Discontinuous Control Systems (eBook)

Frequency-Domain Analysis and Design

Igor Boiko (Autor)

eBook Download: PDF

2008 | 2009
XIV, 212 Seiten
Birkhauser Boston (Verlag)
978-0-8176-4753-7 (ISBN)

Infos

This book provides new insight on the problem of closed-loop performance and oscillations in discontinuous control systems, covering the class of systems that do not necessarily have low-pass filtering properties. The author provides a practical, yet rigorous and exact approach to analysis and design of discontinuous control systems via application of a novel frequency-domain tool: the locus of a perturbed relay system. Presented are a number of practical examples applying the theory to analysis and design of discontinuous control systems from various branches of engineering, including electro-mechanical systems, process control, and electronics.

Discontinuous Control Systems is intended for readers who have knowledge of linear control theory and will be of interest to graduate students, researchers, and practicing engineers involved in systems analysis and design.

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Discontinuous control systems are the oldest type of control system and the mostwidespreadtypeofnonlinearcontrolsystem. Thetheoryofdiscontinuous control, and the theory of relay feedback systems in particular, is usually c- sidered a mature subject. However, many problems in discontinuous control theory still remain open. One problem involves the input-output properties of these systems, knowledge of which is extremely important to every app- cation. Two types of discontinuous control systems are studied in this book. The ?rst is the so-called relay feedback system, which normally encompasses - lay servomechanisms, various on-o? controllers, sigma-delta modulators, relay feedback tests used for process dynamics identi?cation, and controller tuning. Relaysystemsareoftenconsideredthemaintypeofnonlinearsystem,whichis evident by the enormous amount of house temperature control systems (that are usually implemented as on-o? controllers) that exist. The theory of relay systems is an old subject. The problem of analysis of relay feedback systems was ?rst considered by L. MacColl in 1945 [71]; the study was motivated by thedevelopmentofrelayservomechanismsofmissilethrustersontheonehand and vibrational voltage regulators on the other. MacColl's analysis was based on an approximate approach close to the describing function method. Later, exact methods of analysis of relay feedback systems were developed, the most well-known of which is the Tsypkin locus [94]. The exact approach developed by Tsypkin, however, did not consider the servo aspect of relay feedback c- trol. Its purpose was limited to ?nding periodic motions that may occur in a relay system in an autonomous mode or under external excitation.

Inhalt

Preface 6
Contents 9
The locus of a perturbed relay system theory 13
1 The servo problem in discontinuous control systems 14
1.1 Introduction 14
1.2 Fundamentals of frequency-domain analysis of periodic motions in nonlinear systems 16
1.3 Relay servo systems 21
1.4 Symmetric oscillations in relay servo systems: DF analysis 23
1.5 Asymmetric oscillations in relay servo systems: DF analysis 25
1.6 Slow signal propagation through a relay servo system 27
1.7 Conclusions 28
2 The locus of a perturbed relay system (LPRS) theory 29
2.1 Introduction to the LPRS 29
2.2 Computing the LPRS for a non-integrating plant 31
2.3 Computing the LPRS for an integrating plant 36
2.4 Computing the LPRS for a plant with a time delay 41
2.5 LPRS of first-order dynamics 43
2.6 LPRS of second-order dynamics 45
2.7 LPRS of first-order plus dead-time dynamics 48
2.8 Some properties of the LPRS 51
2.9 LPRS of nonlinear plants 53
2.10 Application of periodic signal mapping to computing the LPRS of some special nonlinear plants 58
2.11 Comparison of the LPRS with other methods of analysis of relay systems 62
2.12 An example of analysis of oscillations and transfer properties 63
2.13 Conclusions 64
3 Input-output analysis of relay servo systems 66
3.1 Slow and fast signal propagation through a relay servo system 66
3.2 Methodology of input-output analysis 72
3.3 Example of forced motions analysis with the use of the LPRS 72
3.4 Conclusions 74
4 Analysis of sliding modes in the frequency domain 75
4.1 Introduction to sliding mode control 75
4.2 Representation of a sliding mode system via the equivalent relay system 77
4.3 Analysis of motions in the equivalent relay system 81
4.4 The chattering phenomenon and its LPRS analysis 85
4.5 Reduced-order and non–reduced-order models of averaged motions in a sliding mode system and input- output analysis 93
4.6 On fractal dynamics in sliding-mode control 96
4.7 Examples of chattering and disturbance attenuation analysis 103
4.8 Conclusions 109
5 Performance analysis of second-order SM control algorithms 111
5.1 Introduction 111
5.2 Sub-optimal algorithm 112
5.3 Describing function analysis of chattering 113
5.4 Exact frequency-domain analysis of chattering 114
5.5 Describing function analysis of external signal propagation 116
5.6 Exact frequency-domain analysis of external signal propagation 120
5.7 Example of the analysis of sub-optimal algorithm performance 125
5.8 Conclusions 130
Applications of the locus of a perturbed relay system 131
6 Relay pneumatic servomechanism design 132
6.1 Relay pneumatic servomechanism dynamics and characteristics 132
6.2 LPRS analysis of uncompensated relay electro- pneumatic servomechanism 134
6.3 Compensator design in the relay electro-pneumatic servomechanism 135
6.4 Examples of compensator design in the relay electro- pneumatic servomechanism 139
6.5 Compensator design in the relay electro-pneumatic servomechanism with the use of the LPRS of a nonlinear plant 142
6.6 Conclusions 145
7 Relay feedback test identification and autotuning 146
7.1 The relay feedback test 146
7.2 The LPRS and asymmetric relay feedback test 147
7.3 Methodology of identification of the first-order plus dead- time process 148
7.4 Analysis of potential sources of inaccuracy 150
7.5 Performance analysis of the identification algorithm 152
7.6 Tuning algorithm 154
7.7 Conclusions 158
8 Performance analysis of the sliding mode– based analog differentiator and dynamical compensator 160
8.1 Transfer function "inversion” via sliding mode 160
8.2 Analysis of SM differentiator dynamics 161
8.3 Temperature sensor dynamics compensation via SM application 164
8.4 Analysis of the sliding mode compensator 167
8.5 An example of compensator design 169
8.6 Conclusions 172
9 Analysis of sliding mode observers 173
9.1 The SM observer as a relay servo system 173
9.2 SM observer performance analysis and characteristics 176
9.3 Example of SM observer performance analysis 178
9.4 Conclusions 181
10 Appendix 182
10.1 The LPRS derivation for a non-integrating linear part 182
10.2 Orbital stability of a system with a non-integrating linear part 186
10.3 The LPRS derivation for an integrating linear part 188
10.4 Orbital stability of a system with an integrating linear part 196
10.5 The LPRS derivation for a linear part with time delay 199
10.6 MATLAB code for LPRS computing 203
References 210
Index 216

Produkt-Details

• Erscheint lt. Verlag: 18.11.2008
• Zusatzinfo: XIV, 212 p.
• Verlagsort: Boston
• Sprache: englisch
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Schlagworte: algorithms • closed-loop oscillations • discontinuous systems • Electro-mechanical Systems • frequency domain • Input-output analysis • linear optimization • locus of a perturbed relay system • MATLAB • nonideal closed-loop performance • parasitic dynamics • Process Control • Relay feedback • servomechanism design • sliding mode control
• ISBN-10: 0-8176-4753-8 / 0817647538
• ISBN-13: 978-0-8176-4753-7 / 9780817647537