Showing papers on "Transfer function published in 1998"

Optimal and robust control and estimation of linear paths to transition

Abstract: Optimal and robust control theories are used to determine effective, estimator-based feedback control rules for laminar plane channel flows that effectively stabilize linearly unstable flow perturbations at Re=10 000 and linearly stable flow perturbations, characterized by mechanisms for very large disturbance amplification, at Re=5000. Wall transpiration (unsteady blowing/suction) with zero net mass flux is used as the control, and the flow measurement is derived from the wall skin friction. The control objective, beyond simply stabilizing any unstable eigenvalues (which is relatively easy to accomplish), is to minimize the energy of the flow perturbations created by external disturbance forcing. This is important because, when mechanisms for large disturbance amplification are present, small-amplitude external disturbance forcing may excite flow perturbations with sufficiently large amplitude to induce nonlinear flow instability.The control algorithms used in the present work account for system disturbances and measurement noise in a rigorous fashion by application of modern linear control techniques to the discretized linear stability problem. The disturbances are accounted for both as uncorrelated white Gaussian processes ([Hscr ]2 or ‘optimal’ control) and as finite ‘worst case’ inputs which are maximally detrimental to the control objective ([Hscr ]∞ or ‘robust’ control). Root loci and transient energy growth analyses are shown to be inadequate measures to characterize overall system performance. Instead, appropriately defined transfer function norms are used to characterize all systems considered in a consistent and relevant manner. In order to make a parametric study tractable in this high-dimensional system, a convenient new scaling to the estimation problem is introduced such that three scalar parameters {γ, α, [lscr ]} may be individually adjusted to achieve desired closed-loop characteristics of the resulting systems. These scalar parameters may be intuitively explained, and are defined such that the resulting control equations retain the natural dual structure between the control parameter, [lscr ], and the estimation parameter, α. The performance of the present systems with respect to these parameters is thoroughly investigated, and comparisons are made to simple proportional schemes where appropriate.

Image enhancement in optical coherence tomography using deconvolution

Abstract: The present invention provides an improved optical coherence tomography system and involves estimating the impulse response (which is indicative of the actual reflecting and scattering sites within a tissue sample) from the output interferometric signal of an interferometer according to the following steps: (a) acquiring auto-correlation data from the interferometer system; (b) acquiring cross-correlation data from the interferometer system having the biological tissue sample in the sample arm; and (c) processing the auto-correlation data and the cross correlation data to produce an optical impulse response of the tissue The impulse response may be obtained from the cross-correlation and auto-correlation data by: (d) obtaining an auto-power spectrum from the auto-correlation data by performing a Fourier transform on the auto-correlation data; (e) obtaining a cross-power spectrum from the cross-correlation data by performing a Fourier transform on the cross-correlation data; (f) obtaining a transfer function of the LSI system by taking a ratio of the cross-power spectrum to the auto-power spectrum; and (g) obtaining the optical impulse response of the LSI system by performing an inverse-Fourier transform on the transfer function Preferably, coherent demodulation is used in combination with the above deconvolution technique to resolve closely-spaced reflecting sites in the sample By utilizing both the magnitude and phase data of the demodulated interferometric signals, the OCT system of the present invention is able to distinguish between closely spaced reflecting sites within the sample

