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Table of Contents

Cover

Title

Preface

1 Introduction, Generalities, Definitions of Systems

1.1. Introduction
1.2. Signals and communication systems
1.3. Signals and systems representation
1.4. Convolution and composition products – notions of filtering
1.5. Transmission systems and filters
1.6. Deterministic signals – random signals – analog signals
1.7. Comprehension and application exercises

2 Transforms: Time – Frequency – Scale

2.1. Fourier series applied to periodic functions
2.2. FT applied to non-periodic functions
2.3. Necessary conditions for the Fourier integral
2.4. FT properties
2.5. Fourier series and FT
2.6. Elementary signals and their transforms
2.7. Laplace transform
2.8. FT and LT
2.9. Application exercises

3 Spectral Study of Signals

3.1. Power and signals energy
3.2. Autocorrelation and intercorrelation
3.3. Mathematical application of the correlation and autocorrelation functions
3.4. A few application exercises

4 Representation of Discrete (Sampled) Systems

4.1. Shannon and sampling, discretization methods, interpolation, sample and hold circuits
4.2. Z-transform – representation of discrete (sampled) systems
4.3. A few application exercises

5 Representation of Signals and Systems

5.1. Introduction to modeling
5.2. Representation using system state equations
5.3. Transfer functions
5.4. Change in representation and canonical forms
5.5. Some application exercises

6 Dynamic Responses and System Performance

6.1. Introduction to linear time-invariant systems
6.2. Transition matrix of an LTI system
6.3. Evolution equation of an LTI system
6.4. Time response to the excitation of continuous linear systems
6.5. Sampling and discretization of continuous systems
6.6. Some temporal responses
6.7. Transfer function frequency responses
6.8. Parametric identification
6.9. Dynamics of linear systems
6.10. System performance and accuracy
6.11. Some application exercises

7 System Stability and Robustness Analysis Methods

7.1. Introduction
7.2. Definitions related with the stability of a dynamic system
7.3. Stability criteria
7.4. Some application exercises

Bibliography

Index

End User License Agreement

List of Tables

1 Introduction, Generalities, Definitions of Systems

Table 1.1. The delta function
Table 1.2. Properties of the delta function
Table 1.3. Deterministic signals

2 Transforms: Time – Frequency – Scale

Table 2.1. Properties of the Fourier transform
Table 2.2. Common Fourier transforms
Table 2.3. A few properties of the unilateral Laplace transform
Table 2.4. Inverse Laplace transforms table

4 Representation of Discrete (Sampled) Systems

Table 4.1. Some examples of the bilateral ZT

6 Dynamic Responses and System Performance

Table 6.1. Strejc table
Table 6.2. Values of the speed errors for a ramp input

7 System Stability and Robustness Analysis Methods

Table 7.1. Routh table
Table 7.2. Routh table result
Table 7.3. Routh table results
Table 7.4. Routh table
Table 7.5. Routh table results
Table 7.6. Routh table results
Table 7.7. Jury table
Table 7.8. Jury table results
Table 7.9. Routh table, results system no. 2
Table 7.10. Routh table, results system no. 4
Table 7.11. Routh table, results system no. 5
Table 7.12. Routh table results

List of Illustrations

Preface

Figure 1. Applied scientific and technological resources
Figure 2. Basic concepts of theoretical study and processing methods
Figure 3. Diagram of the model for vehicle operation
Figure 4. Process with multiple input and output quantities
Figure 5. Open-loop process
Figure 6. Open-loop process with disturbances
Figure 7. Functional block diagram of a servo system
Figure 8. Speed regulation of a motor
Figure 9. Temperature regulation of an oven
Figure 10. Control system with correction
Figure 11. Controlled transfer function with feedback
Figure 12. Controlled transfer function without feedback
Figure 13. Control system with closed-loop system controller
Figure 14. System control with correction of a robotized system

1 Introduction, Generalities, Definitions of Systems

Figure 1.1. Peripherals of a system
Figure 1.2. Acquisition, sensors and triggers
Figure 1.3. Observation sequence
Figure 1.4. Communication sequence
Figure 1.5. Time signal with bounded support
Figure 1.6. Signal defined over a bounded medium
Figure 1.7. Harmonic oscillator output signal
Figure 1.8. Unit impulse
Figure 1.9. Dirac’s delta function
Figure 1.10. Input/output of a system
Figure 1.11. Impulse response of the filter or system
Figure 1.12. Input signal with a step Δτ
Figure 1.13. Signal subdivision
Figure 1.14. Heaviside
Figure 1.15. Rectangular pulse
Figure 1.16. Gaussian
Figure 1.17. Triangular pulse
Figure 1.18. Derivative of the triangular signal
Figure 1.19. Exponential
Figure 1.20. Rectangular pulse
Figure 1.21. Gaussian form
Figure 1.22. Exponential form
Figure 1.23. Polynomial form
Figure 1.24. A R L C circuit
Figure 1.25. p₁ and p₂ are two real negative roots of the characteristic equation
Figure 1.26. p₁ and p₂ are two real positive roots
Figure 1.27. p₁ and p₂ are two complex roots with real positive parts
Figure 1.28. Two pure imaginary roots

2 Transforms: Time – Frequency – Scale

Figure 2.1. Amplitude spectrum
Figure 2.2. Fourier series expansion of a square signal
Figure 2.3. Fourier series expansion of a sinusoidal signal
Figure 2.4. Periodized signal
Figure 2.5. Periodic signal
Figure 2.6. Line spectrum at f_n = n/T
Figure 2.7. Spectrum of a sinusoid
Figure 2.8. Sinc function spectrum
Figure 2.9. Process response
Figure 2.10. Transfer function of a process
Figure 2.11. Non-periodic signal
Figure 2.12. Periodic signals
Figure 2.13. Low-pass filter
Figure 2.14. Triangular gate
Figure 2.15. Time signals

