Discontinuous Control Systems : Frequency-Domain Analysis and Design

Discontinuous control systems are one of the most important and oldest types of nonlinear systems; however, the available methods of analysis of their input-output properties are based on the approximate describing function method, which narrows the application of existing techniques to systems having good low-pass filtering properties. 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 (LPRS). LPRS theory is presented in detail beginning with basic concepts and progressing to computing formulas, algorithms, and MATLAB^®^ code. As a result of LPRS properties such as exactness, simplicity, and convenience, many problems of analysis and design of discontinuous systems are solved easily by using the theory described. 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. A few chapters of the book are devoted to frequency-domain theory of sliding mode control, which is presented as a special type of discontinuous control. LPRS analysis of the effects of chattering and nonideal closed-loop performance in sliding mode systems having parasitic dynamics, as well as the relationship of those effects with the ideal sliding mode, are given. **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. 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. "Discontinuous control systems are one of the most important and oldest types of nonlinear systems; however, the available methods of analysis of their input-output properties are based on the approximate describing function method, which narrows the application of existing techniques to systems having good low-pass filtering properties. 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 (LPRS)." "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."--Jacket 9780817647520 081764752X 1 front-matter 2 01. The servo problem in discontinuous control systems 13 02. The locus of a perturbed relay system (LPRS) theory 28 03. Input-output analysis of relay servo systems 65 04. Analysis of sliding modes in the frequency domain 74 05. Performance analysis of second-order SM control algorithms 110 06. Relay pneumatic servomechanism design 130 07. Relay feedback test identification and autotuning 144 08. Performance analysis of the sliding modeùbased analog differentiator and dynamical compensator 158 09. Analysis of sliding mode observers 171 back-matter 180 #,Publisher:,Birkhäuser,Boston,#,Number,Of,Pages:,234,#,Publication,Date:,2008-11-25,#,ISBN-10,/,ASIN:,081764752X #,Publisher:,Birkhäuser Boston,# Number Of Pages:,234,# Publication Date:,2008-11-25,# ISBN-10 / ASIN:,081764752X Front Matter....Pages i-xiv The servo problem in discontinuous control systems....Pages 3-17 The locus of a perturbed relay system (LPRS) theory....Pages 19-55 Input-output analysis of relay servo systems....Pages 57-65 Analysis of sliding modes in the frequency domain....Pages 67-102 Performance analysis of second-order SM control algorithms....Pages 103-122 Relay pneumatic servomechanism design....Pages 125-138 Relay feedback test identification and autotuning....Pages 139-152 Performance analysis of the sliding mode—based analog differentiator and dynamical compensator....Pages 153-165 Analysis of sliding mode observers....Pages 167-175 Back Matter....Pages 177-212