Signal processing and linear systems

Abstract: BACKGROUND B1 Complex Numbers B2 Sinusoids B3 Sketching Signals B4 Cramer's Rule B5 Partial Fraction Expansion B6 Vectors and Matrices B7 Miscellaneous CHAPTER 1 INTRODUCTION TO SIGNALS AND SYSTEMS 11 Size of a Signal 12 Classification of Signals 13 Some Useful Signal Operations 14 Some Useful Signal Models 15 Even and Odd Functions 16 Systems 17 Classification of Systems 18 System Model: Input-Output Description CHAPTER 2 TIME-DOMAIN ANALYSIS OF CONTINUOUS-TIME SYSTEMS 21 Introduction 22 System Response to Internal Conditions: Zero-Input Response 23 The Unit Impulse Response h(t) 24 System Response to External Input: Zero-State Response 25 Classical Solution of Differential Equations 26 System Stability 27 Intuitive Insights into System Behavior 28 Appendix 21: Determining the Impulse Response CHAPTER 3 SIGNAL REPRESENTATION BY FOURIER SERIES 31 Signals and Vectors 32 Signal Comparison: Correlation 33 Signal Representation by Orthogonal Signal Set 34 Trigonometric Fourier Series 35 Exponential Fourier Series 36 Numerical Computation of D[n 37 LTIC System response to Periodic Inputs 38 Appendix CHAPTER 4 CONTINUOUS-TIME SIGNAL ANALYSIS: THE FOURIER TRANSFORM 41 Aperiodic Signal Representation by Fourier Integral 42 Transform of Some Useful Functions 43 Some Properties of the Fourier Transform 44 Signal Transmission through LTIC Systems 45 Ideal and Practical Filters 46 Signal Energy 47 Application to Communications: Amplitude Modulation 48 Angle Modulation 49 Data Truncation: Window Functions CHAPTER 5 SAMPLING 51 The Sampling Theorem 52 Numerical Computation of Fourier Transform: The Discrete Fourier Transform (DFT) 53 The Fast Fourier Transform (FFT) 54 Appendix 51 CHAPTER 6 CONTINUOUS-TIME SYSTEM ANALYSIS USING THE LAPLACE TRANSFORM 61 The Laplace Transform 62 Some Properties of the Laplace Transform 63 Solution of Differential and Integro-Differential Equations 64 Analysis of Electrical Networks: The Transformed Network 65 Block Diagrams 66 System Realization 67 Application to Feedback and Controls 68 The Bilateral Laplace Transform 69 Appendix 61: Second Canonical Realization CHAPTER 7 FREQUENCY RESPONSE AND ANALOG FILTERS 71 Frequency Response of an LTIC System 72 Bode Plots 73 Control System Design Using Frequency Response 74 Filter Design by Placement of Poles and Zeros of H(s) 75 Butterworth Filters 76 Chebyshev Filters 77 Frequency Transformations 78 Filters to Satisfy Distortionless Transmission Conditions CHAPTER 8 DISCRETE-TIME SIGNALS AND SYSTEMS 81 Introduction 82 Some Useful Discrete-Time Signal Models 83 Sampling Continuous-Time Sinusoids and Aliasing 84 Useful Signal Operations 85 Examples of Discrete-Time Systems CHAPTER 9 TIME-DOMAIN ANALYSIS OF DISCRETE-TIME SYSTEMS 91 Discrete-Time System Equations 92 System Response to Internal Conditions: Zero-Input Response 93 Unit Impulse Response h[k] 94 System Response to External Input: Zero-State Response 95 Classical Solution of Linear Difference Equations 96 System Stability 97 Appendix 91: Determining Impulse Response CHAPTER 10 FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS 101 Periodic Signal Representation by Discrete-Time Fourier Series 102 Aperiodic Signal Representation by Fourier Integral 103 Properties of DTFT 104 DTFT Connection with the Continuous-Time Fourier Transform 105 Discrete-Time Linear System Analysis by DTFT 106 Signal Processing Using DFT and FFT 107 Generalization of DTFT to the Z-Transform CHAPTER 11 DISCRETE-TIME SYSTEM ANALYSIS USING THE Z-TRANSFORM 111 The Z-Transform 112 Some Properties of the Z-Transform 113 Z-Transform Solution of Linear Difference Equations 114 System Realization 115 Connection Between the Laplace and the Z-Transform 116 Sampled-Data (Hybrid) Systems 117 The Bilateral Z-Transform CHAPTER 12 FREQUENCY RESPONSE AND DIGITAL FILTERS 121 Frequency Response of Discrete-Time Systems 122 Frequency Response From Pole-Zero Location 123 Digital Filters 124 Filter Design Criteria 125 Recursive Filter Design: The Impulse Invariance Method 126 Recursive Filter Design: The Bilinear Transformation Method 127 Nonrecursive Filters 128 Nonrecursive Filter Design CHAPTER 13 STATE-SPACE ANALYSIS 131 Introduction 132 Systematic Procedure for Determining State Equations 133 Solution of State Equations 134 Linear Transformation of State Vector 135 Controllability and Observability 136 State-Space Analysis of Discrete-Time Systems ANSWERS TO SELECTED PROBLEMS SUPPLEMENTARY READING INDEX Each chapter ends with a Summary

