Adaptive PI Control Using Recursive Least Squares for Centrifugal Pump Pipeline Systems Article Swipe
David A. Brattley
,
Wayne W. Weaver
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.3390/machines13111064
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.3390/machines13111064
Pipeline transportation of petroleum products remains one of the safest and most efficient methods of bulk energy delivery, yet overpressure events continue to pose serious operational and regulatory challenges. Traditional fixed-gain PI controllers, commonly used with centrifugal pump drives, cannot adapt to varying product densities or transient disturbances such as valve closures that generate water hammer. This paper proposes a self-tuning adaptive controller based on Recursive Least Squares (RLS) parameter estimation to improve safety and efficiency in pipeline pump operations. A nonlinear simulation model of a centrifugal pump driven by an induction motor is developed, incorporating pipeline friction losses via the Darcy–Weisbach relation and pressure transients induced by rapid valve closures. The RLS algorithm continuously estimates effective loop dynamics, enabling online adjustment of proportional and integral gains under changing fluid and operating conditions. Simulation results demonstrate that the proposed RLS-based adaptive controller maintains discharge pressure within ±2% of the target setpoint under density variations from 710 to 900 kg/m3 and during severe transient events. Compared to a fixed-gain PI controller, the adaptive strategy reduced pressure overshoot by approximately 31.9% and settling time by 6%. Model validation using SCADA field data yielded an R2 = 0.957, RMSE = 3.95 m3/h, and normalized NRMSE of 12.6% (by range), confirming strong agreement with measured system behavior. The findings indicate that RLS-based self-tuning provides a practical enhancement to existing pipeline control architectures, offering both improved robustness to abnormal transients and greater efficiency during steady-state operation. This work establishes a foundation for higher-level supervisory and game-theoretic coordination strategies to be explored in subsequent studies.
Related Topics
Concepts
No concepts available.
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3390/machines13111064
- https://www.mdpi.com/2075-1702/13/11/1064/pdf?version=1763469232
- OA Status
- gold
- References
- 27
- OpenAlex ID
- https://openalex.org/W4416322405
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4416322405Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.3390/machines13111064Digital Object Identifier
- Title
-
Adaptive PI Control Using Recursive Least Squares for Centrifugal Pump Pipeline SystemsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2025Year of publication
- Publication date
-
2025-11-18Full publication date if available
- Authors
-
David A. Brattley, Wayne W. WeaverList of authors in order
- Landing page
-
https://doi.org/10.3390/machines13111064Publisher landing page
- PDF URL
-
https://www.mdpi.com/2075-1702/13/11/1064/pdf?version=1763469232Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
- OA URL
-
https://www.mdpi.com/2075-1702/13/11/1064/pdf?version=1763469232Direct OA link when available
- Cited by
-
0Total citation count in OpenAlex
- References (count)
-
27Number of works referenced by this work
Full payload
| id | https://openalex.org/W4416322405 |
|---|---|
| doi | https://doi.org/10.3390/machines13111064 |
| ids.doi | https://doi.org/10.3390/machines13111064 |
| ids.openalex | https://openalex.org/W4416322405 |
| fwci | |
| type | article |
| title | Adaptive PI Control Using Recursive Least Squares for Centrifugal Pump Pipeline Systems |
| biblio.issue | 11 |
| biblio.volume | 13 |
| biblio.last_page | 1064 |
| biblio.first_page | 1064 |
| is_xpac | False |
| apc_list.value | 1800 |
| apc_list.currency | CHF |
| apc_list.value_usd | 1949 |
| apc_paid.value | 1800 |
| apc_paid.currency | CHF |
| apc_paid.value_usd | 1949 |
| language | en |
| locations[0].id | doi:10.3390/machines13111064 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S4210219839 |
| locations[0].source.issn | 2075-1702 |
