Showing papers on "Transfer function published in 1987"

A multiple error LMS algorithm and its application to the active control of sound and vibration

Abstract: An algorithm is presented to adapt the coefficients of an array of FIR filters, whose outputs are linearly coupled to another array of error detection points, so that the sum of all the mean square error signals is minimized. The algorithm uses the instantaneous gradient of the total error, and for a single filter and error reduces to the "filtered x LMS" algorithm. The application of this algorithm to active sound and vibration control is discussed, by which suitably driven secondary sources are used to reduce the levels of acoustic or vibrational fields by minimizing the sum of the squares of a number of error sensor signals. A practical implementation of the algorithm is presented for the active control of sound at a single frequency. The algorithm converges on a timescale comparable to the response time of the system to be controlled, and is found to be very robust. If the pure tone reference signal is synchronously sampled, it is found that the behavior of the adaptive system can be completely described by a matrix of linear, time invariant, transfer functions. This is used to explain the behavior observed in simulations of a simplified single input, single output adaptive system, which retains many of the properties of the multichannel algorithm.

Nonlinear signal processing using neural networks: Prediction and system modelling

Abstract: The backpropagation learning algorithm for neural networks is developed into a formalism for nonlinear signal processing We illustrate the method by selecting two common topics in signal processing, prediction and system modelling, and show that nonlinear applications can be handled extremely well by using neural networks The formalism is a natural, nonlinear extension of the linear Least Mean Squares algorithm commonly used in adaptive signal processing Simulations are presented that document the additional performance achieved by using nonlinear neural networks First, we demonstrate that the formalism may be used to predict points in a highly chaotic time series with orders of magnitude increase in accuracy over conventional methods including the Linear Predictive Method and the Gabor-Volterra-Weiner Polynomial Method Deterministic chaos is thought to be involved in many physical situations including the onset of turbulence in fluids, chemical reactions and plasma physics Secondly, we demonstrate the use of the formalism in nonlinear system modelling by providing a graphic example in which it is clear that the neural network has accurately modelled the nonlinear transfer function It is interesting to note that the formalism provides explicit, analytic, global, approximations to the nonlinear maps underlying the various time series Furthermore, the neural net more » seems to be extremely parsimonious in its requirements for data points from the time series We show that the neural net is able to perform well because it globally approximates the relevant maps by performing a kind of generalized mode decomposition of the maps 24 refs, 13 figs « less

l^{1} -optimal feedback controllers for MIMO discrete-time systems

Abstract: The problem considered in this paper is the design of a closed-loop system consisting of a MIMO discrete-time plant and compensator in such a way that the system is internally stable and optimally tracks all persistent bounded inputs. The solution consists of two parts: first the calculation of the minimum value of the performance index (a weighted transfer function), which is done by solving a linear programming problem; and second, construction of the optimal transfer function by solving a set of linear equations. It is shown that, in general, the discrete-time problem will have a rational solution and thus appears to be of considerable practical significance.

Control of linear systems using generalized sampled-data hold functions

Abstract: This paper investigates the use of generalized sampled-data hold functions (GSHF) in the control of linear time-invariant systems. The idea of GSHF is to periodically sample the output of the system, and generate the control by means of a hold function applied to the resulting sequence. The hold function is chosen based on the dynamics of the system to be controlled. This method appears to have several advantages over dynamic controllers: it has the efficacy of state feedback without the requirement of state estimation; it provides the control system designer with substantially more freedom; and it requires few on-line computations. This paper focuses on four questions: pole assignment, specific behavior, noise sensitivity, and robustness. Among the problems solved are: simultaneous arbitrary pole assignment for a finite number of systems by a single GSHF controller, exact model matching, decoupling, and optimal noise rejection. Examples are given.

