Distributed-order dynamic systems: stability, simulation, applications and perspectives
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Springer
2012
|
| Series: | SpringerBriefs in electrical and computer engineering
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 90 S. Ill., graph. Darst. |
| ISBN: | 9781447128526 9781447128519 |
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MARC
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| 245 | 1 | 0 | |a Distributed-order dynamic systems |b stability, simulation, applications and perspectives |c Zhuang Jiao ; YangQuan Chen ; Igor Podlubny |
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| 300 | |a XIII, 90 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804149037774929920 |
|---|---|
| adam_text | Contents
1
Introduction
........................................
I
I
.
I From Integer-Order Dynamic Systems to Fractional-Order
Dynamic Systems
................................. 1
1.2
From Fractional-Order Dynamic Systems to Distributed-Order
Dynamic Systems
................................. 5
1.3
Preview of Chapters
............................... 7
1.4
Chapter Summary
................................ 8
References
.......................................... 8
2
Distributed-Order Linear Time-Invariant System (DOLTIS)
and Its Stability Analysis
............................... 11
2.1
Introduction
.....................................
II
2.2
Stability Analysis of DOLTIS in Four Cases
..............
II
2.3
Time-Domain Analysis: Impulse Responses
.............. 19
2.4
Frequency-Domain Response: Bode Plots
................ 20
2.5
Numerical Examples
.............................. 21
2.6
Chapter Summary
................................ 25
References
.......................................... 28
3
Noncommensurate Constant Orders as Special
Cases of DOLTIS
..................................... 29
3.1
Introduction
..................................... 29
3.2
Stability Analysis of Some Special Cases of DOLTIS
....... 30
3.2.1
Case
1:
Double Noncommensurate Orders
.......... 30
3.2.2
Case
2:
N-Term Noncommensurate Orders
.......... 33
3.3
Numerical Examples
.............................. 34
3.4
Chapter Summary
................................ 36
References
.......................................... 36
x¡¡
Contents
4
Distributed-Order
Filtering
and Distributed-Order
Optimal Damping
.................................... 39
4.1
Application I: Distributed-Order Filtering
............... 39
4.1.1
Distributed-Order Integrator/Differentiator
.......... 39
4.1.2
Distributed-Order Low-Pass Filter
................ 45
4.1.3
Impulse Response Invariant Discretization
of DO-LPF
................................ 47
4.2
Application II: Optimal Distributed-Order Damping
......... 49
4.2.1
Distributed-Order Damping in Mass-Spring Viscoelastic
Damper System
............................. 50
4.2.2
Frequency-Domain Method Based Optimal
Fractional-Order Damping Systems
............... 52
4.3
Chapter Summary
................................ 55
References
.......................................... 56
5
Numerical Solution of Differential Equations
of Distributed Order
.................................. 59
5.1
Introduction
..................................... 59
5.2
Triangular Strip Matrices
........................... 59
5.3 Kronecker
Matrix Product
........................... 61
5.4
Discretization of Ordinary Fractional Derivatives
of Constant Order
................................ 62
5.5
Discretization of Ordinary Derivatives of Distributed Order
... 64
5.6
Discretization of Partial Derivatives of Distributed Order
..... 64
5.7
Initial and Boundary Conditions for Using
the Matrix Approach
.............................. 67
5.8
Implementation in
MATLAB
........................ 67
5.9
Numerical Examples
.............................. 68
5.9.1
Example
1:
Distributed-Order Relaxation
........... 69
5.9.2
Example
2:
Distributed-Order Oscillator
............ 70
5.9.3
Example
3:
Distributed-Order Diffusion
............ 71
5.10
Chapter Summary
................................ 72
References
.......................................... 73
6
Future Topics
....................................... 75
6.1
Geometric Interpretation of Distributed-Order Differentiation
as a Framework for Modeling
........................ 75
6.2
From Positive Linear Time-Invariant Systems
to Generalized Distributed-Order Systems
................ 76
6.3
From
PID
Controllers to Distributed-Order
PID
Controllers
... 78
References
.......................................... 79
Appendix:
MATLAB
Codes
................................
81
Index
................ ......... 89
|
| any_adam_object | 1 |
| author | Jiao, Zhuang Chen, Yangquan 1966- Podlubny, Igor |
| author_GND | (DE-588)121213277 |
| author_facet | Jiao, Zhuang Chen, Yangquan 1966- Podlubny, Igor |
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| id | DE-604.BV040037973 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:16:40Z |
| institution | BVB |
| isbn | 9781447128526 9781447128519 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024894703 |
| oclc_num | 796198096 |
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| owner | DE-703 |
| owner_facet | DE-703 |
| physical | XIII, 90 S. Ill., graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Springer |
| record_format | marc |
| series2 | SpringerBriefs in electrical and computer engineering |
| spelling | Jiao, Zhuang Verfasser aut Distributed-order dynamic systems stability, simulation, applications and perspectives Zhuang Jiao ; YangQuan Chen ; Igor Podlubny London [u.a.] Springer 2012 XIII, 90 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier SpringerBriefs in electrical and computer engineering Dynamisches System (DE-588)4013396-5 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s DE-604 Chen, Yangquan 1966- Verfasser (DE-588)121213277 aut Podlubny, Igor Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024894703&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jiao, Zhuang Chen, Yangquan 1966- Podlubny, Igor Distributed-order dynamic systems stability, simulation, applications and perspectives Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4013396-5 |
| title | Distributed-order dynamic systems stability, simulation, applications and perspectives |
| title_auth | Distributed-order dynamic systems stability, simulation, applications and perspectives |
| title_exact_search | Distributed-order dynamic systems stability, simulation, applications and perspectives |
| title_full | Distributed-order dynamic systems stability, simulation, applications and perspectives Zhuang Jiao ; YangQuan Chen ; Igor Podlubny |
| title_fullStr | Distributed-order dynamic systems stability, simulation, applications and perspectives Zhuang Jiao ; YangQuan Chen ; Igor Podlubny |
| title_full_unstemmed | Distributed-order dynamic systems stability, simulation, applications and perspectives Zhuang Jiao ; YangQuan Chen ; Igor Podlubny |
| title_short | Distributed-order dynamic systems |
| title_sort | distributed order dynamic systems stability simulation applications and perspectives |
| title_sub | stability, simulation, applications and perspectives |
| topic | Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024894703&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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