There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Active noise control (ANC) is achieved by introducing a cancelling "antinoise" wave through an appropriate array of secondary sources. These secondary sources are interconnected through an electronic system using a specific signal processing algorithm for the particular cancellation scheme. ANC has application to a wide variety of problems in manufacturing, industrial operations, and consumer products. The emphasis of this paper is on the practical aspects of ANC systems in terms of adaptive signal processing and digital signal processing (DSP) implementation for real-world applications. In this paper, the basic adaptive algorithm for ANC is developed and analyzed based on single-channel broad-band feedforward control. This algorithm is then modified for narrow-band feedforward and adaptive feedback control. In turn, these single-channel ANC algorithms are expanded to multiple-channel cases. Various online secondary-path modeling techniques and special adaptive algorithms, such as lattice, frequency-domain, subband, and recursive-least-squares, are also introduced. Applications of these techniques to actual problems are highlighted by several examples.

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Active noise control: a tutorial review

Nanogenerators capable of converting energy from mechanical sources to electricity with high effective efficiency using low-cost, nonsemiconducting, organic nanomaterials are attractive for many applications, including energy harvesters. In this work, near-field electrospinning is used to direct-write poly(vinylidene fluoride) (PVDF) nanofibers with in situ mechanical stretch and electrical poling characteristics to produce piezoelectric properties. Under mechanical stretching, nanogenerators have shown repeatable and consistent electrical outputs with energy conversion efficiency an order of magnitude higher than those made of PVDF thin films. The early onset of the nonlinear domain wall motions behavior has been identified as one mechanism responsible for the apparent high piezoelectricity in nanofibers, rendering them potentially advantageous for sensing and actuation applications.

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Direct-Write Piezoelectric Polymeric Nanogenerator with High Energy Conversion Efficiency

This article introduces the genetic algorithm (GA) as an emerging optimization algorithm for signal processing. After a discussion of traditional optimization techniques, it reviews the fundamental operations of a simple GA and discusses procedures to improve its functionality. The properties of the GA that relate to signal processing are summarized, and a number of applications, such as IIR adaptive filtering, time delay estimation, active noise control, and speech processing, that are being successfully implemented are described.

Genetic algorithms and their applications

Active noise control exploits the long wavelengths associated with low frequency sound. It works on the principle of destructive interference between the sound fields generated by the original primary sound source and that due to other secondary sources, acoustic outputs of which can be controlled. The acoustic objectives of different active noise control systems and the electrical control methodologies that are used to achieve these objectives are examined. The importance of having a clear understanding of the principles behind both the acoustics and the electrical control in order to appreciate the advantages and limitations of active noise control is emphasized. A brief discussion of the physical basis of active sound control that concentrates on three-dimensional sound fields is presented. >

Active noise control

Recent technological advances in the development of fast digital signal processors have made the active control of sound a practical proposition. This book brings together results from research in the two disciplinesof acoustics and signal processing and presents the fundamentals of noise control in a unified manner. Practical applications are presented wherever possible although the emphasis is on the algorithmic principles which form the foundation of practical systems. The volume is written in textbook style and aimed at both undergraduate and postgraduate students of acoustics and signal processing, professional acoustical and electrical engineers, and researchers in the field of active control.

