{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,15]],"date-time":"2025-12-15T19:13:58Z","timestamp":1765826038686,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,6,27]],"date-time":"2025-06-27T00:00:00Z","timestamp":1750982400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61174209","2020XJYB001","2356029","EP\/R021961\/1"],"award-info":[{"award-number":["61174209","2020XJYB001","2356029","EP\/R021961\/1"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Scientific Research Project of Hechi University","award":["61174209","2020XJYB001","2356029","EP\/R021961\/1"],"award-info":[{"award-number":["61174209","2020XJYB001","2356029","EP\/R021961\/1"]}]},{"name":"High-level Talent Research Start-up Project of Chongqing Technology and Business University","award":["61174209","2020XJYB001","2356029","EP\/R021961\/1"],"award-info":[{"award-number":["61174209","2020XJYB001","2356029","EP\/R021961\/1"]}]},{"name":"Engineering and Physical Sciences Research Council (EPSRC) of UK","award":["61174209","2020XJYB001","2356029","EP\/R021961\/1"],"award-info":[{"award-number":["61174209","2020XJYB001","2356029","EP\/R021961\/1"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Improving the tracking accuracy and effectiveness of the pressurizer control system with respect to the reference signal is an effective method to enhance the safe and stable operation of nuclear reactors. This paper applies preview tracking control to the pressurizer control system. For the simplified control system model of the pressurizer, we first study its general structure, which can be characterized as a discrete-time system with state delay. Unlike conventional control systems, the system considered in this study features control inputs that are represented as cumulative sums of historical inputs. In order to design a preview tracking controller for such systems, we adopt the difference method and state augmentation technique and introduce an equality containing the reference signal and a discrete integrator to construct an augmented error system. Simultaneously, a performance signal is defined to evaluate the impact of external disturbances on system performance. Thus, the preview tracking control problem of the original system is reformulated as an H\u221e control problem for the augmented error system. Subsequently, a memory-based state feedback controller is designed for the augmented error system. Then, by employing the Lyapunov function and linear matrix inequality (LMI), the H\u221e preview tracking controller for the original system is derived. Finally, the proposed control strategy is applied to a pressurizer control system model, and numerical simulations are conducted to validate the effectiveness of the proposed controller by using MATLAB (R2023a, MathWorks, Natick, MA, USA).<\/jats:p>","DOI":"10.3390\/axioms14070505","type":"journal-article","created":{"date-parts":[[2025,6,30]],"date-time":"2025-06-30T13:06:17Z","timestamp":1751288777000},"page":"505","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["H\u221e Preview Tracking Control of Time-Delay Discrete Systems and Its Application in Nuclear Reactor Problems"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5450-1861","authenticated-orcid":false,"given":"Fucheng","family":"Liao","sequence":"first","affiliation":[{"name":"School of Mathematics and Physics, Hechi University, Hechi 546300, China"},{"name":"School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hao","family":"Xie","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xianchun","family":"Meng","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, Hechi University, Hechi 546300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiang","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yucheng","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, Hechi University, Hechi 546300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiamei","family":"Deng","sequence":"additional","affiliation":[{"name":"School of Built Environment, Engineering and Computing, Leeds Beckett University, Leeds LS6 3QS, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1002\/oca.2106","article-title":"Optimal preview control: A review","volume":"36","author":"Birla","year":"2015","journal-title":"Optim. Control Appl. Methods"},{"key":"ref_2","first-page":"2804","article-title":"Reliable preview tracking control for a class of discrete-time Lipschitz nonlinear systems","volume":"43","author":"Yu","year":"2023","journal-title":"J. Syst. Sci. Math. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.apm.2023.01.027","article-title":"Robust preview control of interconnected continuous-time systems with parametric uncertainties","volume":"118","author":"Xie","year":"2023","journal-title":"Appl. Math. Model."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2592","DOI":"10.1080\/00207721.2019.1672000","article-title":"Preview control for a class of linear stochastic systems with multiplicative noise","volume":"50","author":"Wu","year":"2019","journal-title":"Int. J. Syst. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1049\/cth2.12214","article-title":"Preview repetitive control with equivalent input disturbance for continuous-time linear systems","volume":"16","author":"Lan","year":"2022","journal-title":"IET Control Theory Appl."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1080\/00207179.2019.1581379","article-title":"Data-driven robust fault tolerant linear quadratic preview control of discrete-time linear systems with completely unknown dynamics","volume":"94","author":"Han","year":"2021","journal-title":"Int. J. Control"},{"key":"ref_7","first-page":"99","article-title":"Preview saturated control for uncertain periodic discrete-time systems","volume":"44","author":"Li","year":"2024","journal-title":"J. Syst. Sci. Math. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1109\/THFE.1966.232329","article-title":"Three models of preview control","volume":"7","author":"Sheridan","year":"1966","journal-title":"IEEE Trans. Hum. Factors Electron."},{"key":"ref_9","first-page":"815","article-title":"Introducing virtual axis to path control system using superficial evaluation term","volume":"39","author":"Itoh","year":"1996","journal-title":"JSME Int. J."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1163\/156855391X00340","article-title":"Robot manipulator path control based on variable speed trajectory planning","volume":"6","author":"Abe","year":"1991","journal-title":"Adv. Robot."