Design of Embedded Robust Control Systems Using MATLAB Simulink 1st Edition by Petko Petkov, Tsonyo Slavov, Jordan Kralev 1785613308 978-1785613302

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IET CONTROL, ROBOTICS AND SENSORS SERIES 113
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Other volumes in this series:
Volume 8 A History of Control Engineering, 1800–1930 S. Bennett
Volume 18 Applied Control Theory, 2nd Edition J.R. Leigh
Volume 20 Design of Modern Control Systems D.J. Bell, P.A. Cook and N. Munro (Editors)
Volume 28 Robots and Automated Manufacture J. Billingsley (Editor)
Volume 33 Temperature Measurement and Control J.R. Leigh
Volume 34 Singular Perturbation Methodology in Control Systems D.S. Naidu
Volume 35 Implementation of Self-Tuning Controllers K. Warwick (Editor)
Volume 37 Industrial Digital Control Systems, 2nd Edition K. Warwick and D. Rees (Editors)
Volume 39 Continuous Time Controller Design R. Balasubramanian
Volume 40 Deterministic Control of Uncertain Systems A.S.I. Zinober (Editor)
Volume 41 Computer Control of Real-Time Processes S. Bennett and G.S. Virk (Editors)
Volume 42 Digital Signal Processing: Principles, devices and applications N.B. Jones and J.D. McK. Watson
(Editors)
Volume 44 Knowledge-Based Systems for Industrial Control J. McGhee, M.J. Grimble and A. Mowforth (Editors)
Volume 47 A History of Control Engineering, 1930–1956 S. Bennett
Volume 49 Polynomial Methods in Optimal Control and Filtering K.J. Hunt (Editor)
Volume 50 Programming Industrial Control Systems Using IEC 1131-3 R.W. Lewis
Volume 51 Advanced Robotics and Intelligent Machines J.O. Gray and D.G. Caldwell (Editors)
Volume 52 Adaptive Prediction and Predictive Control P.P. Kanjilal
Volume 53 Neural Network Applications in Control G.W. Irwin, K. Warwick and K.J. Hunt (Editors)
Volume 54 Control Engineering Solutions: A practical approach P. Albertos, R. Strietzel and N. Mort (Editors)
Volume 55 Genetic Algorithms in Engineering Systems A.M.S. Zalzala and P.J. Fleming (Editors)
Volume 56 Symbolic Methods in Control System Analysis and Design N. Munro (Editor)
Volume 57 Flight Control Systems R.W. Pratt (Editor)
Volume 58 Power-Plant Control and Instrumentation: The control of boilers and HRSG systems D. Lindsley
Volume 59 Modelling Control Systems Using IEC 61499 R. Lewis
Volume 60 People in Control: Human factors in control room design J. Noyes and M. Bransby (Editors)
Volume 61 Nonlinear Predictive Control: Theory and practice B. Kouvaritakis and M. Cannon (Editors)
Volume 62 Active Sound and Vibration Control M.O. Tokhi and S.M. Veres
Volume 63 Stepping Motors, 4th Edition P.P. Acarnley
Volume 64 Control Theory, 2nd Edition J.R. Leigh
Volume 65 Modelling and Parameter Estimation of Dynamic Systems J.R. Raol, G. Girija and J. Singh
Volume 66 Variable Structure Systems: From principles to implementation A. Sabanovic, L. Fridman and
S. Spurgeon (Editors)
Volume 67 Motion Vision: Design of compact motion sensing solution for autonomous systems J. Kolodko
and L. Vlacic
Volume 68 Flexible Robot Manipulators: Modelling, simulation and control M.O. Tokhi and A.K.M. Azad
(Editors)
Volume 69 Advances in Unmanned Marine Vehicles G. Roberts and R. Sutton (Editors)
Volume 70 Intelligent Control Systems Using Computational Intelligence Techniques A. Ruano (Editor)
Volume 71 Advances in Cognitive Systems S. Nefti and J. Gray (Editors)
Volume 72 Control Theory: A guided tour, 3rd Edition J.R. Leigh
Volume 73 Adaptive Sampling with Mobile WSN K. Sreenath, M.F. Mysorewala, D.O. Popa and F.L. Lewis
Volume 74 Eigenstructure Control Algorithms: Applications to aircraft/rotorcraft handling qualities design
S. Srinathkumar
Volume 75 Advanced Control for Constrained Processes and Systems F. Garelli, R.J. Mantz and H. De Battista
Volume 76 Developments in Control Theory towards Global Control L. Qiu, J. Chen, T. Iwasaki and H. Fujioka
(Editors)
Volume 77 Further Advances in Unmanned Marine Vehicles G.N. Roberts and R. Sutton (Editors)
Volume 78 Frequency-Domain Control Design for High-Performance Systems J. O’Brien
Volume 80 Control-Oriented Modelling and Identiﬁcation: Theory and practice M. Lovera (Editor)
Volume 81 Optimal Adaptive Control and Differential Games by Reinforcement Learning Principles
D. Vrabie, K. Vamvoudakis and F. Lewis
Volume 83 Robust and Adaptive Model Predictive Control of Nonlinear Systems M. Guay, V. Adetola and
D. DeHaan
Volume 84 Nonlinear and Adaptive Control Systems Z. Ding
Volume 86 Modeling and Control of Flexible Robot Manipulators, 2nd edition M.O. Tokhi and A.K.M. Azad
Volume 88 Distributed Control and Filtering for Industrial Systems M. Mahmoud
Volume 89 Control-Based Operating System Design A. Leva et al.
Volume 90 Application of Dimensional Analysis in Systems Modelling and Control Design P. Balaguer
Volume 91 An Introduction to Fractional Control D. Valério and J. Costa
Volume 92 Handbook of Vehicle Suspension Control Systems H. Liu, H. Gao and P. Li
Volume 93 Design and Development of Multi-Lane Smart Electromechanical Actuators F.Y. Annaz
Volume 94 Analysis and Design of Reset Control Systems Y. Guo, L. Xie and Y. Wang
Volume 95 Modelling Control Systems Using IEC 61499, 2nd Edition R. Lewis and A. Zoitl
Volume 96 Cyber-Physical System Design with Sensor Networking Technologies S. Zeadally and N. Jabeur
(Editors)
Volume 99 Practical Robotics and Mechatronics: Marine, space and medical applications I. Yamamoto
Volume 100 Organic Sensors: Materials and applications E. Garcia-Breijo and P. Cosseddu (Editors)
Volume 102 Recent Trends in Sliding Mode Control L. Fridman J.P. Barbot and F. Plestan (Editors)
Volume 104 Control of Mechatronic Systems L. Guvenc, B.A. Guvenc, B. Demirel and M.T Emirler
Volume 105 Mechatronic Hands: Prosthetic and robotic design P.H. Chappell
Volume 107 Solved Problems in Dynamical Systems and Control D. Valério, J.T. Machado, A.M. Lopes and
A.M. Galhano
Volume 108 Wearable Exoskeleton Systems: Design, control and applications S. Bai, G.S. Virk and T.G. Sugar
Volume 111 The Inverted Pendulum in Control Theory and Robotics: From theory to new innovations
O. Boubaker and R. Iriarte (Editors)
Volume 112 RFID Protocol Design, Optimization, and Security for the Internet of Things Alex X. Liu,
Muhammad Shahzad, Xiulong Liu and Keqiu Li

