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Linear systems:

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1. Verfasser:	Bourlès, Henri (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	London [u.a.] ISTE [u.a.] 2010
Ausgabe:	1. publ.
Schriftenreihe:	Control systems, robotics and manufacturing series
Schlagworte:	Linear systems Lineares System Lineares Regelungssystem
Online-Zugang:	Publisher description Table of contents only Inhaltsverzeichnis Klappentext
Beschreibung:	XX, 572 S. Ill., graph. Darst. 24 cm
ISBN:	9781848211629

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Datensatz im Suchindex

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adam_text	Contents Preface ......................................... xiii Chapter L Physical Models .,....,.,,,,...,.,.,...,.,,, 1 1.1. Electric system ............,,....,.,,...,.,,,.. 1 1.1.1. Mesh rule ................................ 1 1.1.2. Nodal rule ................................ 2 1.2. Mechanical system .............................. 3 1.2.1. Fundamental principle of dynamics .........,....... 3 1.2.2. Lagrangian formalism ......................... 11 1.3. Electromechanical system .......................... 13 1.4. Thermal hydraulic system .......................... 14 1.4.1. Balance in volume ........................... 14 1.4.2. Exit rate: Torricelli s formula ..................... 15 1.4.3. Energy balance ............................. 15 1.5. Exercises ................................... 16 Chapter 2. Systems Theory (I) ........................... 19 2.1. Introductory example ............................ . 19 2.2. General representation and properties ................... 20 2.2.1. Variables ............,...,,,,............ 20 2.2.2. Equations ................................ 21 2.2.3. Time-invariant systems ........................ 21 2.2.4. Linear systems ...... . . , ,................... 21 2.2.5. Linear time-invariant systems ..................... 22 2.2.6. Equilibrium point ........................... 23 2.2.7. Linearization around an equilibrium point ............. 24 2.3. Control systems ................................ 25 2.3.1. Inputs .................................. 25 2.3.2. Outputs ................................. 27 2.3.3. Latent variables ............................. 28 vi Linear Systems 2.3.4. Classification of systems ....................... 30 2.3.5. Rosenbrock representation ...................... 31 2.3.6. State-space representation ....................... 33 2.3.7. Poles and order of a system ...................... 33 2.3.8. Free response arid behavior ...................... 33 2.4. Transfer matrix ................................ 36 2.4.1. Laplace transforms ........................... 36 2.4.2. Transfer matrix: definition ....................... 37 2.4.3. Examples ................................ 38 2.4.4. Transmission poles and zeros ..................... 39 2.4.5. ^MacMillan poles and zeros ..................... 41 2.4.6. Minimal systems ............................ 44 2.4.7. Transmission poles and zeros at infinity ............... 46 2.5. Responses of a control system ....................... 48 2.5.1. Input-output operator ......................... 48 2.5.2. Impulse and step responses ...................... 51 2.5.3. Proper, biproper and strictly proper systems ............. 51 2.5.4. Frequency response .......................... 55 2.6. Diagrams and their algebra ......................... 56 2.6.1. Diagram of a control system ..................... 56 2.6.2. General algebra of diagrams ..................... 57 2.6.3. Specificity of linear systems ...................... 60 2.7. Exercises ................................... 61 Chapter 3. Open-Loop Systems .......................... 63 3.1. Stability and static gain ........................... 63 3.1.1. Stability ................................. 63 3.1.2. Static gain ................................ 64 3.2. First-order systems .............................. 65 3.2.1. Transfer function ............................ 65 3.2.2. Time domain responses ........................ 65 3.2.3. Frequency response .......................... 67 3.2.4. Bode plot ................................ 67 3.2.5. Case of an unstable first-order system ................ 69 3.3. Second-order systems ............................ 70 3.3.1. Transfer function ............................ 70 3.3.2. Time domain responses ........................ 71 3.3.3. Bode plot ................................ 75 3.4. Systems of any order ............................. 78 3.4.1. Stability ................................. 78 3.4.2. Decomposition of the transfer function ............... 