Boiko Discontinuous Control Systems

Frequency-Domain Analysis and Design
1. Auflage 2008
ISBN: 978-0-8176-4753-7
Verlag: Birkhäuser Basel
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 212 Seiten

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.

Autoren/Hrsg.

Boiko, Igor

Inhaltsverzeichnis

1;Preface;6
2;Contents;9
3;The locus of a perturbed relay system theory;13
3.1;1 The servo problem in discontinuous control systems;14
3.1.1;1.1 Introduction;14
3.1.2;1.2 Fundamentals of frequency-domain analysis of periodic motions in nonlinear systems;16
3.1.3;1.3 Relay servo systems;21
3.1.4;1.4 Symmetric oscillations in relay servo systems: DF analysis;23
3.1.5;1.5 Asymmetric oscillations in relay servo systems: DF analysis;25
3.1.6;1.6 Slow signal propagation through a relay servo system;27
3.1.7;1.7 Conclusions;28
3.2;2 The locus of a perturbed relay system (LPRS) theory;29
3.2.1;2.1 Introduction to the LPRS;29
3.2.2;2.2 Computing the LPRS for a non-integrating plant;31
3.2.3;2.3 Computing the LPRS for an integrating plant;36
3.2.4;2.4 Computing the LPRS for a plant with a time delay;41
3.2.5;2.5 LPRS of first-order dynamics;43
3.2.6;2.6 LPRS of second-order dynamics;45
3.2.7;2.7 LPRS of first-order plus dead-time dynamics;48
3.2.8;2.8 Some properties of the LPRS;51
3.2.9;2.9 LPRS of nonlinear plants;53
3.2.10;2.10 Application of periodic signal mapping to computing the LPRS of some special nonlinear plants;58
3.2.11;2.11 Comparison of the LPRS with other methods of analysis of relay systems;62
3.2.12;2.12 An example of analysis of oscillations and transfer properties;63
3.2.13;2.13 Conclusions;64
3.3;3 Input-output analysis of relay servo systems;66
3.3.1;3.1 Slow and fast signal propagation through a relay servo system;66
3.3.2;3.2 Methodology of input-output analysis;72
3.3.3;3.3 Example of forced motions analysis with the use of the LPRS;72
3.3.4;3.4 Conclusions;74
3.4;4 Analysis of sliding modes in the frequency domain;75
3.4.1;4.1 Introduction to sliding mode control;75
3.4.2;4.2 Representation of a sliding mode system via the equivalent relay system;77
3.4.3;4.3 Analysis of motions in the equivalent relay system;81
3.4.4;4.4 The chattering phenomenon and its LPRS analysis;85
3.4.5;4.5 Reduced-order and non–reduced-order models of averaged motions in a sliding mode system and input- output analysis;93
3.4.6;4.6 On fractal dynamics in sliding-mode control;96
3.4.7;4.7 Examples of chattering and disturbance attenuation analysis;103
3.4.8;4.8 Conclusions;109
3.5;5 Performance analysis of second-order SM control algorithms;111
3.5.1;5.1 Introduction;111
3.5.2;5.2 Sub-optimal algorithm;112
3.5.3;5.3 Describing function analysis of chattering;113
3.5.4;5.4 Exact frequency-domain analysis of chattering;114
3.5.5;5.5 Describing function analysis of external signal propagation;116
3.5.6;5.6 Exact frequency-domain analysis of external signal propagation;120
3.5.7;5.7 Example of the analysis of sub-optimal algorithm performance;125
3.5.8;5.8 Conclusions;130
4;Applications of the locus of a perturbed relay system;131
4.1;6 Relay pneumatic servomechanism design;132
4.1.1;6.1 Relay pneumatic servomechanism dynamics and characteristics;132
4.1.2;6.2 LPRS analysis of uncompensated relay electro- pneumatic servomechanism;134
4.1.3;6.3 Compensator design in the relay electro-pneumatic servomechanism;135
4.1.4;6.4 Examples of compensator design in the relay electro- pneumatic servomechanism;139
4.1.5;6.5 Compensator design in the relay electro-pneumatic servomechanism with the use of the LPRS of a nonlinear plant;142
4.1.6;6.6 Conclusions;145
4.2;7 Relay feedback test identification and autotuning;146
4.2.1;7.1 The relay feedback test;146
4.2.2;7.2 The LPRS and asymmetric relay feedback test;147
4.2.3;7.3 Methodology of identification of the first-order plus dead- time process;148
4.2.4;7.4 Analysis of potential sources of inaccuracy;150
4.2.5;7.5 Performance analysis of the identification algorithm;152
4.2.6;7.6 Tuning algorithm;154
4.2.7;7.7 Conclusions;158
4.3;8 Performance analysis of the sliding mode– based analog differentiator and dynamical compensator;160
4.3.1;8.1 Transfer function "inversion” via sliding mode;160
4.3.2;8.2 Analysis of SM differentiator dynamics;161
4.3.3;8.3 Temperature sensor dynamics compensation via SM application;164
4.3.4;8.4 Analysis of the sliding mode compensator;167
4.3.5;8.5 An example of compensator design;169
4.3.6;8.6 Conclusions;172
4.4;9 Analysis of sliding mode observers;173
4.4.1;9.1 The SM observer as a relay servo system;173
4.4.2;9.2 SM observer performance analysis and characteristics;176
4.4.3;9.3 Example of SM observer performance analysis;178
4.4.4;9.4 Conclusions;181
4.5;10 Appendix;182
4.5.1;10.1 The LPRS derivation for a non-integrating linear part;182
4.5.2;10.2 Orbital stability of a system with a non-integrating linear part;186
4.5.3;10.3 The LPRS derivation for an integrating linear part;188
4.5.4;10.4 Orbital stability of a system with an integrating linear part;196
4.5.5;10.5 The LPRS derivation for a linear part with time delay;199
4.5.6;10.6 MATLAB code for LPRS computing;203
5;References;210
6;Index;216