{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T00:13:37Z","timestamp":1774311217191,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,7,24]],"date-time":"2024-07-24T00:00:00Z","timestamp":1721779200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100018537","name":"China, Ministry of Industry and Information Technology","doi-asserted-by":"publisher","award":["J2019-V-0010-0104"],"award-info":[{"award-number":["J2019-V-0010-0104"]}],"id":[{"id":"10.13039\/501100018537","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>As the power unit of an aircraft, the engine\u2019s primary task is to provide the demanded thrust, making research on direct thrust control crucial. However, being a complicated multivariable system, effective multivariable direct thrust control methods are currently lacking. The main content of this paper is threefold. First, it presents a dual-loop multivariable \u03bc-synthesis direct thrust control scheme for mixed-exhaust low-bypass turbofan engines, which is a typical rotationally symmetric machine. The scheme adjusts fuel flow for thrust control and nozzle area to control the turbine pressure ratio, ensuring thrust tracking while maintaining the engine\u2019s key parameters within safe limits. Second, a fast, accurate thrust estimation algorithm based on aerodynamic thermodynamics and component characteristics is introduced. At last, considering the model uncertainties between off-design and design points, a weight function frequency shaping \u03bc-synthesis control design method is proposed to address internal loop coupling and external disturbance suppression. Nonlinear simulations within the flight envelope show that \u03bc-synthesis direct thrust control achieves robust servo tracking and disturbance rejection, with a maximum steady-state thrust error of no more than 0.1%, and the key parameters are not over their safety boundaries.<\/jats:p>","DOI":"10.3390\/sym16080944","type":"journal-article","created":{"date-parts":[[2024,7,24]],"date-time":"2024-07-24T15:47:32Z","timestamp":1721836052000},"page":"944","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Dual-Loop \u03bc-Synthesis Direct Thrust Control for Turbofan Engines"],"prefix":"10.3390","volume":"16","author":[{"given":"Yifu","family":"Long","sequence":"first","affiliation":[{"name":"School of Energy and Power Engineering, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xi","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Energy and Power Engineering, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenshuai","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Energy and Power Engineering, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiashuai","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Energy and Power Engineering, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,24]]},"reference":[{"key":"ref_1","unstructured":"Dennis, C., Sanjay, G., Hiller, S.-J., Horn, W., Kumar, A., Mathews, H.K., Moustapha, H., Pfoertner, H., Rosenfeld, T., and Rybarik, P. (2009). More Intelligent Gas Turbine Engines, North Atlantic Treaty Organisation."},{"key":"ref_2","unstructured":"Hanz, R. (2011). Advanced Control of Turbofan Engines, Springer."},{"key":"ref_3","unstructured":"Wang, X., Yang, S.-B., Zhu, M.-Y., and Kong, X.-X. (2021). Aeroengine Control Principles, Science Press."},{"key":"ref_4","unstructured":"Jack, D.M., William, H.H., and David, T.P. (2002). Aircraft Engine Design, AIAA. [2nd ed.]."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"123255","DOI":"10.1016\/j.energy.2022.123255","article-title":"A Highly Robust Thrust Estimation Method with Dissimilar Redundancy Framework for Gas Turbine Engine","volume":"245","author":"Zhao","year":"2022","journal-title":"Energy"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"100693","DOI":"10.1016\/j.paerosci.2020.100693","article-title":"Gas Turbine Aero-Engines Real Time on-Board Modelling: A Review, Research Challenges, and Exploring the Future","volume":"121","author":"Wei","year":"2020","journal-title":"Prog. Aerosp. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"011601","DOI":"10.1115\/1.2747254","article-title":"An Optimal Orthogonal Decomposition Method for Kalman Filter-Based Turbofan Engine Thrust Estimation","volume":"130","author":"Litt","year":"2007","journal-title":"J. Eng. Gas Turbine Power"},{"key":"ref_8","unstructured":"Litt, J.S., Sowers, T.S., Corporation, A., and Garg, S. (2007, January 2\u20137). A Retro-Fit Control Architecture to Maintain Engine Performance with Usage. Proceedings of the 18th ISABE Conference, Beijing, China."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/j.ast.2018.10.019","article-title":"A Novel Distributed Extended Kalman Filter for Aircraft Engine Gas-Path Health Estimation with Sensor Fusion Uncertainty","volume":"84","author":"Lu","year":"2019","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1748","DOI":"10.2514\/1.J059044","article-title":"Hybrid State Estimation for Aircraft Engine Anomaly Detection and Fault Accommodation","volume":"58","author":"Lu","year":"2020","journal-title":"AIAA J."},{"key":"ref_11","first-page":"437","article-title":"Turbojet Direct-Thrust Control Scheme for Full-Envelope Fuel Consumption Minimization","volume":"93","year":"2020","journal-title":"Aircr. Eng. Aerosp. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1515\/tjj-2016-0051","article-title":"Aircraft Engine Thrust Estimator Design Based on GSA-LSSVM","volume":"34","author":"Sheng","year":"2017","journal-title":"Int. J. Turbo Jet Engines"},{"key":"ref_13","first-page":"25","article-title":"Novel Weighted Least Squares Support Vector Regression for Thrust Estimation on Performance Deterioration of Aero-Engine","volume":"29","author":"Su","year":"2012","journal-title":"Trans. Nanjing Univ. Aeronaut. Astronaut."