79 3.4.3. Asymptotic Bode plot ......................... 80 3.4.4. Amplitude/phase relation ....................... 82 3.5. Time-delay systems ............................. 85 Contents vii 3.5.1. Left form time-delay Systems..................... 85 3.5.2. Transfer function ............................ 86 3.5.3. Bode plot ................................ 86 3.5.4. Example: first-order time-delay system ............... 86 3.5.5. Approximations of a time-delay system ............... 87 3.6. Exercises ................................... 91 Chapter 4. Closed-Loop Systems ......................... 95 4.1. Closed-loop stability ............................. 95 4.1.1. Standard feedback system ....................... 95 4.1.2. Closed-loop equations ......................... 95 4.1.3. Stability of a closed-loop system ................... 97 4.1.4. Nyquist criterion ............................ 99 4.1.5. Small gain theorem ........................... 103 4.2. Robustness and performance ........................ 104 4.2.1. Generalities ............................... 104 4.2.2. Robustness margins .......................... 105 4.2.3. Use of the Nichols chart ........................ 110 4.2.4. Robustness against neglected dynamics ............... 11 J 4.2.5. Performance .............................. і 13 4.2.6. Sensitivity to measurement noise ................... 114 4.2.7. Loopshaping of L (s) ......................... 115 4.2.8. Degradation of robustness/performance trade-off .......... 116 4.2.9. * Extension to the MIMO case .................... 119 4.3. Exercises ................................... 127 Chapter 5. Compensation and PID Controller ................. 129 5.1. One degree of freedom controller ...................... 129 5.1.1. Closed-loop system .......................... 129 5.1.2. Closed-loop equations and static error ................ 129 5.2. Lead compensator .............................. 131 5.2.1. Characteristics of a lead compensator ................ 131 5.2.2. Principles of a lead compensator .................. . 132 5.2.3. PD controller .............................. 134 5.3. PI controller .....................,,.......,.,. 135 5.3.1. Principle .......,...,..,..,....,,....,.,.. 135 5.3.2, Example . . ,.............,...,.,,..,....,. 136 5.4. PID controller ................................. 138 5.4.1. Integral action and lead compensator . ................ 138 5.4.2. Classic form of a PID controller ................... 139 5.5. Exercises ................................... 142 Chapter 6. RST Controller ............................. 143 6.1. Structure and implementation of an RST controller ............ 143 viii Linear Systems 6.2. Closed loop.................................. 145 6.2.1. Closed-loop equations ......................... 145 6.2.2. Pole placement and stability ...................... 146 6.3. Usual case ................................... 146 6.3.1. Disturbance rejection ......................... 146 6.3.2. Absence of static error ......................... 147 6.3.3. Measurement noise filtering ...................... 147 6.3.4. Problem resolution ........................... 148 6.3.5. Choice of the poles ........................... 150 6.3.6. Examples ................................ 156 6.4. - General case ................................. 162 6.4.1. Disturbance rejection ......................... 162 6.4.2. Reference tracking ........................... 162 6.4.3. Internal modei principle ........................ 163 6.4.4. Filtering of measurement noise .................... 164 6.4.5. Problem resolution ........................... 164 6.4.6. Choice of poles ............................. 166 6.4.7. Examples ................................ 167 6.5. Exercises ................................... 171 Chapter 7. Systems Theory (II) .......................... 175 7.1. Structure of a linear system ......................... 176 7.1.1. The notion of a linear system .................... 176 7.1.2. State-space representation ....................... 176 7.1.3. Controllability ............................. 178 7.1.4. Observability .............................. 182 7.1.5. Canonical structure of a system .................... 186 7.2. Zeros of a system ............................... 189 7.2.1. Invariant zeros and transmission zeros ................ 189 7.2.2. Input-decoupling zeros ........................ 190 7.2.3. Output-decoupling zeros ........................ 191 7.2.4. Input-ouput decoupling zeros ..................... 192 7.2.5. Hidden modes ............................. 192 7.2.6. Relationships between poles and zeros . ............... 