Process Dynamics: Modeling, Analysis and Simulation

Abstract: I. PROCESS MODELING. 1. Introduction. Motivation. Models. Systems. Background of the Reader. How To Use This Textbook. Courses Where This Textbook Can Be Used. 2. Process Modeling. Background. Balance Equations. Material Balances. Constitutive Relationships. Material and Energy Balances. Distributes Parameter Systems. Dimensionless Models. Explicit Solutions to Dynamic Models. General Form of Dynamic Models. II. NUMERICAL TECHNIQUES. 3. Algebraic Equations. Notations. General Form for a Linear System of Equations. Nonlinear Functions of a Single Variable. MATLAB Routines for Solving Functions of a Single Variable. Multivariable Systems. MATLAB Routines for Systems of Nonlinear Algebraic Equations. 4. Numerical Integration. Background. Euler Integration. Runge-Kutta Integration. MATLAB Integration Routines. III. LINEAR SYSTEMS ANALYSIS. 5. Linearization of Nonlinear Models: The State-Space Formulation. State Space Models. Linearization of Nonlinear Models. Interpretation of Linearization. Solution of the Zero-Input Form. Solution of the General State-Space Form. MATLAB Routines step and initial. 6. Solving Linear nth Order ODE Models. Background. Solving Homogeneous, Linear ODEs with Constant Coefficients. Solving Nonhomogeneous, Linear ODEs with Constant Coefficients. Equations with Time-Varying Parameters. Routh Stability Criterion-Determining Stability Without Calculating Eigenvalues. 7. An Introduction to Laplace Transforms. Motivation. Definition of the Laplace Transform. Examples of Laplace Transforms. Final and Initial Value Theorems. Application Examples. Table of Laplace Transforms. 8. Transfer Function Analysis of First-Order Systems. Perspective. Responses of First-Order Systems. Examples of Self-Regulating Processes. Integrating Processes. Lead-Lag Models. 9. Transfer Function Analysis of Higher-Order Systems. Responses of Second-Order Systems. Second-Order Systems with Numerator Dynamics. The Effect of Pole-Zero Locations on System Step Responses. Pad Approximation for Deadtime. Converting the Transfer Function Model to State-Space Form. MATLAB Routines for Step and Impulse Response. 10. Matrix Transfer Functions. A Second-Order Example. The General Method. MATLAB Routine ss2tf. 11. Block Diagrams. Introduction to Block Diagrams. Block Diagrams of Systems in Series. Pole-Zero Cancellation. Systems in Series. Blocks in Parallel. Feedback and Recycle Systems. Routh Stability Criterion Applied to Transfer Functions. SIMULINK. 12. Linear Systems Summary. Background. Linear Boundary Value Problems. Review of Methods for Linear Initial Value Problems. Introduction to Discrete-Time Models. Parameter Estimation of Discrete Linear Systems. IV. NONLINEAR SYSTEMS ANALYSIS. 13. Phase-Plane Analysis. Background. Linear System Examples. Generalization of Phase-Plane Behavior. Nonlinear Systems. 14. Introduction Nonlinear Dynamics: A Case Study of the Quadratic Map. Background. A Simple Population Growth Model. A More Realistic Population Model. Cobweb Diagrams. Bifurcation and Orbit Diagrams. Stability of Fixed-Point Solutions. Cascade of Period-Doublings. Further Comments on Chaotic Behavior. 15. Bifurcation Behavior of Single ODE Systems. Motivation. Illustration of Bifurcation Behavior. Types of Bifurcations. 16. Bifurcation Behavior of Two-State Systems. Background. Single-Dimensional Bifurcations in the Phase-Plane. Limit Cycle Behavior. The Hopf Bifurcation. 17. Introduction to Chaos: The Lorenz Equations. Introduction. Background. The Lorenz Equations. Stability Analysis of the Lorenz Equations. Numerical Study of the Lorenz Equations. Chaos in Chemical Systems. Other Issues in Chaos. IV. REVIEW AND LEARNING MODULES. Module 1 Introduction to MATLAB. Module 2 Review of Matrix Algebra. Module 3 Linear Regression. Module 4 Introduction to SIMULINK. Module 5 Stirred Tank Heaters. Module 6 Absorption. Module 7 Isothermal Continuous Stirred Tank Chemical Reactors. Module 8 Biochemical Reactors. Module 9 Diabatic Continuous Stirred Tank Reactors. Module 10 Ideal Binary Distillation. Index.