A versatile CMOS linear transconductor/square-law function

Abstract: A simple CMOS circuit technique for realizing both linear transconductance and a precision square-law function is described. The circuit provides two separate outputs in the linear as well as square-law modes. The linear outputs both have a range of 100% or more of the total quiescent current value. The theory of operation is presented and effects of transistor nonidealities on the performance are investigated. Design optimization techniques are developed. Experimental results measured on nonoptimized prototypes are: distortion of 0.2% for input signals up to 2.4 V/SUB p-p/ in the case of linear transfer function and 1.3% in the case of the square-law transfer function, with a DC to -3-dB bandwidth of up to 20 MHz. Improved performance is expected when the optimization techniques developed are applied. The circuit is versatile in application: diverse applications are demonstrated in the fields of linear amplifiers, continuous-time filters, and nonlinear function implementation.

Identification of continuous systems

Abstract: Introduction. Continuous-Time Models of Dynamical Systems. Nonparametric Models. Parametric Models. Stochastic Models of Linear Time-Invariant Systems. Models of Distributed Parameter Systems (DPS). Signals and their Representations. Functions in the Ordinary Sense. Distribution or Generalized Functions. Identification of Linear Time-Invariant (LTIV) Systems via Nonparametric Models. The Role of Nonparametric Models in Continuous System Identification. Test Signals for System Identification. Identification of Linear Time-Invariant Systems - Time-Domain Approach. Frequency-Domain Approach. Methods for Obtaining Transfer Functions from Nonparametric Models. Numerical Transformations between Time- and Frequency-Domains. Parameter Estimation for Continuous-Time Models. The Primary Stage. The Secondary Stage: Parameter Estimation. Identification of Linear Systems Using Adaptive Models. Gradient Methods. Frequency-Domain. Stability Theory. Linear Filters. Identification of Multi-Input Multi-Output (MIMO) Systems, Distributed Parameter Systems (DPS) and Systems with Unknown Delays and Nonlinear Elements. MIMO Systems. Time-Varying Parameter Systems (TVPS). Lumped Systems with Unknown Time-Delays. Identification of Systems with Unknown Nonlinear Elements. Identification of Distributed Parameter Systems. Determination of System Structure. Index.

The selection and application of an IIR adaptive filter for use in active sound attenuation

Abstract: The use of infinite impulse response (IIR) adaptive filters has lagged behind that of finite impulse response (FIR) adaptive filters. This has been due, in part, to the increased complexity of IIR filters and the potential for instability that exists due to the presence of poles in the transfer function. This paper discusses the use of adaptive filters for the active cancellation of acoustic noise. It is shown that IIR filters possess certain characteristics that are highly desirable for this problem. The selection of an appropriate IIR adaptive algorithm is discussed using observability considerations. It is shown that the recursive least mean square (RLMS) algorithm of Feintuch possesses significant advantages for use in a practical active attentuation system. Results are presented from computer simulations as well as an actual system using a TI TMS32010 digital signal processing microprocessor.

Cumulants: A powerful tool in signal processing

Abstract: The impulse response of a linear, time-invariant system is related in a simple closed-form solution to the output cumulants, when the input is assumed to be non-Gaussian and independent. This expression permits the use of one-dimensional processing of the output cumulants for identification of non-minimum-phase systems, and opens new directions in other signal processing applications.

Robust stability with structured real parameter perturbations

Abstract: This paper considers the problem of robust stabilization of a linear time-invariant system subject to variations of a real parameter vector. For a given controller the radius of the largest stability hypersphere in this parameter space is calculated. This radius is a measure of the stability margin of the closed-loop system. The results developed are applicable to all systems where the closed-loop characteristic polynomial coefficients are linear functions of the parameters of interest. In particular, this always occurs for single-input (multioutput) or single-output (multiinput) systems where the transfer function coefficients are linear or affine functions of the parameters. Many problems with transfer function coefficients which are nonlinear functions of physical parameters can be cast into this mathematical framework by suitable weighting and redefinition of functions of physical parameters as new parameters. The largest stability hyperellipsoid for the case of weighted perturbations and a stability polytope in parameter space are also determined. Based on these calculations a design procedure is proposed to robustify a given stabilizing controller. This algorithm iteratively enlarges the stability hypersphere or hyperellipsoid in parameter space and can be used to design a controller Io stabilize a plant subject to given ranges of parameter excursions. These results are illustrated by an example.