194 7.3. Stability, stabilizability and detectability .................. 195 7.4. Realization .................................. 197 7.4.1. Introduction ............................... 197 7.4.2. SISO systems .............................. 197 7.4.3. ♦MIMO systems ............................ 202 7.5. Flatness .................................... 209 7.5.1. Flatness of nonlinear sj stems .................... 210 7.5.2. Flatness of linear systems ..............,........ 210 7.6. Exercises ................................... 211 Contents ix Chapter 8. State Feedback............................. 217 8.1. Elementary state feedback.......................... 217 8.1.1. General principle ............................ 217 8.1.2. Pole placement by state feedback ................... 219 8.1.3. Choice of the pole placement in the SISO case ........... 223 8.1.4. Choice of the pole placement in the MIMO case ......... 224 8.2. State feedback with integral action ..................... 237 8.2.1. Insufficiency of state feedback .................... 237 8.2.2. Feedback control in the presence of disturbances .......... 237 8.2.3. Resolution of the static problem ................... 238 8.2.4. Resolution of the dynamic problem ................. 239 8.3. ^Internal model principle .......................... 243 8.3.1. Problem setting ............................. 243 8.3.2. Solution ................................. 245 8.4. Exercises ................................... 248 Chapter 9. Observers ................................ 251 9.1. Full-order observers ...............,,,.,........, 251 9.1.1. General principle ............................ 251 9.1.2. State feedback/observer synthesis .................. 253 9.1.3. State feedback/observer synthesis and RST controller ....... 255 9.1.4. LTR method ............................... 257 9.2. State feedback/observer synthesis with integral action .......... 264 9.2.1. Problem setting ............................. 264 9.2.2. Algebraic solution ........................... 265 9.2.3. Extension of the LTR method ..................... 267 9.3. General theory of observers ........................ 275 9.3.1. Reduced-order observer ........................ 275 9.3.2. General formalism ........................... 277 9.4. Exercises ................................... 279 Chapter 10. Discrete-Time Control .......... ............ 281 10.1. Introduction ................................. 281 10.2. Discrete-time signals ............................ 281 10.2.1. Discretization of a signal ....................... 281 10.2.2. z-transform .............................. 282 10.2.3. Sampled signal ............................ 282 10.2.4. Poisson summation formula ..................... 283 10.2.5. Sampling theorem .......................... 284 10.2.6. Hold .................................. 288 10.3. Discrete-time systems ..............,....,,...,.. 289 10.3.1. General description .......................... 289 10.3.2. Sampled system ............................ 290 10.3.3. Discretized system .......................... 291 χ Linear Systems 10.3.4. State-space representation of a discrete-time system ....... 293 10.3.5. Calculation of the state of a discretized system .......... 295 10.4. Structural properties of di s crete- time systems .............. 296 10.4.1. Poles and zeros ............................ 296 10.4.2. Controllability ............................. 297 10.4.3. Observability ............................. 301 10.4.4. Rosenbrock representation ...................... 304 10.4.5. Stability ................................ 304 10.5. Pseudocontinuous systems ......................... 306 10.5.1. Bilinear transform .......................... 306 10.5.2. Pseudocontinuous representations .................. 308 10.5.3. * Intrinsic definition of a pseudocontinuous system ........ 310 10.5.4. Structural properties of pseudocontinuous systems ........ 313 10.6. Synthesis of discrete-time control ..................... 313 10.6.1. Direct approaches ........................... 313 10.6.2. Discretization by approximation ................., 313 10.6.3. Passage through a pseudocontinuous system ............ 314 10.7. Exercises ................................... 319 Chapter 11. Identification ............................. 321 11.1. Random signals ............................... 321 11.1.1. Moments of order 1 and 2...................... 322 11.1.2. Correlation and cross-correlation .................. 322 11.1.3. Pseudo-random signals ........................ 325 11.1.4. Filtering and factorization ...................... 326 11.1.5. Ergodic random signals ....................... 