 oo at the same time as the model order employed tends to oo. 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.

A control theory approach to the stability and transient analysis of the filtered-x LMS adaptive notch filter

Abstract: A method is presented for analyzing the stability and transient response of the filtered-x LMS adaptive notch filter by formulating the problem in the complex weight domain and applying standard control theory. Examples are given for pure delay and second-order low-pass cancellation path transfer functions. The method is also extended to the multichannel case, where the eigenvalues of the equivalent open-loop transfer function matrix characterize the behavior. >

Robust stabilization in the gap metric: controller design for distributed plants

Abstract: The problem of robustness in the gap metric for infinite-dimensional systems is considered. The problem of computing the optimal controller and the optimal robustness radius for a class of systems whose normalized coprime factors have elements which are H/sub infinity / functions with continuous boundary values is studied. The underlying Hankel and related operators, which are important in the gap optimization problem, are studied, and relations between their singular values and vectors are established. A computational approach to the optimal robustness problem is developed for single-input/single-output systems whose transfer function is an inner function in H/sub infinity / times a rational function. The procedure is applied to a general first-order delay system and a closed-form formula is obtained for the optimal controller. The frequency response plots of the compensated system for various values of time delay are examined. >

On the use of the Hilbert transform for processing measured CW data

Abstract: The Hilbert transform is a commonly used technique for relating the real and imaginary parts of a causal spectral response. It is found in both continuous and discrete forms and is widely used in circuit analysis, digital signal processing, image reconstruction and remote sensing. One useful application in the area of high-power microwave (HPM) technology is in correcting measured continuous wave (CW) transfer function data, so as to insure causality in reconstructed transient responses. Another application of the Hilbert transform is in the area of complex spectral estimation using magnitude-only data. Here, the applications of the transform to several specific spectral filtering and phase reconstruction problems are illustrated. >

New class of discrete-time models for continuous-time systems

Abstract: Digital computing in estimation, control or signal processing for continuous-time systems requires the use of discrete-time models. While conventional difference equation or z-transfer function models are widely popular, a class of methods exists that uses discrete approximations of continuous signals and operators, retaining the continuous-time parameters. Some important advantages of this class have been demonstrated in the contexts of parameter estimation, adaptive control and controller design. This paper proposes a new class of discrete-time models that originates from the z transfer function but which is close to continuous-time models in structure and parameters, thereby retaining its advantageous features. The recently proposed ‘delta’ model is seen to be a member of this class. The interrelations among various digital model types are brought out. Better sensitivity properties over z transfer function models are established. Finite word length properties of these models vis-a-vis the z-transfer fu...

Identifying linear reduced-order models for systems with arbitrary initial conditions using Prony signal analysis

Abstract: A method of identifying reduced-order linear models for systems operating in the neighborhood of an equilibrium point is presented. The method is based on Prony signal analysis, which has recently received considerable attention in the study of power system electromechanical oscillations. Prior to the application of the input test signal, the system can be in a transient state. The system input test signal is piecewise continuous and allows several Prony analyses to be performed during a transient, with each analysis conducted between input discontinuities. Results of these Prony analyses can be combined in various ways to obtain system eigenvalues, transfer-function residues, and initial condition residues. Two examples are given to illustrate the use of the method. >

Frequency domain synthesis of trajectory learning controllers for robot manipulators

Abstract: Trajectory learning control is a method for generating near to optimal feedforward control for systems that are controlled along a reference trajectory in repeated cycles. Iterative refinements of a stored feedforward control sequence corresponding to one cycle of the control trajectory is computed based upon the recorded trajectory error from the previous cycle. Several learning operators have been proposed in earlier work, and convergence proofs are developed for certain classes of systems, but no satisfactory method for design and analysis of learning operators under the presence of uncertainties in the system model have been presented. This article presents frequency domain methods for analyzing the convergence properties and performance of the learning controller when the amplitude and phase of the system transfer function is assumed to be within specified windows. Experimental results with an industrial robot manipulator confirm the theoretical results.

Design of stabilizer for a multimachine power system based on the sensitivity of PSS effect

Abstract: A new approach for designing power system stabilizers (PSS) in multimachine power systems is proposed. It is found that the sensitivity of PSS effect (SPE) defined earlier by the authors for PSS location selection is equal to the sensitivity of a mode with respect to the change of the PSS transfer function. The displacement of a system mode caused by the installation of a PSS can be predicted from the SPE. Based on this prediction the PSS location can be selected and the PSS parameters tuned. The proposed method has been used to design a PSS for a 13-machine power system to increase the damping of an interarea model. The time-domain simulation results indicate that the proposed method can predict the best PSS location to increase damping of the interarea mode. It is very simple to use SPE to tune PSS parameters. >

An indirect method for transfer function estimation from closed loop data

Abstract: An indirect method is introduced that is able to consistently estimate the transfer function of a linear plant on the basis of data obtained from closed loop experiments, even in the situation when the model of the noise disturbance on the data is not accurate. The primary interest is not the consistent identification of the system, but the gathering of a good approximation of its input-output transfer function. The method allows approximate identification of the open loop plant with an explicit and tunable expression from the bias distribution of the resulting model. >