Nonconvex optimization by fast simulated annealing

Abstract: Recent advances in the solution of nonconvex optimization problems use simulated annealing techniques that are considerably faster than exhaustive global search techniques. This letter presents a simulated annealing technique, which is t/log (t) times faster than conventional simulated annealing, and applies it to a multisensor location and tracking problem.

First Principles of Discrete Systems and Digital Signal Processing

Abstract: 1. Introduction. Preview. Processing of Speech Signals. Processing of Seismic Signals. Radar Signal Processing. Image Processing. Kalman Filtering and Estimators. Review. References and Other Sources of Information 2. Signals and Systems. Preview. Types of Signals. Sequences Some Basic Sequences. Shifted and Special Sequences. Exponential and Sinusoidal Sequences. General Periodic Sequences. Sampling Continuous-Time Sinusoids and the Sampling Theorem. Systems and Their Properties. Linearity. Time-Invariance. Linear-Time Invariant (LTI) Systems. Stability. Causality. Approximation of Continuous-Time Processes by Discrete Models. Discrete Approximation of Integration. Discrete Approximation of Differentiation. Review. Vocabulary and Important Relations. Problems. References and Other Sources of Information. 3. Linear Time-Invariant Systems. Preview. Linear Constant-Coefficient Difference Equations. The Geometric Series--An Important Relationship. Difference Equations for Nth-Order Systems. Computer Solution of Difference Equations. System Diagrams or Realizations. Unit Sample Response. Convolution. A General Way to Find System Response. Computer Evaluation of Convolution. Analytical Evaluation of Convolution. An Application: Stability and the Unit Sample Response. Interconnected Systems. Cascade Connection. Parallel Connection. Initial Condition Response and Stability of LTI Systems. Forced and Total Response of LTI Systems. Review. Vocabulary and Important Relations Problems. References and Other Sources of Information. 4. Frequency Response and Filters. Preview. Sinusoidal Steady-State Response of LTI Systems. Frequency Response. Sinusoidal Steady--State Response--General Statement. The Nature of H(Ejq). Computer Evaluation of Frequency Response. Frequency Response from the System Difference Equations. Filters. A Typical Filtering Problem. Comparison of Two Filters. Ideal Filters. Interconnected Systems. Review. Vocabulary and Important Relations Problems. References and Other Sources of Information. 5. Frequency Response--A Graphical Method. Preview. Graphical Concepts. Geometric Algorithms for Sketching the Frequency Response. Graphical Design of Filters. Stability. Effects of Poles and Zeros on the Frequency Response. Correspondence Between Analog and Digital Frequencies. Some Design Problems. Review. Vocabulary and Important Relations Problems. References and Other Sources of Information. 6. Z-Transforms. Preview. Definitions. Right-Sided Sequences--Some Transform Pairs. Sample (Impulse) Sequence. Step Sequence. Real Exponential Sequence. Complex Exponential Sequence. General Oscillatory Sequence. Cosine Sequence. Properties and Relations. Linearity. Shifting Property. Multiplication by n and Derivatives In z. Convolution. Transfer Functions. Stability. Frequency Response Revisited. The Evaluation of Inverse Transforms. Inverse Transforms from the Definition. Inverse Transforms from Long Division. Inverse Transforms from Partial Fraction Expansions and Table Look-Up. Partial Fraction Expansion--General Statement. Checking Partial Fraction Expansions and Inverse Transforms. Solution of Difference Equations. Connections Between the Time Domain and the z-Domain. Poles and Zeros and Time Response. System Response to Some Special Inputs. General Results and Miscellany. Noncausal Systems. Convergence and Stability. The Inversion Formula. Review. Vocabulary and Important Relations. Problems. References and Other Sources of Information. 