329 11.2. Open-loop identification .......................... 331 11.2.1. Notation ................................ 331 11.2.2. Least squares method ......................... 331 11.2.3. Models and prediction ........................ 340 11.2.4. Output Error method and ARM AX method ............ 342 11.2.5. Consistency of the estimator and residues ............. 344 11.2.6. Filtering of data ............................ 347 11.3. Closed-loop identification ......................... 356 11.3.1. Direct and indirect approach ..................... 356 11.3.2. Consistency of estimator in the direct approach .......... 360 11.3.3. A third path .............................. 363 11.4. Exercises ................................... 365 Chapter 12. Appendix І : Analysis ........................ 369 12,1. Topology ................................... 369 12.1.1. Topological spaces .......................... 369 12.1.2. Topological vector spaces ...................... 371 12.1.3. Continuous linear operators ..................... 374 Contents xi 12.2. Sequences, functions and distributions .................. 375 12.2.1. Sequences ............................... 375 12.2.2. Functions ............................... 377 12.2.3. Distributions .............................. 380 12.3. Fourier, Laplace and z transforms ..................... 387 12.3.1. Fourier transforms of distributions ................. 387 12.3.2. Fourier series ............................. 389 12.3.3. Fourier transforms of sequences ................... 393 12.3.4. Laplace transform ........................... 394 12.3.5. ^-transform .............................. 401 12.4. Functions of one complex variable .................... 404 12.4.1. Holomorphic functions ........................ 404 12.4.2. Functions of a matrix ......................... 406 12.4.3. Integration in the complex plane ........., ,....... 408 12.4.4. Applications to inverse transforms ................. 412 12.4.5. Argument principle .......................... 416 12.5. Differential equations ............................ 417 12.5.1. Generalities .............................. 417 12.5.2. Linear differential equations: constant coefficients .,.,,... 421 12.6. Functions of several variables; optimization ............... 428 12.6.1. Functions of class C1 ......................... 428 12.6.2. Functions of class C2 ......................... 429 12.6.3. Taylor s formula ........................... 429 12.6 A. Convexity, coercivity, ellipticity ................... 430 12.6.5. Optimization algorithms ....................... 432 12.7. Probabilistic notions ............................ 438 12.7.1. Probability space ........................... 438 12.7.2. Random variable ........................... 439 12.7.3. Conditional expectation ....................... 443 Chapter 13. Appendix 2: Algebra ......................... 447 13.1. Commutative rings and fields ....................... 447 13.1.1. Generalities ..........................., , . 447 13.1.2. Divisibility ............................... 450 13.1.3. Principal ideal domains ....................... 453 13.1.4. Matrices over commutative rings .................. 455 13.1.5. Bézout equation ............................ 460 13.2. Matrices over principal ideal domains ..,..,....,.,..... 463 13.2.1. Invertible matrices over principal ideal domains , ...,,..,. 463 13.2.2. Hermite form ............................. 463 13.2.3. Smith form .............................. 464 13.2.4. Elementary divisors .......................... 468 13.2.5. Smith zeros .............................. 469 13.2.6. Divisibility of matrices ........................ 470 xii Linear Systems 13.2.7. Coprirne factorizations........................ 471 13.2.8. Bézout matrix equations ....................... 472 13.3. Homomorphisms of vector spaces ..................... 473 13.3.1. Vector spaces ............................. 473 13.3.2. Homomorphisms and matrices ................... 475 13.3.3. Endomorphisms of vector spaces .................. 479 13.3.4. * Jordan form ............................. 485 13.4. * The language of modules ......................... 491 13.4.1. General notions ............................ 491 13.4.2. Modules over principal ideal domains ............... 496 13.4.3. Structure of endomorphisms ..................... 501 13.5. Orthogonality and symmetry ........................ 504 13.5.1. Orthonormal basis .....,.................... 505 13.5.2. Orthogonality ............................. 505 13.5.3. Adjoint endomorphism ........................ 506 13.5.4. Unitary endomorphism ........................ 