| locations[0].source.type | journal |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | 2075-1702 |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | True |
| locations[0].source.display_name | Machines |
| locations[0].source.host_organization | https://openalex.org/P4310310987 |
| locations[0].source.host_organization_name | Multidisciplinary Digital Publishing Institute |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310310987 |
| locations[0].source.host_organization_lineage_names | Multidisciplinary Digital Publishing Institute |
| locations[0].license | cc-by |
| locations[0].pdf_url | https://www.mdpi.com/2075-1702/13/11/1064/pdf?version=1763469232 |
| locations[0].version | publishedVersion |
| locations[0].raw_type | journal-article |
| locations[0].license_id | https://openalex.org/licenses/cc-by |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | Machines |
| locations[0].landing_page_url | https://doi.org/10.3390/machines13111064 |
| locations[1].id | pmh:oai:doaj.org/article:030812602a4f4eb29e4b500012e42205 |
| locations[1].is_oa | False |
| locations[1].source.id | https://openalex.org/S4306401280 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | False |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | DOAJ (DOAJ: Directory of Open Access Journals) |
| locations[1].source.host_organization | |
| locations[1].source.host_organization_name | |
| locations[1].license | |
| locations[1].pdf_url | |
| locations[1].version | submittedVersion |
| locations[1].raw_type | article |
| locations[1].license_id | |
| locations[1].is_accepted | False |
| locations[1].is_published | False |
| locations[1].raw_source_name | Machines, Vol 13, Iss 11, p 1064 (2025) |
| locations[1].landing_page_url | https://doaj.org/article/030812602a4f4eb29e4b500012e42205 |
| indexed_in | crossref, doaj |
| authorships[0].author.id | https://openalex.org/A5120455778 |
| authorships[0].author.orcid | https://orcid.org/0009-0005-6743-510X |
| authorships[0].author.display_name | David A. Brattley |
| authorships[0].countries | US |
| authorships[0].affiliations[0].institution_ids | https://openalex.org/I11957088 |
| authorships[0].affiliations[0].raw_affiliation_string | Department of Mechanical and Aerospace Engineering, Michigan Technological University, Houghton, MI 49931, USA |
| authorships[0].institutions[0].id | https://openalex.org/I11957088 |
| authorships[0].institutions[0].ror | https://ror.org/0036rpn28 |
| authorships[0].institutions[0].type | education |
| authorships[0].institutions[0].lineage | https://openalex.org/I11957088 |
| authorships[0].institutions[0].country_code | US |
| authorships[0].institutions[0].display_name | Michigan Technological University |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | David A. Brattley |
| authorships[0].is_corresponding | True |
| authorships[0].raw_affiliation_strings | Department of Mechanical and Aerospace Engineering, Michigan Technological University, Houghton, MI 49931, USA |
| authorships[1].author.id | https://openalex.org/A5025373438 |
| authorships[1].author.orcid | https://orcid.org/0000-0002-3612-799X |
| authorships[1].author.display_name | Wayne W. Weaver |
| authorships[1].countries | US |
| authorships[1].affiliations[0].institution_ids | https://openalex.org/I11957088 |
| authorships[1].affiliations[0].raw_affiliation_string | Department of Mechanical and Aerospace Engineering, Michigan Technological University, Houghton, MI 49931, USA |
| authorships[1].institutions[0].id | https://openalex.org/I11957088 |
| authorships[1].institutions[0].ror | https://ror.org/0036rpn28 |
| authorships[1].institutions[0].type | education |
| authorships[1].institutions[0].lineage | https://openalex.org/I11957088 |
| authorships[1].institutions[0].country_code | US |
| authorships[1].institutions[0].display_name | Michigan Technological University |
| authorships[1].author_position | last |
| authorships[1].raw_author_name | Wayne W. Weaver |
| authorships[1].is_corresponding | False |
| authorships[1].raw_affiliation_strings | Department of Mechanical and Aerospace Engineering, Michigan Technological University, Houghton, MI 49931, USA |