Design of Embedded Robust
Control Systems Using
MATLAB®
/Simulink®
Petko H. Petkov, Tsonyo N. Slavov and Jordan K. Kralev
The Institution of Engineering and Technology

Published by The Institution of Engineering and Technology, London, United Kingdom
The Institution of Engineering and Technology is registered as a Charity in England &
Wales (no. 211014) and Scotland (no. SC038698).
© The Institution of Engineering and Technology 2018
First published 2018
This publication is copyright under the Berne Convention and the Universal Copyright
Convention. All rights reserved. Apart from any fair dealing for the purposes of research
or private study, or criticism or review, as permitted under the Copyright, Designs and
Patents Act 1988, this publication may be reproduced, stored or transmitted, in any
form or by any means, only with the prior permission in writing of the publishers, or in
the case of reprographic reproduction in accordance with the terms of licences issued
by the Copyright Licensing Agency. Enquiries concerning reproduction outside those
terms should be sent to the publisher at the undermentioned address:
The Institution of Engineering and Technology
Michael Faraday House
Six Hills Way, Stevenage
Herts, SG1 2AY, United Kingdom
www.theiet.org
While the authors and publisher believe that the information and guidance given in this
work are correct, all parties must rely upon their own skill and judgement when making
use of them. Neither the authors nor publisher assumes any liability to anyone for any
loss or damage caused by any error or omission in the work, whether such an error or
omission is the result of negligence or any other cause. Any and all such liability
is disclaimed.
The moral rights of the authors to be identiﬁed as authors of this work have been
asserted by them in accordance with the Copyright, Designs and Patents Act 1988.
British Library Cataloguing in Publication Data
A catalogue record for this product is available from the British Library
ISBN 978-1-78561-330-2 (hardback)
ISBN 978-1-78561-331-9 (PDF)
Typeset in India by MPS Limited
Printed in the UK by CPI Group (UK) Ltd, Croydon