Transfer function estimation from noisy input and output data

Abstract: Two new types of bias-eliminated least-squares (BELS) based algorithms are proposed for consistent identification of linear systems with noisy input and output measurements. It is shown that estimation of the noise variances can be implemented through one-dimension over-parametrization of the system transfer function. The two modified BELS algorithms are attractive and meaningful in that noisy data are used directly in identification with no prefiltering and a direct estimate of system parameters is given without any parameter transformation. Simulation examples are included to demonstrate the effectiveness of the two proposed algorithms. © 1998 John Wiley & Sons, Ltd.

Combined phase and modal domain calculation of transmission line transients based on vector fitting

Abstract: This paper introduces two highly accurate transmission line models In the first one, particularly suitable for overhead lines, the matrix transfer functions for both characteristic admittance and propagation are fitted directly in the phase domain using the method of vector fitting by optimal scaling In the second model we use for propagation a modal decomposition with a constant transformation matrix and an optional phase domain correction term Both models are computationally highly efficient due to their time domain realizations based an vector fitting

PRIMO: probability interpretation of moments for delay calculation

Abstract: Moments of the impulse response are widely used for interconnect delay analysis, from the explicit Elmore delay (first moment of the impulse response) expression, to moment matching methods which create reduced order transimpedance and transfer function approximations. However, the Elmore delay is fast becoming ineffective for deep submicron technologies, and reduced order transfer function delays are impractical for use as early-phase design metrics or as design optimization cost functions. This paper describes an approach for fitting moments of the impulse response to probability density functions so that delays can be estimated from probability tables. For RC trees it is demonstrated that the incomplete gamma function provides a provably stable approximation. The step response delay is obtained from a one-dimensional table lookup.

Optimization of a predictive controller for closed-loop adaptive optics.

Abstract: For closed-loop adaptive optics systems limited by time delay and measurement noise, we demonstrate that the ideal rejection transfer function is proportional to the frequency signal-to-noise ratio of the wave-front input. We describe a new modal linear predictive controller that approaches this ideal transfer function. Its parameters are optimized by minimization of the residual wave-front error with a modified recursive least-squares algorithm. The optimization can be performed with closed-loop data in the case of evolving turbulent conditions. We present numerical simulations to show the significant improvements brought by the predictor.

Stabilization and disturbance rejection for the beam equation

Abstract: We consider a system described by the one-dimensional linear wave equation in a bounded domain with appropriate boundary conditions. To stabilize the system, we propose a dynamic boundary controller applied at the free end of the system. The transfer function of the proposed controller is a proper rational function of the complex variable and may contain a single pole at the origin and a pair of complex conjugate poles on the imaginary axis, provided that the residues corresponding to these poles are nonnegative; the rest of the transfer function is required to be a strictly positive real function. We then show that depending on the location of the pole on the imaginary axis, the closed-loop system is asymptotically stable. We also consider the case where the output of the controller is corrupted by a disturbance and show that it may be possible to attenuate the effect of the disturbance at the output if we choose the controller transfer function appropriately. We also present some numerical simulation results which support this argument.

Multivariable continuous-time generalised predictive control: a state-space approach to linear and nonlinear systems

Abstract: The multivariable continuous-time generalised predictive controller (CGPC) is recast in a state-space form and shown to include generalised minimum variance (GMV) and a new algorithm, predictive GMV (PGMV) as special cases. Comparisons are drawn with the exact linearisation methods of nonlinear control, and it is noted that, unlike the transfer function approach, the state-space approach extends readily to the nonlinear case. The resulting state space design algorithms are conceptually and algorithmically simpler than the corresponding transfer function based versions and have been realised as a freely available Matlab tool-box.