| has_content.pdf | True |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://www.mdpi.com/2075-1702/13/11/1064/pdf?version=1763469232 |
| open_access.oa_status | gold |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-11-18T00:00:00 |
| display_name | Adaptive PI Control Using Recursive Least Squares for Centrifugal Pump Pipeline Systems |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-28T23:14:17.795251 |
| primary_topic | |
| cited_by_count | 0 |
| locations_count | 2 |
| best_oa_location.id | doi:10.3390/machines13111064 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4210219839 |
| best_oa_location.source.issn | 2075-1702 |
| best_oa_location.source.type | journal |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | 2075-1702 |
| best_oa_location.source.is_core | True |
| best_oa_location.source.is_in_doaj | True |
| best_oa_location.source.display_name | Machines |
| best_oa_location.source.host_organization | https://openalex.org/P4310310987 |
| best_oa_location.source.host_organization_name | Multidisciplinary Digital Publishing Institute |
| best_oa_location.source.host_organization_lineage | https://openalex.org/P4310310987 |
| best_oa_location.source.host_organization_lineage_names | Multidisciplinary Digital Publishing Institute |
| best_oa_location.license | cc-by |
| best_oa_location.pdf_url | https://www.mdpi.com/2075-1702/13/11/1064/pdf?version=1763469232 |
| best_oa_location.version | publishedVersion |
| best_oa_location.raw_type | journal-article |
| best_oa_location.license_id | https://openalex.org/licenses/cc-by |
| best_oa_location.is_accepted | True |
| best_oa_location.is_published | True |
| best_oa_location.raw_source_name | Machines |
| best_oa_location.landing_page_url | https://doi.org/10.3390/machines13111064 |
| primary_location.id | doi:10.3390/machines13111064 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4210219839 |
| primary_location.source.issn | 2075-1702 |
| primary_location.source.type | journal |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | 2075-1702 |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | True |
| primary_location.source.display_name | Machines |
| primary_location.source.host_organization | https://openalex.org/P4310310987 |
| primary_location.source.host_organization_name | Multidisciplinary Digital Publishing Institute |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310310987 |
| primary_location.source.host_organization_lineage_names | Multidisciplinary Digital Publishing Institute |
| primary_location.license | cc-by |
| primary_location.pdf_url | https://www.mdpi.com/2075-1702/13/11/1064/pdf?version=1763469232 |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | https://openalex.org/licenses/cc-by |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | Machines |
| primary_location.landing_page_url | https://doi.org/10.3390/machines13111064 |
| publication_date | 2025-11-18 |
| publication_year | 2025 |
| referenced_works | https://openalex.org/W2014016750, https://openalex.org/W2155329774, https://openalex.org/W4412476984, https://openalex.org/W2963210314, https://openalex.org/W4382811888, https://openalex.org/W4413170101, https://openalex.org/W4387774762, https://openalex.org/W4254969936, https://openalex.org/W2106110872, https://openalex.org/W4402129736, https://openalex.org/W4399786075, https://openalex.org/W4321378057, https://openalex.org/W4396560541, https://openalex.org/W4394819331, https://openalex.org/W4412397352, https://openalex.org/W4395680485, https://openalex.org/W4413165816, https://openalex.org/W4297339063, https://openalex.org/W4213031934, https://openalex.org/W4402238841, https://openalex.org/W4399896677, https://openalex.org/W4288032558, https://openalex.org/W3196363223, https://openalex.org/W3186679965, https://openalex.org/W3146551586, https://openalex.org/W2144292232, https://openalex.org/W3005207360 |
| referenced_works_count | 27 |
| abstract_inverted_index.= | 193, 196 |
| abstract_inverted_index.A | 80 |
| abstract_inverted_index.a | 59, 85, 166, 220, 244 |
| abstract_inverted_index.PI | 31, 168 |
| abstract_inverted_index.R2 | 192 |
| abstract_inverted_index.an | 90, 191 |
| abstract_inverted_index.as | 49 |
| abstract_inverted_index.be | 254 |