This page intentionally left blank

Contents
Preface xiii
1 Embedded control systems 1
1.1 Introduction 1
1.2 Structure and elements of embedded control systems 2
1.2.1 Typical block diagram 2
1.2.2 A/D and D/A conversion 4
1.2.3 Sensors 5
1.2.4 Actuators 6
1.2.5 Processors 7
1.2.6 Software 8
1.3 Sampling and aliasing 10
1.4 Fixed-point arithmetic 12
1.4.1 Fixed-point numbers 12
1.4.2 Scaling 15
1.4.3 Range and precision 18
1.4.4 Fixed-point arithmetic operations 19
1.5 Floating-point arithmetic 22
1.5.1 Floating-point numbers 22
1.5.2 IEEE arithmetic 23
1.5.3 Floating-point arithmetic operations 25
1.6 Quantization effects 25
1.6.1 Truncation and roundoff 25
1.6.2 Quantization errors in A/D conversion 28
1.7 Design stages 29
1.7.1 Controller design 32
1.7.2 Closed-loop system simulation 34
1.7.3 Embedded code generation 36
1.8 Hardware configuration 36
1.8.1 Microprocessing architectures 37
1.8.2 Hardware description language 41
1.8.3 Module level development 44
1.8.4 System level development 48
1.9 Software configuration 54
1.9.1 Board support package 54
1.9.2 Application programing interface 56

viii Design of embedded robust control systems using MATLAB®
/Simulink®
1.9.3 Code generation 56
1.9.4 Code validation 60
1.10 Notes and references 61
2 System modeling 63
2.1 Plant modeling 63
2.2 Linearization 66
2.2.1 Analytic linearization 66
2.2.2 Symbolic linearization 68
2.2.3 Numeric linearization 71
2.3 Discretization 71
2.3.1 Discrete-time models 73
2.3.2 Discrete-time frequency responses 74
2.3.3 Discretization of continuous-time models 76
2.3.4 Discretization of time delay systems 80
2.3.5 Choice of the sampling period 81
2.3.6 Discretization of nonlinear models 82
2.4 Stochastic modeling 84
2.4.1 Stochastic linear systems 84
2.4.2 Discretization of stochastic models 86
2.4.3 Optimal estimation 88
2.5 Plant identification 91
2.5.1 Identification of black box model 92
2.5.2 Identification of gray-box model 102
2.6 Uncertainty modeling 111
2.6.1 Structured uncertainty models 111
2.6.2 Representing uncertain models by LFT 117
2.6.3 Deriving uncertain state-space models from
Simulink®
models 119
2.6.4 Unstructured uncertainty models 120
2.6.5 Mixed uncertainty models 124
2.6.6 Discretization of uncertain models 125
2.6.7 Deriving uncertainty models by identification 128
2.7 Sensor modeling 131
2.7.1 Allan variance 132
2.7.2 Stochastic gyro model 133
2.7.3 Stochastic accelerometer model 138
2.7.4 Sensor data filtering 142
3 Performance requirements and design limitations 147
3.1 SISO closed-loop systems 147
3.2 Performance specifications of SISO systems 151
3.2.1 Time-domain specifications 151
3.2.2 Frequency-domain specifications 152