Photonic crystal waveguide arrays

Abstract: A waveguide device for optical signals in an optical communication system relies upon photonic bandgap material to guide the optical signal via a plurality of pathways. A two-dimensional photonic bandgap material is formed in a planar slab of dielectric medium by a two-dimensional lattice in which discontinuities in the lattice region define waveguides. A waveguide array formed in the device allows multiple Mach-Zehnder interferometer devices to be constructed including small radius turns without significant losses. An optical signal equalizer formed of such a device relies upon the transfer function defined by a multiple arm Mach-Zehnder having arms of different length. By applying controlled modulation to propagation through the arms, an adaptive equalizer is formed. The adaptive equalizer has application in correcting gain tilt in line amplifiers of optical communications systems. The method of applying equalization may include measurement of the spectrum of the output optical signal and providing feedback to control the transfer function applied by the adaptive equalizer.

Time-frequency transfer function calculus (symbolic calculus) of linear time-varying systems (linear operators) based on a generalized underspread theory

Abstract: We introduce a generalized concept of underspread linear time-varying systems (linear operators) which contains a previous definition as a special case. We show that an existing approximate transfer function calculus (symbolic calculus) can be extended to this wider and practically more relevant class of underspread operators. As a mathematical underpinning of this calculus, we establish explicit bounds on various error quantities associated with it. The transfer function calculus provides a theoretical basis for various methods recently proposed for nonstationary signal processing, and it has important implications in the theory of time-varying power spectra.

On a least-squares-based algorithm for identification of stochastic linear systems

Abstract: A new form of bias-eliminated least-squares (BELS) algorithm is developed to identify transfer function parameters of a linear time-invariant system, irrespective of noise dynamics. Unlike the BELS estimator previously presented, the main feature with the developed algorithm is that the transfer function parameters are consistently estimated in such a direct way that there is no need to prefilter observed data or to deal with a high-order augmented system. This greatly simplifies implementation of the BELS-based algorithms and reduces numerical efforts, whereas a desirable estimation accuracy can still be achieved. Two simulation examples are presented that clearly illustrate the good performances of the developed algorithm, including its superiority over one type of simple instrumental variable method.

Transfer function analysis of the constant voltage anemometer

Abstract: The transfer function for the constant voltage anemometer (CVA) circuit has been derived in terms of circuit and hot-wire parameters and the expressions for the natural frequency and damping ratio have been obtained. Bandwidth in each case was determined from the plot of the normalized transfer function. The theoretical bandwidth behavior calculated from the transfer function plots for the prototype agrees with independent tests of the prototype using laser radiation heating of the hot wire in an air jet. The near constant value of the bandwidth of the CVA with the variation in the hot-wire overheat and its Reynolds number that were observed with the laser tests have been substantiated with the theoretical values from the transfer function. Bandwidth testing with sine wave injection, in situ time constant measurement for proper compensation setting, method to optimize the design to have nearly a constant bandwidth even with different compensation time constants and the operational advantages of CVA are also discussed.

Lighting space controller

Abstract: An illumination control system uses two photocells, one directed toward an illuminated lamp and the other directed from the ceiling downwardly into the illuminated zone. A feedback signal is derived from the two photocell signals and a reference intercept signal. The feedback signal and a reference set point signal are input into an error amplifier. The error amplifier generates a control signal for setting the illumination in controlled lamps. The photocell signals are variously scaled to provide balancing between them and matching with the intercept signal. Scaling factors and intercept signal level arc set in a calibration procedure that establishes feedback circuit response consistent with a design set point transfer function.

On-chip measurement of the jitter transfer function of charge-pump phase-locked loops

Abstract: An all-digital technique for the measurement of the jitter transfer function of charge-pump phase-locked loops (PLLs) is introduced. Input jitter may be generated using one of two methods. Both rely on delta-sigma modulation to shape the unavoidable quantization noise to high frequencies. This noise is filtered by the low-pass characteristic of the device and has little impact on the test results. For an input-output response measurement, the output jitter is compared against a threshold. As the stimulus generation and output analysis circuits are digital, do not require calibration, and demand a small area overhead, this jitter transfer function measurement scheme may be placed on the die to adaptively tune a PLL after fabrication. The technique can also implement built-in self-test (BIST) for the characterization or manufacture test of PLLs. The validity of the scheme was verified experimentally with off-the-shelf components.