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Youn, I., and Ahmad, E. (2022). Anti-jerk optimal preview control strategy to enhance performance of active and semi-active suspension systems. Electronics, 11.","DOI":"10.3390\/electronics11101657"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2489","DOI":"10.1007\/s12555-017-0663-4","article-title":"Fuzzy preview control for half-vehicle electro-hydraulic suspension system","volume":"16","author":"Choi","year":"2018","journal-title":"Int. J. Control Autom. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"899","DOI":"10.1016\/j.renene.2020.12.009","article-title":"Vibration and power regulation control of a floating wind turbine with hydrostatic transmission","volume":"167","author":"Tong","year":"2021","journal-title":"Renew. Energy"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Guo, F., Schlipf, D., Zhang, Z., and Cheng, P.W. (2022, January 8\u201310). Investigation on the wind preview quality for lidar-assisted wind turbine control under wake conditions. Proceedings of the 2022 American Control Conference, Atlanta, GA, USA.","DOI":"10.23919\/ACC53348.2022.9867301"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Huang, Y., Luo, W., and Lan, H. (2022). Adaptive pre-aim control of driverless vehicle path tracking based on a SSA-BP neural network. World Electr. Veh. J., 13.","DOI":"10.3390\/wevj13040055"},{"key":"ref_16","first-page":"266","article-title":"Optimal preview tracking control algorithm for ATO system","volume":"37","author":"Zhang","year":"2017","journal-title":"J. Comput. Appl."},{"key":"ref_17","first-page":"1102","article-title":"Disturbance rejection based on discrete-time adaptive preview control for unmanned aerial vehicle shipboard landing under structure damage","volume":"238","author":"Xue","year":"2024","journal-title":"Proc. Inst. Mech. Eng. Part I-J. Syst. Control Eng."},{"key":"ref_18","unstructured":"Yan, C.Q. (2020). Nuclear Reactor Engineering, Harbin Engineering University Press. [3rd ed.]."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"682","DOI":"10.1016\/j.anucene.2018.06.023","article-title":"History review of nuclear reactor safety","volume":"120","author":"Gu","year":"2018","journal-title":"Ann. Nucl. Energy"},{"key":"ref_20","first-page":"35","article-title":"Research on water level and pressure control system of nuclear reactor regulator","volume":"40","author":"Zhang","year":"2013","journal-title":"Control Instrum. Chem. Ind."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"128472","DOI":"10.1016\/j.energy.2023.128472","article-title":"System-level modeling, analysis and coordinated control design for the pressurized water reactor nuclear power system","volume":"283","author":"Cui","year":"2023","journal-title":"Energy"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"113875","DOI":"10.1016\/j.nucengdes.2025.113875","article-title":"Research on the intelligent control strategy of pressurizer pressure in PWRs based on a fuzzy neural network PID controller","volume":"433","author":"Wei","year":"2025","journal-title":"Nucl. Eng. Des."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"608","DOI":"10.4028\/www.scientific.net\/AMM.336-338.608","article-title":"Research on pressurizer water level control in nuclear reactor based on active disturbances rejection controller","volume":"336","author":"Xue","year":"2013","journal-title":"Appl. Mech. Mater."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"7953358","DOI":"10.1155\/2022\/7953358","article-title":"Optimal Tracking Control for a Discrete Time Nonlinear Nuclear Power System","volume":"2022","author":"Luan","year":"2022","journal-title":"Math. Probl. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"16544","DOI":"10.1109\/ACCESS.2022.3149790","article-title":"Nonlinear model predictive control using feedback linearization for a pressurized water nuclear power plant","volume":"10","author":"Naimi","year":"2022","journal-title":"IEEE Access"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1016\/j.anucene.2014.05.024","article-title":"Fuzzy logic control for improved pressurizer systems in nuclear power plants","volume":"72","author":"Brown","year":"2014","journal-title":"Ann. Nucl. Energy"},{"key":"ref_27","unstructured":"Mydlo, P., and Schreiber, P. (2011, January 20\u201322). Fuzzy controller for the control of nuclear reactor\u2019s power-control rods. Proceedings of the 22nd Central European Conference on Information and Intelligent Systems, Dubrovnik, Croatia."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Wang, M., Deng, J., Pattinson, C., and Richardson, S. (2017, January 14\u201316). A fuzzy controller for fault tolerant control of nuclear reactor. Proceedings of the 2017 International Conference on Computational Science and Computational Intelligence, Las Vegas, NV, USA.","DOI":"10.1109\/CSCI.2017.64"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1080\/0020718508961156","article-title":"Design of an optimal controller for a discrete-time system subject to previewable demand","volume":"41","author":"Katayama","year":"1985","journal-title":"Int. J. Control"},{"key":"ref_30","unstructured":"Yu, L. (2002). Robust Control: Linear Matrix Inequality Approach, Tsinghua University Press."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"9982","DOI":"10.3182\/20080706-5-KR-1001.01689","article-title":"Bounded real lemma for linear discrete-time descriptor systems","volume":"41","author":"Yung","year":"2008","journal-title":"IFAC Proc."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1496","DOI":"10.1002\/acs.3769","article-title":"Robust and quantized repetitive tracking control for fractional-order fuzzy large-scale systems","volume":"38","author":"Tharanidharan","year":"2024","journal-title":"Int. J. Adapt. Control Signal Process."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/7\/505\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:00:23Z","timestamp":1760032823000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/7\/505"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,27]]},"references-count":32,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2025,7]]}},"alternative-id":["axioms14070505"],"URL":"https:\/\/doi.org\/10.3390\/axioms14070505","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,6,27]]}}}