Contents ix
3.3 Trade-offs in the design of SISO systems 155
3.3.1 Limitations on S and T 155
3.3.2 Right half-plane poles and zeros 156
3.3.3 Limitations imposed by time delays 158
3.3.4 Limitations imposed by measurement noise 159
3.3.5 Limitations, imposed by disturbances 160
3.3.6 Limitations on control action 160
3.3.7 Limitations due to model errors 161
3.4 MIMO closed-loop systems 168
3.5 Performance specifications of MIMO systems 171
3.5.1 Using singular values for performance analysis 171
3.5.2 H∞ Norm of a system 174
3.5.3 Hankel norm 176
3.6 Trade-offs in the design of MIMO systems 176
3.6.1 Disturbance rejection 177
3.6.2 Noise suppression 178
3.6.3 Model errors 178
3.7 Uncertain systems 180
3.8 Robust-stability analysis 182
3.8.1 Unstructured uncertainty 183
3.8.2 Structured singular value 183
3.8.3 Robust-stability analysis with μ 185
3.9 Robust performance analysis 188
3.9.1 Using μ for robust performance analysis 189
3.9.2 Worst case gain 194
3.9.3 Worst case margin 196
3.10 Numerical issues in robustness analysis 197
4 Controller design 203
4.1 PID controller 204
4.2 LQG controller with integral action 219
4.2.1 Discrete-time LQG controller 220
4.2.2 Colored measurement noise 223
4.2.3 LQG controller with bias compensation 233
4.3 LQ regulator with H∞ filter 240
4.3.1 Discrete-time H∞ filter 241
4.3.2 H∞ Filter with bias compensation 247
4.4 H∞ Design 252
4.4.1 The H∞ design problem 252
4.4.2 Mixed-sensitivity H∞ control 258
4.4.3 Two degrees-of-freedom controllers 261
4.4.4 Numerical issues in H∞ design 263
4.5 μ Synthesis 272
4.5.1 The μ synthesis problem 273

x Design of embedded robust control systems using MATLAB®
/Simulink®
4.5.2 Replacing μ with its upper bound 274
4.5.3 DK iteration 276
4.5.4 Numerical issues in μ synthesis 278
4.6 Controller comparison 287
4.7 HIL simulation 288
5 Case study 1: embedded control of tank physical model 299
5.1 Hardware configuration of embedded control system 300
5.1.1 Water tank 301
5.1.2 ARDUINO MEGA 2560 301
5.1.3 Voltage divider 303
5.1.4 Relay block 305
5.2 Plant identification 305
5.3 LQR and LQG controllers design 314
5.4 H∞ Controller design 319
5.5 Experimental evaluation 324
6 Case study 2: robust control of miniature helicopter 335
6.1 Helicopter model 336
6.1.1 Nonlinear helicopter model 336
6.1.2 Linearized model 341
6.1.3 Uncertain model 346
6.2 μ Synthesis of attitude controller 348
6.2.1 Performance requirements 349
6.2.2 Controller design 353
6.2.3 Frequency responses 356
6.2.4 Transient responses of the linear system 362
6.2.5 Position controller design 362
6.3 Hardware-in-the-loop simulation 365
6.3.1 Nonlinear system simulation 366
6.3.2 HIL simulation setup 367
6.3.3 Results of HIL simulation 369
7 Case study 3: robust control of two-wheeled robot 377
7.1 Robot description 378
7.2 Closed-loop identification of robot model 380
7.2.1 Dynamic models from u to φ̇ 385
7.2.2 Dynamic models from φ̇ to θ̇ 389
7.2.3 Dynamic model of the yaw motion 391

Contents xi
7.3 Derivation of uncertain models 395
7.3.1 Signal-based uncertainty representation 395
7.3.2 Input multiplicative uncertainty representation 395
7.4 LQG controller design 399
7.5 μ Controller design 404
7.6 Comparison of designed controllers 407
7.7 Experimental evaluation 410
Appendix A: Elements of matrix analysis 419
A.1 Vectors and matrices 419
A.2 Eigenvalues and eigenvectors 420
A.3 Singular value decomposition 421
A.4 Vector and matrix norms 423
A.4.1 Vector norms 423
A.4.2 Matrix norms 424
A.4.3 Relationships between matrix norms 426
A.5 Notes and references 427
Appendix B: Elements of linear system theory 429
B.1 Description 429
B.2 Stability 430
B.3 Controllability and observability 430
B.4 Lyapunov equations 433
B.5 Poles and zeros 435
B.6 Notes and references 436
Appendix C: Stochastic processes 437
C.1 Random variables 437
C.2 Stochastic processes 439
C.3 White noise 443
C.4 Gauss–Markov processes 444
C.5 Generation of white noise in MATLAB®
446
C.6 Notes and references 447
Appendix D: Identification of linear models 449
D.1 Identification of linear black-box model 449
D.1.1 Experiment design and input/output data acquisition 450
D.1.2 Model structure selection and parameters estimation 455
D.1.3 Model validation 468
D.2 Identification of linear gray-box model 472
D.3 Notes and references 472