Active Control of Sound

Introduction to Mechanical Vibrations: Terminology. Single-degree-of-freedom (SDOF) Systems. Free Motion of SDOF Systems. Damped Motion of SDOF Systems. Forced Response of SDOF Systems. Transient Response of SDOF Systems. Multi-degree-of-freedom (MDOF) Systems. Free Motion of MDOF Systems. Forced Response of MDOF Systems. Damped Motion of MDOF Systems. Finite Element Analysis of Vibrating Mechanical Systems. Introduction to Waves in Structures: Longitudinal Waves. Flexural Waves. Flexural Response of an Infinite Beam to an Oscillating Point Force. Flexural Wave Power Flow. Flexural Response of an Infinite Thin Beam to an Oscillating Line Moment. Free Flexural Motion of Finite Thin Beams. Response of a Finite Thin Beam to an Arbitrary Oscillating Force Distribution. Vibration of Thin Plates. Free Vibration of Thin Plates. Response of a Thin Rectangular Simply Supported Plate to an Arbitrary Oscillating Force Distribution. Vibration of Infinite Thin Cylinders. Free Vibration of Finite Thin Cylinders. Harmonic Forced Vibration of Infinite Thin Cylinders. Feedback Control: Single-channel Feedback Control. Stability of a Single-Channel System. Modification of the Response of an SDOF System. The Effect of Delays in the Feedback Loop. The State Variable Approach. Example of a Two-degree-of-freedom System. Output Feedback and State Feedback. State Estimation and Observers. Optimal Control. Modal Control. Feedforward Control: Single Channel Feedforward Control. The Effect of Measurement Noise. Adaptive Digital Controllers. Multichannel Feedforward Control. Adaptive Frequency Domain Controllers. Adaptive Time Domain Controllers. Equivalent Feedback Controller Interpretation. Distributed Transducers for Active Control of Vibration. Active Control of Vibration in Structures: Feedforward Control of Finite Structures. Feedback Control of Finite Structures. Feedforward Control of Wave Transmission. Actuator Arrays for Control of Flexural Waves. Sensor Arrays for Control of Flexural Waves. Feedforward Control of Flexural Waves. Feedback Control of Flexural Waves. Active Isolation of Vibrations: Isolation of Periodic Vibrations of an SDOF System. Vibration Isolation From a Flexible Receiver the Effects of Secondary Force Location. Active Isolation of Periodic Vibrations Using Multiple Secondary Force Inputs. Finite Element Analysis of an Active System for the Isolation of Periodic Vibrations. Practical Examples of Multi-Channel Feedforward Control for the Isolation of Periodic Vibrations. Isolation of Unpredictable Vibrations from a Receiving Structure. Isolation of Vibrating Systems from Random External Excitation the Possibilities for Feedforward Control. Isolation of Vibrating Systems from Random External Excitation Analysis of Feedback Control Strategies. Isolation of Vibrating Systems from Random External Excitation Formulation in Terms of Modern Control Theory. Active Isolation of Vehicle Vibrations from Road and Track Irregularities. Active Structural Acoustic Control, I. Plate Systems: Sound Radiation by Planar Vibrating Surfaces the Rayleigh Integral. The Calculation of Radiated Sound Fields by Using Wavenumber Fourier Transforms. Sound Power Radiation From Structures in Terms of Their Multi-Modal Response. General Analysis of Active Structural Acoustic Control (ASAC) for Plate Systems. Active Control of Sound Transmission Through a Rectangular Plate Using Point Force Actuators. Active Control of Structurally Radiated Sound Using Multiple Piezoelectric Actuator Interpretation of Behaviour in Terms of the Spatial Wavenumber Spectrum. The Use of Piezoelectric Distributed Structural Error Sensors in ASAC. An Example of the Implementation of Feedforward ASAC. Feeback Control of Sound Radiation From a Vibrating Baffled Piston. Feedback Control of Sound Radiation From Distributed Elastic Structures. Active Structural Acoustic Control, II. Cylinder Systems: Coupled Cylinder Acoustic Fields. Response of an Infinite Cylinder to a Harmonic Forcing Function. Active Control of Cylinder Interior Acoustic Fields Using Point Forces. Active Control of Vibration and Acoustic Transmission in Fluid-Filled Piping Systems. Active Control of Sound Radiation From Vibrating Cylinders. Active Control of Sound in Finite Cylinder Systems. Control of Interior Noise in a Full Scale Jet Aircraft Fuselage. Appendix. References. Index.

Active Control of Vibration

Signal Processing for Active Control sets out the signal processing and automatic control techniques that are used in the analysis and implementation of active systems for the control of sound and vibration. After reviewing the performance limitations introduced by physical aspects of active control, Stephen Elliott presents the calculation of the optimal performance and the implementation of adaptive real time controllers for a wide variety of active control systems. Active sound and vibration control are technologically important problems with many applications. 'Active control' means controlling disturbance by superimposing a second disturbance on the original source of disturbance. Put simply, initial noise + other specially-generated noise or vibration = silence [or controlled noise]. This book presents a unified approach to techniques that are used in the analysis and implementation of different control systems. It includes practical examples at the end of each chapter to illustrate the use of various approaches. This book is intended for researchers, engineers, and students in the field of acoustics, active control, signal processing, and electrical engineering.

Signal Processing for Active Control

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.

Stephen J. Elliott

Papers

Active Control of Sound

Active Control of Vibration

Active noise control

Signal Processing for Active Control

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