Volterra series approach for optimizing fiber-optic communications system designs

Abstract: A new methodology for designing long-haul fiber-optic communication systems is presented. We derive the overall Volterra series transfer function of the system including linear dispersion, fiber nonlinearities, amplified spontaneous emission (ASE) noise from the fiber amplifiers, and the square-law nature of the direct detection (DD) system. Since analytical expressions for the probability of error are difficult to derive for the complex systems being used, we derive analytical expressions for an upper bound on probability of error for integrate-and-threshold detection at the receiver. Using this bound as a performance criterion, we determine the optimal dispersion parameters of each fiber segment required to minimize the effects of linear dispersion, fiber nonlinearities and ASE noise from the amplifiers. We study the dependence of optimal dispersion parameters on the average power levels in the fiber by varying the peak input power levels and the amplifier gains. Analytical expressions give us the freedom to choose system parameters in a practical manner, while providing optimum system performance. Using a simple system as an example, we demonstrate the power of the Volterra series approach to design optimal optical communication systems. The analysis and the design procedure presented in this work can be extended to the design of more complex wavelength division multiplexed (WDM) systems.

Multiphase sinusoidal oscillator using inverting-mode operational amplifiers

Abstract: This paper describes a simple multiphase sinusoidal oscillator based on inverting operational amplifiers (OPAs). The system comprises n cascaded inverting first-order low-pass stages and produces n odd-phase equal amplitude signals that are equally spaced in phase, from low-impedance sources. The basic scheme utilizes self-oscillation and can produce 2n even-phase signals by the inclusion of n unity gain inverters. A modified system employing signal injection through the associated phase-shifting network is also discussed. The negative feedback around the OPA's results in extremely good frequency and distortion performances that are unmatched by other multiphase system implementations. Moreover, the system has a large output voltage swing, high current drive capacity, and utilizes readily available components.

A new way of solving transient radiative-conductive heat transfer problems

Abstract: One-dimensional transient energy transfer by conduction and radiation is solved for a finite medium. The semitransparent layer emits, absorbs, and scatters radiation (participating medium). The coupled transfer is solved analytically by considering the well-known two-flux approximation, assuming linear transfer and using the Laplace transform. The semitransparent layer can then be modeled by a matrix transfer function. The accuracy of the solution is verified in the case of sharp thermal excitation by a heat pulse on the front face. It is shown that this general model is very accurate for simulating both the limiting cases of purely scattering and purely absorbing media. In the latter case, the same modeling is derived using the kernel substitution technique, and very good agreement is achieved compared with numerical simulations. The resulting computation times are very small, and suggest that such a model can be used in the inverse approach of thermal problems involving semitransparent materials.

Neural network-based control design: an LMI approach

Abstract: In this paper we address a neural network-based control design for a discrete-time nonlinear system. Our design approach is to approximate the nonlinear system with a multilayer perceptron of which the activation functions are of the sigmoid type symmetric to the origin. The linear difference inclusion representation is then established for this class of approximating neural networks and is used to design a state-feedback control law for the nonlinear system based on the certainty equivalence principle. The control design equations are shown to be a set of linear matrix inequalities where a convex optimization algorithm can be applied to determine the control signal. Further, the stability of the closed-loop is guaranteed in the sense that there exists a unique global attraction region in the neighborhood of the origin to which every trajectory of the closed-loop system converges. Finally, a simple example is presented so as to illustrate our control design procedure.

Halfband filters and Hilbert transformers

Abstract: This paper presents in summarizing form a description of halfband filters and the related symmetrical Hilbert transformers. It starts with the two complemetary relations by which halfband filters are defined and the consequences for their impulse responses. The idealized versions of the frequency responses of halfband lowpasses and Hilbert transformers are introduced, and the related tolerance schemes that realized systems must satisfy are described. Using their frequency responses, the transformation of one filter type into the other is presented in general form. The design of finite impulse response (FIR)-halfband filters and their relation to corresponding Hilbert transformers are recalled, using maximally flat and Chebyshev approximations as examples. It is shown that the relation between both types of systems can be used for the infinite impulse response (IIR) case as well. The design of IIR-halfband filters is presented for systems with approximately linear phase and for those with minimum phase again for maximally flat and Chebyshev approximations. The design methods are partly new. The general procedure for the transformation into Hilbert transformers yields noncausal solutions, one of which is already known from the literature. By modifying this operation, phase-splitting systems are obtained, one of them related to corresponding continuous ones, discussed in papers published around 1950. Another system with approximately linear phase corresponds to a paper presented in 1987. Finally, the coupled form of these phase splitting allpasses is found to be a Hilbert transformer with precise phase difference, but with deviations of the magnitudes of the frequency responses.