xii Design of embedded robust control systems using MATLAB®
/Simulink®
Appendix E: Interfacing IMU with target microcontroller 473
E.1 Driving SPI communication 474
E.2 Design of Simulink®
interface block 476
Appendix F: Measuring angular velocity with hall encoder 481
References 487
Index 503

Preface
The aim of the book
The aim of this book is to give the necessary knowledge about the implementa-
tion of MATLAB®
and Simulink®
in the development of embedded control systems.
Together, MATLAB and Simulink present a sophisticated programing environment
which may be used for the design as well as for the implementation of embedded
control systems. In this book, the authors exploit the opportunity to generate auto-
matically and embed control code from Simulink models which allows to develop
quickly efficient and error free code.The automated code generation and the availabil-
ity of powerful processors make possible the implementation of complex high-order
controllers which achieve fast and high-performance closed-loop dynamics.
The book is oriented toward the application of modern Control Theory to the
development of high-performance control laws which ensure good dynamics and
robustness of the closed-loop system to plant uncertainties. The theoretical develop-
ments are reduced to the possible minimum the accent being put on the application
issues. The basic results of Control Theory are given without proofs, and for more
information, the reader is advised to consult the notes and references given at the end
of the corresponding chapter. The presentation contains lots of nontrivial examples,
which allow to illustrate the practical implementation of theoretical results. Most of
the examples are taken from the area of motion control, but the book may also be
used by designers in other areas.
The book covers mainly the design of linear controllers which are most frequently
used in practice. This approach is justified by the principle of linearity of small
increments which states that almost any natural process is linear in small amounts
almost everywhere. Fortunately, as noted by Kostrikin and Manin [1], the small
neighborhood in which this principle is valid is sufficiently large.
An important part of the book is the freely downloadable material which contains
MATLAB and Simulink files for all examples presented in the corresponding chap-
ters. The usage of this material can help in understanding the different issues arising
in the analysis and design of embedded control systems.
Expected audience
The book is intended as a reference source for MSc and PhD students who study
in the field of Control Engineering as well as for control engineers working in the

xiv Design of embedded robust control systems using MATLAB®
/Simulink®
industry. It can also be used as a reference for researchers in Control Engineering
who are interested in the implementation of MATLAB and Simulink in the design of
Control Systems. The first four chapters may also be used for a masters course on the
design of embedded control systems.
The contents
The book consists of seven chapters and six appendices.
Chapter 1 presents a brief overview of the embedded control systems and the
corresponding design process.
InChapter2, wedescribeseveralfundamentalissuesrelatedtothedevelopmentof
plant model, like linearization, discretization, stochastic modeling, and identification.
This chapter contains also a section on uncertainty modeling.
Chapter 3 is entirely devoted to the performance requirements and design limita-
tions arising in embedded controller design. A significant part of this chapter are the
sections on robust stability and robust performance analysis of uncertain systems.
In Chapter 4, we present in detail the design of five basic controllers used in the
modern Control Theory: proportional-integral-derivative (PID) controllers, linear-
quadratic-Gaussian (LQG) controllers, and linear-quadratic (LQ) regulators with H∞
filters, H∞, and μ controllers. For comparison purposes, all controllers are imple-
mented on the same plant which represents the well-known cart–pendulum system.
We consider the possible difficulties in the design of these controllers and give a com-
parison of the properties of corresponding closed-loop systems. These properties are
illustrated by the hardware-in-the-loop (HIL) simulation of the closed-loop systems
for the worst combination of plant parameters values.
In the last three chapters, we present three case studies which describe in detail
the theoretical and practical issues arising in the design of three embedded control
systems.
In Chapter 5, we consider the design of a low-cost control system for a two-tank
plant. This chapter should be of interest to the readers who want to use low-cost
processors in the design of embedded systems.
Chapter 6 is devoted to the robust control of a miniature helicopter. We consider
the implementation of high-order controller which ensures robust performance of the
closed-loop system in the presence of severe wind disturbances.
Finally, in Chapter 7, we present the design of embedded control system of a
two-wheeled robot. In this case, we demonstrate experimentally the implementation
of 30th-order controller which ensures robust stability and performance of the closed-
loop system in the presence of plant uncertainty.
In Appendices A–D, we give some necessary facts from matrix analysis, linear
system theory, stochastic processes, and identification of linear models, respec-
tively. In Appendices E and F, we discuss important practical issues like connection
between sensors and DSP and measurement of angular velocities by Hall encoders,
respectively.