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1515\/tjj-2016-0002","article-title":"Metaheuristic and Machine Learning Models for TFE-731-2, PW4056, and JT8D-9 Cruise Thrust","volume":"34","author":"Baklacioglu","year":"2017","journal-title":"Int. J. Turbo Jet Engines"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.apenergy.2018.02.175","article-title":"A Robust Extreme Learning Machine for Modeling a Small-Scale Turbojet Engine","volume":"218","author":"Zhao","year":"2018","journal-title":"Appl. Energy"},{"key":"ref_16","unstructured":"Song, H.-Q., Li, B.-W., and Zhu, F.-X. (2017, January 3\u20135). Research on Aero-Engine Thrust Estimate Based on Extreme Learning Machine. Proceedings of the 2016 IEEE Advanced Information Management, Communicates, Electronic and Automation Control Conference (IMCEC), Xi\u2019an, China."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"103253","DOI":"10.1016\/j.engappai.2019.103253","article-title":"A Size-Transferring Radial Basis Function Network for Aero-Engine Thrust Estimation","volume":"87","author":"Zhao","year":"2020","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.ast.2019.01.033","article-title":"A Proposed Self-Organizing Radial Basis Function Network for Aero-Engine Thrust Estimation","volume":"87","author":"Li","year":"2019","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"012009","DOI":"10.1088\/1757-899X\/752\/1\/012009","article-title":"Thrust Estimation for Aero-Engine Based on Deep Convolution Neural Network","volume":"752","author":"Wang","year":"2020","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2182","DOI":"10.1177\/0954410021993303","article-title":"A Proposed Algorithm Based on Long Short-Term Memory Network and Gradient Boosting for Aeroengine Thrust Estimation on Transition State","volume":"235","author":"Zhao","year":"2021","journal-title":"Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng."},{"key":"ref_21","unstructured":"Wang, B. (2014). Intelligent Direct Thrust Control of Turbofan Engines based on Mathematical Dynamic Models. [Ph.D. Thesis, Beihang University]."},{"key":"ref_22","first-page":"554","article-title":"On-Board Real-Time Optimization Control for Turbofan Engine Thrust under Flight Emergency Condition","volume":"231","author":"Zheng","year":"2017","journal-title":"Proc. Inst. Mech. Eng. Part J. Syst. Control Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"933","DOI":"10.1007\/s42405-019-00191-4","article-title":"A Study on Aero-Engine Direct Thrust Control with Nonlinear Model Predictive Control Based on Deep Neural Network","volume":"20","author":"Zheng","year":"2019","journal-title":"Int. J. Aeronaut. Space Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1515\/tjj-2018-0049","article-title":"Direct Thrust Inverse Control of Aero-Engine Based on Deep Neural Network","volume":"38","author":"Zheng","year":"2021","journal-title":"Int. J. Turbo Jet-Engines"},{"key":"ref_25","first-page":"354","article-title":"Direct Thrust Predictive Control of Aeroengine Based on Compact Propulsion System Dynamic Model-State Variable Model","volume":"43","author":"Jin","year":"2022","journal-title":"J. Propuls. Technol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.cja.2021.09.018","article-title":"Direct Thrust Control for Multivariable Turbofan Engine Based on Affine Linear Parameter-Varying Approach","volume":"35","author":"Zhu","year":"2022","journal-title":"Chin. J. Aeronaut."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"108457","DOI":"10.1016\/j.ast.2023.108457","article-title":"\u03bc-Synthesis-based Robust L1 Adaptive Control for Aeropropulsion System Test Facility","volume":"140","author":"Liu","year":"2023","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Gu, D.-W., Petkov, P.H., and Konstantinov, M.M. (2013). Robust Control Design with MATLAB\u00ae, Springer. Advanced Textbooks in Control and Signal Processing.","DOI":"10.1007\/978-1-4471-4682-7"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"071027","DOI":"10.1115\/1.4049296","article-title":"Multi-Variable Adaptive Control Method for Turbofan Engine with Dynamic and Input Uncertainties","volume":"143","author":"Liu","year":"2021","journal-title":"J. Eng. Gas Turbine Power"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2557","DOI":"10.1109\/TCST.2018.2871957","article-title":"Supervisory Control of Multiple Switching Laws with Performance Guidance for Aeroengines","volume":"27","author":"Shi","year":"2019","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"121601","DOI":"10.1115\/1.4027820","article-title":"Aeroengine Multivariable Nonlinear Tracking Control Based on Uncertainty and Disturbance Estimator","volume":"136","author":"Xiao","year":"2014","journal-title":"J. Eng. Gas Turbine Power"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"107787","DOI":"10.1016\/j.ast.2022.107787","article-title":"An Anti-windup Design with Local Sector and H2\/H\u221e Optimization for Flight Environment Simulation System","volume":"128","author":"Liu","year":"2022","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1016\/j.cja.2023.06.016","article-title":"\u03bc-Synthesis Control with Reference Model for Aeropropulsion System Test Facility Under Dynamic Coupling and Uncertainty","volume":"36","author":"Liu","year":"2023","journal-title":"Chin. J. Aeronaut."},{"key":"ref_34","first-page":"1413","article-title":"Research of aero-engine two degrees-of-freedom robust controller based on linear matrix inequality approach","volume":"24","author":"Wang","year":"2009","journal-title":"J. Aerosp. Power"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/8\/944\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:22:13Z","timestamp":1760109733000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/8\/944"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,24]]},"references-count":34,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2024,8]]}},"alternative-id":["sym16080944"],"URL":"https:\/\/doi.org\/10.3390\/sym16080944","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,24]]}}}