Power converter analysis and design using Matlab: a transfer function approach

Abstract: The design and steady-state analysis of static power converters has usually been realized in the time domain. This approach however is subject to numerical convergence problems and long simulation times, which worsen as the converter's switching frequency increases. This paper proposes a novel design and steady-state analysis method to overcome these problems using Matlab. The method is based on the Fourier transform (FT) and a generalized converter transfer function. Thus obtains steady-state results without requiring the transient power-up, neither the circuit components' initial conditions. The FT and converter transfer function are used to model and solve the converter in the frequency domain. Desired variables are then obtained in the time domain using the inverse FT. The method eliminates numerical problems and reduces simulation times significantly. For example, the simulation of a PWM voltage source inverter operating at 5 kHz takes 320 times longer in PSpice than in the proposed method. It also presents a minor processing time dependency from the converter's switching frequency. The paper includes a detailed presentation of the proposed method, a complete analysis example using Matlab 4.02, together with an evaluation comparing it to conventional simulating techniques. Finally, experimental results with a 10 kVA AC motor drive are presented to validate the proposed analysis and design method.

Small-signal modeling of a single-switch AC/DC power factor correction circuit

Abstract: In this paper, a small-signal model for a new single-switch single-stage switched-mode power-factor-correction (PFC) converter is presented. The model is obtained by applying the small-signal perturbation technique to the circuit equations derived from the state-space averaging method. By applying the perturbation and averaging techniques over one switching cycle, the DC and small-signal equivalent circuit representations of this converter are derived. The result shows that this converter exhibits the transfer characteristics of a second-order low-pass system for the output-to-input transfer function and that of a combined second-order low-pass and band-pass system for the output-to-control transfer function. The validity of the proposed mathematical model was verified by the given experimental results for a specified design example.

Reduced-order modelling of linear time-varying systems

Abstract: We present a theory for reduced order modelling of linear time varying systems, together with efficient numerical methods for application to large systems. The technique, called TVP (Time-Varying Pade), is applicable to deterministic as well as noise analysis of many types of communication subsystems, such as mixers and switched capacitor filters, for which existing model reduction techniques cannot be used. TVP is therefore suitable for hierarchical verification of entire communication systems. We present practical applications in which TVP generates macromodels which are more than two orders of magnitude smaller but still replicate the input-output behaviour of the original systems accurately. The size reduction results in a speedup of more than 500.

System and method for modeling mixed signal RF circuits in a digital signal environment

Abstract: A behavioral model for mixed signal RF circuits. The model approximates non-linear filtering effects for base-band (i.e. suppressed carrier) end-to-end systems analysis. The new model, the K-model, is a linear MIMO (multi-input-multi-output) model with output radius corrected by a non-linear SISO (single-input-single output) model and output angle corrected by a non-linear rotation. The SISO model uses a multi-tanh structure to synthesize a non-linear filter. The multi-tanh structure simulates non-linear behavior by gently switching between transfer functions as the base-band input varies. For excursions well into the steady state non-linear region of operation the K-model simulates large-signal base-band transients to within about 10 percent of those simulated with detailed unsuppressed-carrier models.

Novel control design for the buck converter

Abstract: A novel control design approach for average current-mode controlled buck converters is presented. The buck converter large-signal averaged model is shown to be easily large-signal linearisable. The linear model is then examined as a multivariable system with no inner and outer loops, using both the state-space and frequency domain descriptions. Transfer functions of the system are derived as a function of the desired closed-loop poles, simplifying the design procedure and bringing forward all the important characteristics of the closed-loop system. Several advantages can be gained by the use of capacitor current instead of inductor current feedback. Theoretical analysis is applied and confirmed with simulation and experimental results on a 250 W prototype. The proposed approach can be used with all small-signal linear models of DC–DC converters, offering simplicity and a better insight on system characteristics.