{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T21:09:03Z","timestamp":1774127343059,"version":"3.50.1"},"reference-count":26,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2014,6,5]],"date-time":"2014-06-05T00:00:00Z","timestamp":1401926400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, an improved cascade control strategy is presented for hydroturbine speed governors. Different from traditional proportional-integral-derivative (PID) control and model predictive control (MPC) strategies, the performance index of the outer controller is constructed by integrating the entropy and mean value of the tracking error with the constraints on control energy. The inner controller is implemented by a proportional controller. Compared with the conventional PID-P and MPC-P cascade control methods, the proposed cascade control strategy can effectively decrease fluctuations of hydro-turbine speed under non-Gaussian disturbance conditions in practical hydropower plants. Simulation results show the advantages of the proposed cascade control method.<\/jats:p>","DOI":"10.3390\/e16063136","type":"journal-article","created":{"date-parts":[[2014,6,5]],"date-time":"2014-06-05T11:18:20Z","timestamp":1401967100000},"page":"3136-3148","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Minimum Entropy-Based Cascade Control for Governing Hydroelectric Turbines"],"prefix":"10.3390","volume":"16","author":[{"given":"Mifeng","family":"Ren","sequence":"first","affiliation":[{"name":"State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources,  North China Electric Power University, Beijing 102206, China"},{"name":"School of Control and Computer Engineering, North China Electric Power University,  Beijing 102206, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Di","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Control and Computer Engineering, North China Electric Power University,  Beijing 102206, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianhua","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources,  North China Electric Power University, Beijing 102206, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Man","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Control and Computer Engineering, North China Electric Power University,  Beijing 102206, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2014,6,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"776","DOI":"10.1016\/j.rser.2005.06.003","article-title":"A review on hydropower plant models and control","volume":"11","author":"Kishor","year":"2007","journal-title":"Renew. 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