7. Discrete Fourier Transform. Preview. Periodic Sequences. Complex Exponentials. Discrete Fourier Series. Finite Duration Sequences and the Discrete Fourier Transform. Some Important Relationships. DFTs and the Fourier Transform. Relationships Among Record Length, Frequency Resolution, and Sampling Frequency. Properties of the DFT. Linearity. Circular Shift of a Sequence. Symmetry Properties. Alternative Inversion Formula. Duality and the DFT. Computer Evaluation of DFTs and Inverse DFTs. Another Look at Convolution. Periodic Convolution. Circular Convolution. Frequency Convolution. Correlation. Some Properties of Correlation Sequences. Circular Correlation. Computer Evaluation of Correlation. Block Filtering or Sectioned Convolution. Spectrum Analysis. Periodogram Methods for Spectrum Estimation. Use of Windows In Spectrum Analysis. Review. Vocabulary and Important Relations Problems. References and Other Sources of Information. 8. The Fast Fourier Transform. Preview. Decomposition in Time. Development of the Basic Algorithm. Computer Evaluation of the Algorithm. Decomposition in Frequency.Variations of the Basic Algorithms. Fast Convolution. Review. Vocabulary and Important Relations Problems. References and Other Sources of Information. 9. Nonrecursive Filter Design. Preview. Design by Fourier Series. Fourier Coefficients. Lowpass Design. Highpass, Bandpass and Bandstop Design. Gibbs' Phenomenon. Windows in the Fourier design. Design of a Differentiator. Linear Phase Characteristics. Comb Filters. Design by Frequency Sampling. Design Using the Inverse Discrete Fourier Transform. Frequency Sampling Filters. Computer-Aided Design (CAD) of Linear Phase Filter. Review. Vocabulary and Important Relations Problems. References and Other Sources of Information. 10. Recursive Filter Design. Preview. Analog Filter Characteristics Sinusoidal Steady-State. Frequency Response, Graphical Method. Computer Evaluation of Frequency Response. Determination of Filter Transfer Function from Frequency Response. Analog Filter Design. Butterworth Lowpass Prototype Design. Chebyshev Lowpass Prototype Design. Elliptic Lowpass Prototype Design. Analog Frequency Transformations. Design of Lowpass, Highpass, Bandpass, and Bandstop Filters. Digital Filter Design. Matched z-Transform Design. Impulse and Step-Invariant Design. Bilinear Transform Design. Digital Frequency Transformations. Direct Design of Digital Lowpass, Highpass, Bandpass, and Bandstop Filters. Optimization. Some Comments on Recursive and Nonrecursive Filters. Review. Vocabulary and Important Relations Problems. References and Other Sources of Information. 11. Structures, State Equations, and Applications. Preview. System Implementations. Direct Structure. Second-Order Substructures. Cascade Realization. Parallel Realization (Partial Fraction Expansion). Lattice Filters. Mason's Gain Rule. State Difference Equations. Writing State Equations. Solution of State Equations. Computer Solution of State Equations. Two Different Systems. Digital Control of a Continuous-Time System. Deconvolution Review. Vocabulary and Important Relations Problems. References and Other Sources of Information. Appendix A: Complex Numbers. Appendix B: Fourier Series. Appendix C: Laplace Transform. Appendix D: Frequency Response of Continuous-Time (Analog) Systems. Appendix E: .A Summary of Fourier Paris. Appendix F: Matrices and Determinants. Appendix G: Continuous-Time Systems with a Piecewise Constant Input. Answers to Selected Problems. Index.