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School Days 177

The Sea 191
The Father-Lan 201
A Roman Girl 213
The Appenines 225
Enrica 235
II Noon—Which Is the Present 245
Early Friends 249
School Revisited 259
College 267
The Packet of Bella 275
III Evening—Which Is the Future 287
Carry 293
The Letter 303
New Travel 311
Home 327

PREFACE
This book is neither more nor less than it pretends to be; it is a
collection of those floating reveries which have, from time to time,
drifted across my brain. I never yet met with a bachelor who had not
his share of just such floating visions; and the only difference
between us lies in the fact that I have tossed them from me in the
shape of a book.
If they had been worked over with more unity of design I dare say
I might have made a respectable novel; as it is, I have chosen the
honester way of setting them down as they came seething from my
thought, with all their crudities and contrasts, uncovered.
As for the truth that is in them, the world may believe what it
likes; for, having written to humor the world, it would be hard if I
should curtail any of its privileges of judgment. I should think there
was as much truth in them as in most Reveries.
The first story of the book has already had some publicity; and the
criticisms upon it have amused and pleased me. One honest
journalist avows that it could never have been written by a bachelor.
I thank him for thinking so well of me, and heartily wish that his
thought were as true as it is kind.
Yet I am inclined to think that bachelors are the only safe and
secure observers of all the phases of married life. The rest of the
world have their hobbies; and by law, as well as by immemorial
custom, are reckoned unfair witnesses in everything relating to their
matrimonial affairs.

Perhaps I ought, however, to make an exception in favor of
spinsters, who, like us, are independent spectators, and possess just
that kind of indifference to the marital state, which makes them
intrepid in their observations, and very desirable for—authorities.
As for the style of the book I have nothing to say for it except to
refer to my title. These are not sermons, nor essays, nor criticisms;
they are only Reveries. And if the reader should stumble upon
occasional magniloquence, or be worried with a little too much of
sentiment, pray let him remember—that I am dreaming.
But while I say this, in the hope of nicking off the wiry edge of my
reader’s judgment, I shall yet stand up boldly for the general tone
and character of the book. If there is bad feeling in it, or insincerity,
or shallow sentiment, or any foolish depth of affection betrayed—I
am responsible; and the critics may expose it to their hearts’
content.
I have, moreover, a kindly feeling for these Reveries, from their
very private character; they consist mainly of just such whimseys
and reflections as a great many brother bachelors are apt to indulge
in, but which they are too cautious, or too prudent to lay before the
world. As I have in this matter shown a frankness and naïveté which
are unusual, I shall ask a corresponding frankness in my reader; and
I can assure him safely that this is eminently one of those books
which were “never intended for publication.”
In the hope that this plain avowal may quicken the reader’s
charity, and screen me from cruel judgment,
I remain, with sincere good wishes,
Ik Marvel.
New York, November, 1850.

OVER A WOOD FIRE
I have got a quiet farmhouse in the country, a very humble place to
be sure, tenanted by a worthy enough man, of the old New England
stamp, where I sometimes go for a day or two in the winter, to look
over the farm accounts, and to see how the stock is thriving on the
winter’s keep.
One side the door, as you enter from the porch, is a little parlor,
scarce twelve feet by ten, with a cozy-looking fireplace—a heavy oak
floor—a couple of armchairs and a brown table with carved lions’
feet. Out of this room opens a little cabinet, only big enough for a
broad bachelor bedstead, where I sleep upon feathers, and wake in
the morning, with my eye upon a saucy colored, lithographic print of
some fancy “Bessy.”
It happens to be the only house in the world, of which I am bona
fide owner; and I take a vast deal of comfort in treating it just as I
choose. I manage to break some article of furniture almost every
time I pay it a visit; and if I can not open the window readily of a
morning, to breathe the fresh air, I knock out a pane or two of glass
with my boot. I lean against the walls in a very old armchair there is
on the premises, and scarce ever fail to worry such a hole in the
plastering as would set me down for a round charge for damages in
town, or make a prim housewife fret herself into a raging fever. I
laugh out loud with myself, in my big armchair, when I think that I
am neither afraid of one nor the other.
As for the fire, I keep the little hearth so hot as to warm half the
cellar below, and the whole space between the jambs roars for hours
together with white flame. To be sure the windows are not very