| abstract_inverted_index.by | 89, 107, 176, 182 |
| abstract_inverted_index.in | 76, 256 |
| abstract_inverted_index.is | 93 |
| abstract_inverted_index.of | 2, 7, 14, 84, 122, 147, 202 |
| abstract_inverted_index.on | 64 |
| abstract_inverted_index.or | 45 |
| abstract_inverted_index.to | 22, 41, 71, 156, 165, 223, 232, 253 |
| abstract_inverted_index.(by | 204 |
| abstract_inverted_index.6%. | 183 |
| abstract_inverted_index.710 | 155 |
| abstract_inverted_index.900 | 157 |
| abstract_inverted_index.RLS | 112 |
| abstract_inverted_index.The | 111, 213 |
| abstract_inverted_index.and | 10, 26, 74, 103, 124, 130, 159, 179, 199, 235, 249 |
| abstract_inverted_index.for | 246 |
| abstract_inverted_index.one | 6 |
| abstract_inverted_index.the | 8, 100, 137, 148, 170 |
| abstract_inverted_index.via | 99 |
| abstract_inverted_index.yet | 18 |
| abstract_inverted_index.3.95 | 197 |
| abstract_inverted_index.RMSE | 195 |
| abstract_inverted_index.This | 56, 241 |
| abstract_inverted_index.both | 229 |
| abstract_inverted_index.bulk | 15 |
| abstract_inverted_index.data | 189 |
| abstract_inverted_index.from | 154 |
| abstract_inverted_index.loop | 117 |
| abstract_inverted_index.most | 11 |
| abstract_inverted_index.pose | 23 |
| abstract_inverted_index.pump | 37, 78, 87 |
| abstract_inverted_index.such | 48 |
| abstract_inverted_index.that | 52, 136, 216 |
| abstract_inverted_index.time | 181 |
| abstract_inverted_index.used | 34 |
| abstract_inverted_index.with | 35, 209 |
| abstract_inverted_index.work | 242 |
| abstract_inverted_index.±2% | 146 |
| abstract_inverted_index.(RLS) | 68 |
| abstract_inverted_index.12.6% | 203 |
| abstract_inverted_index.31.9% | 178 |
| abstract_inverted_index.Least | 66 |
| abstract_inverted_index.Model | 184 |
| abstract_inverted_index.NRMSE | 201 |
| abstract_inverted_index.SCADA | 187 |
| abstract_inverted_index.adapt | 40 |
| abstract_inverted_index.based | 63 |
| abstract_inverted_index.field | 188 |
| abstract_inverted_index.fluid | 129 |
| abstract_inverted_index.gains | 126 |
| abstract_inverted_index.kg/m3 | 158 |
| abstract_inverted_index.m3/h, | 198 |
| abstract_inverted_index.model | 83 |
| abstract_inverted_index.motor | 92 |
| abstract_inverted_index.paper | 57 |
| abstract_inverted_index.rapid | 108 |
| abstract_inverted_index.under | 127, 151 |
| abstract_inverted_index.using | 186 |
| abstract_inverted_index.valve | 50, 109 |
| abstract_inverted_index.water | 54 |
| abstract_inverted_index.0.957, | 194 |
| abstract_inverted_index.cannot | 39 |
| abstract_inverted_index.driven | 88 |
| abstract_inverted_index.during | 160, 238 |
| abstract_inverted_index.energy | 16 |
| abstract_inverted_index.events | 20 |
| abstract_inverted_index.losses | 98 |
| abstract_inverted_index.online | 120 |
| abstract_inverted_index.safest | 9 |
| abstract_inverted_index.safety | 73 |
| abstract_inverted_index.severe | 161 |
| abstract_inverted_index.strong | 207 |
| abstract_inverted_index.system | 211 |
| abstract_inverted_index.target | 149 |
| abstract_inverted_index.within | 145 |
| abstract_inverted_index.Squares | 67 |
| abstract_inverted_index.control | 226 |
| abstract_inverted_index.density | 152 |
| abstract_inverted_index.drives, | 38 |
| abstract_inverted_index.events. | 163 |
| abstract_inverted_index.greater | 236 |
| abstract_inverted_index.hammer. | 55 |
| abstract_inverted_index.improve | 72 |
| abstract_inverted_index.induced | 106 |
| abstract_inverted_index.methods | 13 |
| abstract_inverted_index.product | 43 |
| abstract_inverted_index.range), | 205 |
| abstract_inverted_index.reduced | 173 |
| abstract_inverted_index.remains | 5 |
| abstract_inverted_index.results | 134 |
| abstract_inverted_index.serious | 24 |
| abstract_inverted_index.varying | 42 |
| abstract_inverted_index.yielded | 190 |
| abstract_inverted_index.Compared | 164 |
| abstract_inverted_index.Pipeline | 0 |
| abstract_inverted_index.abnormal | 233 |
| abstract_inverted_index.adaptive | 61, 140, 171 |
| abstract_inverted_index.changing | 128 |
| abstract_inverted_index.closures | 51 |
| abstract_inverted_index.commonly | 33 |
| abstract_inverted_index.continue | 21 |
| abstract_inverted_index.enabling | 119 |
