Signal Processing for Active Control

Stephen Elliott

• Publisher: Academic Press
• Year: 2000
• Print ISBN: 9780122370854
• eBook ISBN: 9780080517131
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

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.

1

The Physical Basis for Active Control

1.1 Introduction

1.1.1 Chapter outline

1.1.2 The wave equation

1.1.3 Source control

1.2 Control of wave transmission

1.2.1 Single secondary actuator

1.2.2 Two secondary actuators

1.2.3 Control of multiple modes

1.3 Control of power in infinite systems

1.3.1 Point forces on an infinite panel

1.3.2 Minimisation of power input

1.3.3 Acoustic monopoles in free space

1.4 Strategies of control in finite systems

1.4.1 Acoustic impedances in a finite duct

1.4.2 Cancellation of pressure

1.4.3 Absorption of incident wave

1.4.4 Maximisation of secondary power absorption

1.4.5 Minimisation of total power input

1.5 Control of energy in finite systems

1.5.1 Power input and total energy

1.5.2 Control of vibrational energy on a finite panel

1.5.3 Control of acoustic energy in an enclosure

1.5.4 The effect of modal overlap

1.6 Control of sound radiation from structures

1.6.1 Sound radiation from a vibrating panel

1.6.2 Radiation modes

1.6.3 Cancellation of volume velocity

1.7 Local control of sound and vibration

1.7.1 Cancellation of vibration on a large panel

1.7.2 Cancellation of pressure in a large room

1.1 INTRODUCTION

In this chapter the physical basis for the active control of both sound and vibration is described. Although examples of the active control of specific acoustical and structural systems will be presented, an attempt has been made to use a common description for both of these applications, to emphasise their underlying physics. It is important at the early stages of an active control project to develop simple analytical models of the physical system under control so that the fundamental physical limitations of the proposed control strategy can be assessed. Several of the most common types of physical model are presented in this chapter. The objectives of this simple model are:

(1) to investigate the effects of different physical strategies of control, e.g. cancellation of pressure or minimisation of power output;

(2) to determine the parameters that affect the physical limits of performance in a given control arrangement, e.g. the distance from the primary to the secondary source;

(3) to allow the effect of different kinds of control actuator to be assessed;

(4) to determine the number and type of sensors that are required to measure the physical quantity of interest and thus maintain control.

In most cases these physical limitations can be made clear by assuming that the disturbance is tonal, which considerably simplifies the analysis. It should be emphasised, however, that active control can be applied to systems that are excited by disturbances with considerably more complicated waveforms than pure tones, but in order to determine the limitations of performance due to the physical aspects, rather than the electronic control aspects, of the problem it is convenient to initially assume a single-frequency excitation. In this chapter it will also be assumed that all signals are continuous functions of the time variable, t.

1.1.1 Chapter Outline

In the remainder of this section the complex form of the acoustic wave equation for tonal signals is introduced, before considering the active control of plane sound waves in a one dimensional duct in Section 1.2. Section 1.2 goes on to describe the physical consequences of using a single secondary source to reflect the sound wave or of using a pair of secondary sources to absorb the sound wave.

Section 1.3 considers the limitations of an active control system that uses multiple secondary sources to minimise the power radiated by a compact primary source in an infinite medium. The two-dimensional case is discussed first, by considering flexural waves of vibration propagating in a plate, and this is extended to three dimensions by considering acoustic waves in free space. It is shown that in order to achieve significant reductions in radiated power, a single secondary source must be placed a distance from the primary source that is less than one-tenth of a wavelength and that if an array of secondary sources is used, each must be separated by a distance of less than half a wavelength.

A closed duct provides a simple example of a finite acoustic system that can resonate at certain frequencies, and in Section 1.4 this system is used to illustrate the variety of active control strategies that can be employed in a finite system. These include reflection and absorption of the incident wave, the maximisation of the power absorbed by the secondary source, and the minimisation of the total power generated by both the primary and secondary source. It turns out that the minimisation of total power is a very useful strategy in finite systems, and in Section 1.5 it is shown that such a strategy is almost equivalent to minimising the energy stored in the system. Section 1.5 goes on to present simulations of the minimisation of vibrational kinetic energy in a finite plate and of acoustic potential energy in an enclosure. The physical performance limitations of an active control system are shown to be imposed by the number of modes that significantly contribute to the response at any one frequency in both cases.

Although in these sections the active control of sound and the active control of vibration have been considered individually, vibration control is sometimes implemented with the objective of minimising the sound rad...

Table of contents

• Cover image
• Title page
• Table of Contents
• Signal Processing and its Applications
• Copyright
• Series Preface
• Dedication
• Preface
• Glossary
• Chapter 1: The Physical Basis for Active Control
• Chapter 2: Optimal and Adaptive Digital Filters
• Chapter 3: Single-Channel Feedforward Control
• Chapter 4: Multichannel Control of Tonal Disturbances
• Chapter 5: Multichannel Control of Stochastic Disturbances
• Chapter 6: Design and Performance of Feedback Controllers
• Chapter 7: Adaptive Feedback Controllers
• Chapter 8: Active Control of Nonlinear Systems
• Chapter 9: Optimisation of Transducer Location
• Chapter 10: Hardware for Active Control
• Appendix: Linear Algebra and the Description of Multichannel Systems
• References
• Index