How Far Should Poles Be Placed? Selecting Positive Feedback Controllers for Damping and Tracking Applications: A Complete Characterisation
Designers of Positive Feedback Controllers (PFCs) arbitrarily place poles into the left-hand half-plane of the complex plane without any detailed understanding of where to stop. This works aims to clearly demonstrate, via rigorous mathematical derivation, the conditions for which pole–placement beco...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Vibration |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2571-631X/5/4/38 |
| _version_ | 1797454984496807936 |
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| author | James MacLean Majid Aleyaasin Sumeet S. Aphale |
| author_facet | James MacLean Majid Aleyaasin Sumeet S. Aphale |
| author_sort | James MacLean |
| collection | DOAJ |
| description | Designers of Positive Feedback Controllers (PFCs) arbitrarily place poles into the left-hand half-plane of the complex plane without any detailed understanding of where to stop. This works aims to clearly demonstrate, via rigorous mathematical derivation, the conditions for which pole–placement becomes possible. It also highlights the design limits for the family of second–order PFCs—the most popular PFC group. To this end, the complete family of PFCs, namely, Positive Acceleration Velocity Position Feedback and its derivatives, are analysed in great depth with respect to pure damping and also with respect to combined damping and tracking applications. To showcase the practical value and validity of this work, experimental results on a piezoelectric nanopositioner are also presented and discussed. |
| first_indexed | 2024-03-09T15:45:01Z |
| format | Article |
| id | doaj.art-a6da49114d8241d0b813eeb805b3f1b5 |
| institution | Directory Open Access Journal |
| issn | 2571-631X |
| language | English |
| last_indexed | 2024-03-09T15:45:01Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Vibration |
| spelling | doaj.art-a6da49114d8241d0b813eeb805b3f1b52023-11-24T18:35:49ZengMDPI AGVibration2571-631X2022-09-015464165810.3390/vibration5040038How Far Should Poles Be Placed? Selecting Positive Feedback Controllers for Damping and Tracking Applications: A Complete CharacterisationJames MacLean0Majid Aleyaasin1Sumeet S. Aphale2School of Engineering, University of Aberdeen, Aberdeen AB24 3FX, UKSchool of Engineering, University of Aberdeen, Aberdeen AB24 3FX, UKSchool of Engineering, University of Aberdeen, Aberdeen AB24 3FX, UKDesigners of Positive Feedback Controllers (PFCs) arbitrarily place poles into the left-hand half-plane of the complex plane without any detailed understanding of where to stop. This works aims to clearly demonstrate, via rigorous mathematical derivation, the conditions for which pole–placement becomes possible. It also highlights the design limits for the family of second–order PFCs—the most popular PFC group. To this end, the complete family of PFCs, namely, Positive Acceleration Velocity Position Feedback and its derivatives, are analysed in great depth with respect to pure damping and also with respect to combined damping and tracking applications. To showcase the practical value and validity of this work, experimental results on a piezoelectric nanopositioner are also presented and discussed.https://www.mdpi.com/2571-631X/5/4/38positive–feedback–controlPAVPFPVPFPPFresonanceoptimisation |
| spellingShingle | James MacLean Majid Aleyaasin Sumeet S. Aphale How Far Should Poles Be Placed? Selecting Positive Feedback Controllers for Damping and Tracking Applications: A Complete Characterisation Vibration positive–feedback–control PAVPF PVPF PPF resonance optimisation |
| title | How Far Should Poles Be Placed? Selecting Positive Feedback Controllers for Damping and Tracking Applications: A Complete Characterisation |
| title_full | How Far Should Poles Be Placed? Selecting Positive Feedback Controllers for Damping and Tracking Applications: A Complete Characterisation |
| title_fullStr | How Far Should Poles Be Placed? Selecting Positive Feedback Controllers for Damping and Tracking Applications: A Complete Characterisation |
| title_full_unstemmed | How Far Should Poles Be Placed? Selecting Positive Feedback Controllers for Damping and Tracking Applications: A Complete Characterisation |
| title_short | How Far Should Poles Be Placed? Selecting Positive Feedback Controllers for Damping and Tracking Applications: A Complete Characterisation |
| title_sort | how far should poles be placed selecting positive feedback controllers for damping and tracking applications a complete characterisation |
| topic | positive–feedback–control PAVPF PVPF PPF resonance optimisation |
| url | https://www.mdpi.com/2571-631X/5/4/38 |
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