tight, between broken panes and bad joints, so that the fire, large as
it is, is by no means an extravagant comfort.

As night approaches, I have a huge pile of oak and hickory placed
beside the hearth; I put out the tallow candle on the mantel (using
the family snuffers, with one leg broken) then, drawing my chair
directly in front of the blazing wood, and setting one foot on each of
the old iron fire-dogs (until they grow too warm), I dispose myself
for an evening of such sober and thoughtful quietude, as I believe,
on my soul, that very few of my fellow men have the good fortune
to enjoy.
My tenant, meantime, in the other room I can hear now and then
—though there is a thick stone chimney and broad entry between—
multiplying contrivances with his wife to put two babies to sleep.
This occupies them, I should say, usually an hour; though my only
measure of time (for I never carry a watch into the country), is the
blaze of my fire. By ten, or thereabouts, my stock of wood is nearly
exhausted; I pile upon the hot coals what remains, and sit watching
how it kindles, and blazes, and goes out—even like our joys! and
then slip by the light of the embers into my bed, where I luxuriate in
such sound and healthful slumber as only such rattling window
frames and country air can supply.
But to return: the other evening—it happened to be on my last
visit to my farmhouse—when I had exhausted all the ordinary rural
topics of thought, had formed all sorts of conjectures as to the
income of the year; had planned a new wall around one lot, and the
clearing up of another, now covered with patriarchal wood, and
wondered if the little rickety house would not be, after all, a snug
enough box to live and to die in—I fell on a sudden into such an
unprecedented line of thought, which took such a deep hold of my
sympathies—sometimes even starting tears—that I determined, the
next day, to set as much of it as I could recall on paper.
Something—it may have been the home-looking blaze (I am a
bachelor of—say six and twenty), or possibly a plaintive cry of the
baby in my tenant’s room had suggested to me the thought of—
Marriage.

I piled upon the heated fire-dogs, the last armful of my wood; and
now, said I, bracing myself courageously between the arms of my
chair—I’ll not flinch; I’ll pursue the thought wherever it leads,
though it lead me to the d—— (I am apt to be hasty) at least—
continued I, softening—until my fire is out.
The wood was green, and at first showed no disposition to blaze.
It smoked furiously. Smoke, thought I, always goes before blaze;
and so does doubt go before decision: and my reverie, from that
very starting point, slipped into this shape:

SMOKE—SIGNIFYING DOUBT
A wife? thought I; yes, a wife! And why?
And pray, my dear sir, why not—why? Why not doubt; why not
hesitate; why not tremble?
Does a man buy a ticket in a lottery—a poor man, whose whole
earnings go in to secure the ticket—without trembling, hesitating,
and doubting?
Can a man stake his bachelor respectability, his independence,
and comfort, upon the die of absorbing, unchanging, relentless
marriage, without trembling at the venture?
Shall a man who has been free to chase his fancies over the wide
world, without let or hindrance, shut himself up to marriageship,
within four walls called home, that are to claim him, his time, his
trouble, and his tears, thenceforward forever more, without doubts
thick and thick-coming as smoke?
Shall he who has been hitherto a mere observer of other men’s
cares and business, moving off where they made him sick of heart,
approaching whenever and wherever they made him gleeful—shall
he now undertake administration of just such cares and business
without qualms? Shall he, whose whole life has been but a nimble
succession of escapes from trifling difficulties, now broach, without
doubtings, that matrimony, where if difficulty beset him there is no
escape? Shall this brain of mine, careless-working, never tired with
idleness, feeding on long vagaries, and high, gigantic castles,
dreaming out beatitudes hour by hour—turn itself at length to such
dull task-work, as thinking out a livelihood for wife and children?

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