| abstract_inverted_index.existing | 224 |
| abstract_inverted_index.explored | 255 |
| abstract_inverted_index.findings | 214 |
| abstract_inverted_index.friction | 97 |
| abstract_inverted_index.generate | 53 |
| abstract_inverted_index.improved | 230 |
| abstract_inverted_index.indicate | 215 |
| abstract_inverted_index.integral | 125 |
| abstract_inverted_index.measured | 210 |
| abstract_inverted_index.offering | 228 |
| abstract_inverted_index.pipeline | 77, 96, 225 |
| abstract_inverted_index.pressure | 104, 144, 174 |
| abstract_inverted_index.products | 4 |
| abstract_inverted_index.proposed | 138 |
| abstract_inverted_index.proposes | 58 |
| abstract_inverted_index.provides | 219 |
| abstract_inverted_index.relation | 102 |
| abstract_inverted_index.setpoint | 150 |
| abstract_inverted_index.settling | 180 |
| abstract_inverted_index.strategy | 172 |
| abstract_inverted_index.studies. | 258 |
| abstract_inverted_index.RLS-based | 139, 217 |
| abstract_inverted_index.Recursive | 65 |
| abstract_inverted_index.agreement | 208 |
| abstract_inverted_index.algorithm | 113 |
| abstract_inverted_index.behavior. | 212 |
| abstract_inverted_index.closures. | 110 |
| abstract_inverted_index.delivery, | 17 |
| abstract_inverted_index.densities | 44 |
| abstract_inverted_index.discharge | 143 |
| abstract_inverted_index.dynamics, | 118 |
| abstract_inverted_index.effective | 116 |
| abstract_inverted_index.efficient | 12 |
| abstract_inverted_index.estimates | 115 |
| abstract_inverted_index.induction | 91 |
| abstract_inverted_index.maintains | 142 |
| abstract_inverted_index.nonlinear | 81 |
| abstract_inverted_index.operating | 131 |
| abstract_inverted_index.overshoot | 175 |
| abstract_inverted_index.parameter | 69 |
| abstract_inverted_index.petroleum | 3 |
| abstract_inverted_index.practical | 221 |
| abstract_inverted_index.transient | 46, 162 |
| abstract_inverted_index.Simulation | 133 |
| abstract_inverted_index.adjustment | 121 |
| abstract_inverted_index.confirming | 206 |
| abstract_inverted_index.controller | 62, 141 |
| abstract_inverted_index.developed, | 94 |
| abstract_inverted_index.efficiency | 75, 237 |
| abstract_inverted_index.estimation | 70 |
| abstract_inverted_index.fixed-gain | 30, 167 |
| abstract_inverted_index.foundation | 245 |
| abstract_inverted_index.normalized | 200 |
| abstract_inverted_index.operation. | 240 |
| abstract_inverted_index.regulatory | 27 |
| abstract_inverted_index.robustness | 231 |
| abstract_inverted_index.simulation | 82 |
| abstract_inverted_index.strategies | 252 |
| abstract_inverted_index.subsequent | 257 |
| abstract_inverted_index.transients | 105, 234 |
| abstract_inverted_index.validation | 185 |
| abstract_inverted_index.variations | 153 |
| abstract_inverted_index.Traditional | 29 |
| abstract_inverted_index.centrifugal | 36, 86 |
| abstract_inverted_index.challenges. | 28 |
| abstract_inverted_index.conditions. | 132 |
| abstract_inverted_index.controller, | 169 |
| abstract_inverted_index.demonstrate | 135 |
| abstract_inverted_index.enhancement | 222 |
| abstract_inverted_index.establishes | 243 |
| abstract_inverted_index.operational | 25 |
| abstract_inverted_index.operations. | 79 |
| abstract_inverted_index.self-tuning | 60, 218 |
| abstract_inverted_index.supervisory | 248 |
| abstract_inverted_index.continuously | 114 |
| abstract_inverted_index.controllers, | 32 |
| abstract_inverted_index.coordination | 251 |
| abstract_inverted_index.disturbances | 47 |
| abstract_inverted_index.higher-level | 247 |
| abstract_inverted_index.overpressure | 19 |
| abstract_inverted_index.proportional | 123 |
| abstract_inverted_index.steady-state | 239 |
| abstract_inverted_index.approximately | 177 |
| abstract_inverted_index.incorporating | 95 |
| abstract_inverted_index.architectures, | 227 |
| abstract_inverted_index.game-theoretic | 250 |
| abstract_inverted_index.transportation | 1 |
| abstract_inverted_index.Darcy–Weisbach | 101 |
| cited_by_percentile_year | |
| corresponding_author_ids | https://openalex.org/A5120455778 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 2 |
| corresponding_institution_ids | https://openalex.org/I11957088 |
| citation_normalized_percentile |