Robust control with structured perturbations

Abstract: This paper considers the problem of robustification of a given stabilizing controller to make the closed loop system remain stable for prescribed ranges of variations of a set of physical parameters in the plant. The problem is treated in the state space and transfer function domains. In the state space domain a stability hypersphere is determined in the parameter space using Lyapunov theory. The radius of this hypersphere is iteratively increased by adjusting the controller parameters until the prescribed perturbation ranges are contained in the stability hypersphere. In the transfer function domain a corresponding stability margin is defined and optimized based on the recently introduced concept of the largest stability hypersphere in the space of coefficients of the closed loop characteristic polynomial. The design algorithms are illustrated by examples.

Asymptotic behaviour of transfer function synthesis methods

Abstract: This paper presents an analysis of the asymptotic behaviour of the solutions to various iterative linear least-squares methods that synthesize transfer functions from frequency-response data. The methods of Sanathanan and Koerner and Lawrence and Rogers are shown to possess asymptotic solutions that do not coincide with the solution to a fundamental non-linear least-squares criterion. Several methods with more appropriate asymptotic behaviour are then suggested. The analytical tools presented should allow analysis of conditions for the convergence of iterative linear least-squares methods.

Adaptive process control system

Abstract: An adaptive process control system comprises a controller of an I-P type generating a manipulating variable signal with a feed forward circuit responsive to the set-point signal r(t), an integrator responsive to a difference between a process variable signal y(t) and set-point signal r(t), and a feedback circuit responsive to the process variable signal y(t). An identification signal generator superposes a persistantly exciting identification signal h(t) to the control system. A frequency characteristic identifying circuit receives a discrete controlled data u(k) and y(k), estimates the parameters of the ARMA model by the least square method to identify the pulse transfer function, and obtains the transfer function in the continuous system as the frequency characteristics of gain and phase. A controller parameter calculating circuit calculates the controller parameters of the controller, such as integration gain K, proportional gain fo, and feed forward gain ff, using the frequency characteristics of gain and phase, and the overshoot, gain and phase margins, and attenuation ratio. The controller parameters are supplied via a switch to the controller.

A sensitivity tradeoff for plants with time delay

Abstract: In this paper we show that the sensitivity function of a scalar feedback system must satisfy an integral constraint when the open-loop transfer function is strictly proper and contains a time delay. The integral constraint is identical to the classical Bode sensitivity integral, which holds provided the open-loop gain has greater than a one-pole rolloff. The design implications of the two constraints are somewhat different, however, and this difference is discussed. The relation between open-loop phase and a conflict between bandwidth and sensitivity properties is explored.

The application of discrete linear control theory to the analysis and simulation of multi-product, multi-level production control systems

Abstract: This paper examines how multi-product, multi-level production control systems may be represented in terms of discrete linear control theory models. The transfer functions are derived for material requirements planning (MRP) and re-order cycle systems. The performance of each type of system is derived under selected conditions and the way in which a general system may be analysed is described. The method has proved easy to use. Computer programs exist which enable one to assemble the elements of proposed forecasting, inventory and production control systems, and hence determine the stability and transient and steady state responses to standard inputs. This has proved to be a quick and efficient way of evaluating alternative production systems and examining whether better methods of, for example, stock re-ordering or forecasting are required.

Black-box identification of MIMO transfer functions : asymptotic properties of prediction error models

Abstract: Identification of multi-input/multi-output (MIMO) transfer functions is considered. The transfer function matrix is parametrized as black-box models which have certain shift properties; no structure or order is chosen a priori. In order to obtain a good transfer function estimate, we allow the order of the model to increase to infinity as the number of data tends to infinity. The expression of asymptotic covariance of the transfer function estimates is derived, which is asymptotic both in the number of data and in the model order. The result indicates that the joint covariance matrix of the transfer function estimates of the process and of the noise filter is proportional to the (generalized) ratio of output noise to imput signal; the factor of proportionality is the ratio of model order to number of data. The result is independent of the particular model structure used. This result is the MIMO extension of the theory of Ljung. The application of this theory for defining the upper bounds of identification errors is highlighted.

Design of multivariable linear‐quadratic controllers using transfer functions

Abstract: Optimal linear-quadratic (LQ) controller design is usually associated with state space techniques. However, when one has measurements of the outputs to be controlled, there are many advantages to designing these LQ controllers using input-output transfer function models. The design procedure leads to a discrete equivalent of the Wiener-Hopf equation, which can be solved using a spectral factorization approach. In this paper the design procedure is presented and various interpretations of the resulting controllers are discussed. In particular, the controllers are shown to be of the internal model controller (IMC) form, and the Wiener-Hopf procedure is shown to be a powerful way of selecting approximate model inverses and filters that yield good performance and robustness characteristics. The approach treats the problem of simultaneous disturbance rejection and set-point tracking, and it easily handles nonsquare systems. The design approach, its performance/robustness trade-offs, and the structure of the resulting controllers are demonstrated using models for several processes, including a two-input/one-output sheet forming process, a (3 × 3) multivariable level control problem, and a (2 × 2) multivariable catalytic reactor.

Parameterized linear systems and linearization families for nonlinear systems

Abstract: The question of characterizing parameterized linear systems that can arise as linearization families of a nonlinear system about a family of constant operating points is addressed. The parameterization can be in terms of operating-point inputs or operating-point outputs. For both parameterized linear state equations and parameterized transfer functions, existence conditions, and constructions, for a corresponding nonlinear system are presented.