507 13.5.5. Normal endomorphism ........................ 507 13.5.6. Self-adjoint endomorphism ...................., 508 13.5.7. Singular values ............................ 510 13.6. Fractions and special rings ......................... 515 13.6.1. Rational functions .......................... 515 13.6.2. Algebra ЗШос ............................. 516 13.6.3. * Algebra П^ ............................. 518 13.6.4. ^Classification of rings ........................ 519 13.6.5. * Change of rings ........................... 519 Chapter 14. Solutions of Exercises ........................ 521 14.1. Exercises of Chapter 1........................... 521 14.2. Exercises of Chapter 2........................... 522 14.3. Exercises of Chapter 3........................... 524 14.4. Exercises of Chapter 4........................... 526 14.5. Exercises of Chapter 5........................... 528 14.6. Exercises of Chapter 6........................... 529 14.7. Exercises of Chapter 7......,.................... 531 14.8. Exercises of Chapter 8........................... 537 14.9. Exercises of Chapter 9..................,..,.,... 540 14.10. Exercises of Chapter 10.......................... 543 14.11. Exercises of Chapter 11.............,....,.,....,, 549 Bibliography ..................................... jíi3 Index .......................................... 56) Linear systems comprise all the necessary elements (modeling, identification, analysis and control), from an analytical and academic point of view, to provide an understanding of the discipline of automation and to apply it efficiently. This book - which addresses the field in a comprehensive manner - is structured in a way that is both progressive and organized so that different levels of readership are possible. It is suitable for both students or professionals new to the subject and for those with a good understanding of automation technologies who wish to enhance their knowledge on the subject. The theory content is rigorously developed and illustrated by numerous examples that can be reproduced with the help of appropriate computation software, and 60 exercises and their solutions are included to enable readers to test and enhance their knowledge.
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id	DE-604.BV042323934
illustrated	Illustrated
indexdate	2024-07-10T01:18:26Z
institution	BVB
isbn	9781848211629
language	English
lccn	010016973
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-027760806
oclc_num	731239616
open_access_boolean
owner	DE-739
owner_facet	DE-739
physical	XX, 572 S. Ill., graph. Darst. 24 cm
publishDate	2010
publishDateSearch	2010
publishDateSort	2010
publisher	ISTE [u.a.]
record_format	marc
series2	Control systems, robotics and manufacturing series
spelling	Bourlès, Henri Verfasser aut Systèmes linéaires <english> Linear systems Henri Bourles 1. publ. London [u.a.] ISTE [u.a.] 2010 XX, 572 S. Ill., graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Control systems, robotics and manufacturing series Linear systems Lineares System (DE-588)4125617-7 gnd rswk-swf Lineares Regelungssystem (DE-588)4167730-4 gnd rswk-swf Lineares System (DE-588)4125617-7 s DE-604 Lineares Regelungssystem (DE-588)4167730-4 s http://www.loc.gov/catdir/enhancements/fy1009/2010016973-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy1402/2010016973-t.html Table of contents only Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027760806&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027760806&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext
spellingShingle	Bourlès, Henri Linear systems Linear systems Lineares System (DE-588)4125617-7 gnd Lineares Regelungssystem (DE-588)4167730-4 gnd
subject_GND	(DE-588)4125617-7 (DE-588)4167730-4
title	Linear systems
title_alt	Systèmes linéaires <english>
title_auth	Linear systems
title_exact_search	Linear systems
title_full	Linear systems Henri Bourles
title_fullStr	Linear systems Henri Bourles
title_full_unstemmed	Linear systems Henri Bourles
title_short	Linear systems
title_sort	linear systems
topic	Linear systems Lineares System (DE-588)4125617-7 gnd Lineares Regelungssystem (DE-588)4167730-4 gnd
topic_facet	Linear systems Lineares System Lineares Regelungssystem
url	http://www.loc.gov/catdir/enhancements/fy1009/2010016973-d.html http://www.loc.gov/catdir/enhancements/fy1402/2010016973-t.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027760806&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027760806&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT bourleshenri systemeslineairesenglish AT bourleshenri linearsystems

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