3 Spectral Study of Signals

Figure 3.1. RL and RC circuits
Figure 3.2. Signal and its spectrum
Figure 3.3. Support-bounded time function
Figure 3.4. x(t)² probability density
Figure 3.5. Coefficient a_n of the Fourier transform
Figure 3.6. Low-pass filter time constant
Figure 3.7. Rectangular window
Figure 3.8. Impulse response of the filter
Figure 3.9. RC filter
Figure 3.10. Modeling of the tires of a vehicle

4 Representation of Discrete (Sampled) Systems

Figure 4.1. Temporal comb distribution
Figure 4.2. Frequency comb distribution
Figure 4.3. Spectral representation of a sampled signal
Figure 4.4. Shannon filter
Figure 4.5. Shannon interpolation
Figure 4.6. Average sampling signal
Figure 4.7. Region of convergence of the bilateral ZT
Figure 4.8. Disc of convergence of the unilateral ZT
Figure 4.9. Convergence of the bilateral ZT
Figure 4.10. Contour for the computation of the inverse ZT
Figure 4.11. Unit circle
Figure 4.12. Correlation
Figure 4.13. Discrete systems
Figure 4.14. Input/output system with feedback
Figure 4.15. Spectrum after sampling
Figure 4.16. Spectrum of a given signal
Figure 4.17. Given filter
Figure 4.18. Spectrum after sampling
Figure 4.19. Spectrum of a given signal
Figure 4.20. Discrete Fourier transform of a filter
Figure 4.21. Comb filter

5 Representation of Signals and Systems

Figure 5.1. Organizational chart
Figure 5.2. Approximating model adapted by identification
Figure 5.3. Servo systems
Figure 5.4. RLC circuit
Figure 5.5. Functional diagram
Figure 5.6. Cascade diagram
Figure 5.7. Parallel diagram
Figure 5.8. Diagram 1 in parallel in negative feedback
Figure 5.9. Diagram 2 in parallel in negative feedback
Figure 5.10. Inverse pendulum
Figure 5.11. Conservative system
Figure 5.12. Circles
Figure 5.13. Two real negative roots of the characteristic equation
Figure 5.14. Two positive real roots of the characteristic equation
Figure 5.15. Two real roots with opposite signs of the characteristic equation
Figure 5.16. Two complex roots of the characteristic equation with real negative parts
Figure 5.17. Two complex roots of the characteristic equation with real positive parts
Figure 5.18. Two pure imaginary roots of the characteristic equation (stable system)
Figure 5.19. State–space representation of the modeled process: companion form
Figure 5.20. State–space representation of the modeled process: Jordan form
Figure 5.21. State–space representation of the modeled process: cascade form
Figure 5.22. Linear motor
Figure 5.23. Block diagram Exercise 2
Figure 5.24. Car suspension process
Figure 5.25. Op–amp circuit
Figure 5.26. Direct current electric motor
Figure 5.27. Liquid level control

6 Dynamic Responses and System Performance

Figure 6.1. Block diagram for a discrete system
Figure 6.2. Step response
Figure 6.3. Form of the step response with respect to the damping coefficient
Figure 6.4. Damped response
Figure 6.5. Modulus and phase Bode plot of a first-order system
Figure 6.6. Modulus Bode plot of a second-order system
Figure 6.7. Phase Bode plot of a second-order system
Figure 6.8. Nyquist plot of a first-order system
Figure 6.9. Nyquist plot of a second-order system
Figure 6.10. Black–Nichols plot of a first-order system
Figure 6.11. Black–Nichols plot of a second-order system
Figure 6.12. Step response Strejc method
Figure 6.13. Noisy controlled system
Figure 6.14. Step response of a mechanical system
Figure 6.15. Controlled system with no feedback
Figure 6.16. Step response
Figure 6.17. Impulse response
Figure 6.18. Closed-loop controlled system
Figure 6.19. Step response of the system in CL
Figure 6.20. Unit step response of an unknown system
Figure 6.21. Unit step response of an unknown system 2
Figure 6.22. Unit step response of an unknown system 3
Figure 6.23. Unit step response of an unknown system 4
Figure 6.24. Controlled system with correction
Figure 6.25. Unit step response of
Figure 6.26. Controlled system
Figure 6.27. Step response
Figure 6.28. Step response

7 System Stability and Robustness Analysis Methods

Figure 7.1. Cascade diagrams
Figure 7.2. Parallel diagrams
Figure 7.3. Negative feedback parallel diagrams 1
Figure 7.4. Negative feedback parallel diagrams 2
Figure 7.5. Closed Gamma contour
Figure 7.6. Closed Omega contour
Figure 7.7. Nyquist plot, contour of s
Figure 7.8. Nyquist plot, contour of H(s)
Figure 7.9. Bode plot of
Figure 7.10. Nyquist plot of
Figure 7.11. Bode plot of
Figure 7.12. Nyquist plot of
Figure 7.13. Bode plot of
Figure 7.14. Nyquist plot of
Figure 7.15. Bode plot of
Figure 7.16. Nyquist plot of
Figure 7.17. Bode plot of
Figure 7.18. Nyquist plot of
Figure 7.19. Bode plot of
Figure 7.20. Nyquist plot of
Figure 7.21. Bode plot of
Figure 7.22. Nyquist plot of
Figure 7.23. Bode plot of
Figure 7.24. Black–Nichols plot of
Figure 7.25. Amplitude of the maximum of resonance Mr with respect to ξ

First published 2017 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

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 only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

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The rights of Smain Femmam to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2016957651

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ISBN 978-1-78630-098-0