Introduction to the linear algebraic method for control system design

Abstract: This tutorial article discusses some basic issues in the design of control systems. The concepts of well posedness and total stability are introduced to deal with noise and disturbance problems. The implementable transfer function is developed and is shown to solve completely pole-and-zero assignment and model matching problems. Two feedback configurations are introduced to realize the implementable transfer functions, and feedback compensation is obtained by solving sets of linear algebraic equations.

On-line estimation of time delay and continuous-time process parameters†

Abstract: A simple technique is presented for on-line estimation of constant or slowly-varying continuous-time process parameters and time delay. The method is shown to allow considerable flexibility for application to systems of varying complexity. A major advantage of the algorithm lies in its ability to track time-delay variations over a practically unlimited range. The technique is based on approximation of time delay in the frequency domain by a rational transfer function, construction of the derivatives of process input and output using multiple filters, and estimation using a model which is non-linear in the desired parameters. In spite of this inherent non-linearity with respect to the sought parameters, in general the estimation schemes lead to the true, unique solution. The cases when this is not true are shown not to be of serious consequence.

Multidriver loudspeaker apparatus with improved crossover filter circuits

Abstract: A loudspeaker system includes at least two loudspeaker drivers, together with an electrical crossover network having filter circuits with at least two separate mutually exclusive frequency passbands. The filter circuits comprising the crossover network each possess brick-wall amplitude responses, i.e., passbands with very high band-edge amplitude vs. frequency response slops, on the order of 100 dB/octave in the better embodiments. The high passband band-edge slopes, which are realized by the inclusion of transmission zeros in the separate crossover filter transfer functions, takes together with further appropriate crossover filter transfer function synthesis causes the separate loudspeaker drivers comprising the loudspeaker system to function independently of one another in their contribution to total system acoustic output. It is shown that the loudspeaker system permits an accurate approximation to the ideal delay function in acoustic space, while minimizing acoustic wave interference among drivers operating in adjacent frequency band, and also reducing overall system nonlinear distortion.

Very low sensitivity realization of IIR digital filters using a cascade of complex all-pass structures

Abstract: A new realization of recursive digital filters based on a cascade of complex all-pass structures is proposed. The cascade realization ensures low stopband sensitivity, whereas the all-pass sections, being structurally bounded, guarantee low passband sensitivity. The proposed structure can exactly realize any elliptic transfer function, and it is easy to derive the multiplier coefficients associated with this structure from the original transfer function expression. To reduce the computational complexity, some of the coefficients are rounded to integer values and an optimum approximation to the original transfer function is obtained by using a minimax optimization procedure. Several examples show that the proposed structure requires significantly fewer bits than other known cascade-form realizations. Another advantage of the proposed structure is that it is free of overflow oscillations.

Small signal ac equivalent circuit modelling of the series resonant converter

Abstract: The small signal dynamics of the series resonant converter are investigated using an equivalent circuit modelling approach. The converter input and output ports behave essentially as nonideal current sources, so the most suitable form is the two-port y parameter model. Two such models are proposed: a continuous time version valid for low perturbation frequencies, aand a discrete time version which models the inherent sampling in the converter and is valid for any perturbation frequency less than the switching frequency. Experimental verification of the control to output transfer function and the output impedance is presented, and good agreement between theory and experiment is obtained.

Parametric models of linear multivariable systems for adaptive control

Abstract: This paper presents a parametrization method for direct adaptive control of linear multivariable systems with strictly proper discrete-time or continuous-time transfer functions. The necessary a priori information is shown to be a diagonal matrix with the noninvertible zeros of the Smith form and appropriate polynomial degrees.

On the minimal state-space realizations of all-pole and all-zero 2-D systems

Abstract: A simple method is presented for the minimal state-space representation, described by the Roesser model, of a 2-D all-pole and all-zero transfer function. The state-space representation is derived, from a block diagram, by inspection. General expressions for the system matrices (A, b, c) of very simple form are derived explicitely in terms of the parameters of the transfer function.