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The proposed controller is designed to address the main challenges posed by a class of complex systems characterized by uncertain high-gain and pure integrator dynamics, including high-frequency noise amplification and poor robustness against parameter variations. Designing such a controller involves three main steps: First, a proportional\u2013integral\u2013derivative (PID) controller is designed, with its parameters auto-tuned online using the BPNN algorithm, resulting in the primary (BPNN-PID) controller. Second, the obtained parameters of the previous controller are utilized to compute those of a low-pass filter offline. This filter is then cascaded with the integral parts of a PID controller, forming a P-FI controller structure. This configuration introduces a phase lead within a specific frequency range without amplifying high-frequency noise, overcoming the primary disadvantage of the derivative term. Finally, the parameters of the resulting P-FI controller are again auto-tuned online using the BPNN algorithm, resulting in the final robust (BPNN-P-FI) controller. This novel controller structure and its parameters tuning procedure, based on a two-stage BPNN learning approach, constitute the main contributions of this paper. Simulation results demonstrate the superiority of the proposed controller in terms of time-domain performance, sensor noise attenuation, and closed-loop robustness compared to those obtained with the BPNN-PID and optimally tuned PID controllers.<\/jats:p>","DOI":"10.1177\/01423312241266011","type":"journal-article","created":{"date-parts":[[2024,8,29]],"date-time":"2024-08-29T09:20:58Z","timestamp":1724923258000},"page":"1796-1806","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["A robust proportional filtered integral controller based on backpropagation neural network"],"prefix":"10.1177","volume":"47","author":[{"given":"Ibtihal","family":"Benharkou","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Faculty of Technology, University of 20 August 1955 Skikda, Algeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0328-6561","authenticated-orcid":false,"given":"Sofiane","family":"Gherbi","sequence":"additional","affiliation":[{"name":"Laboratory of Automation and Signals Annaba (LASA), Department of Electronics, Faculty of Technology, Badji Mokhtar - Annaba University, Algeria"}]},{"given":"Moussa","family":"Sedraoui","sequence":"additional","affiliation":[{"name":"Universit\u00e9 8 Mai 1945 Guelma, Algeria"}]},{"given":"Mohcene","family":"Bechouat","sequence":"additional","affiliation":[{"name":"D\u00e9partement d\u2019Automatique et d\u2019\u00c9lectrom\u00e9canique, Facult\u00e9 des Sciences et de la Technologie, Universit\u00e9 de Ghardaia, Algeria"}]}],"member":"179","published-online":{"date-parts":[[2024,8,29]]},"reference":[{"key":"e_1_3_2_2_1","volume-title":"Advanced PID control. 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