A simple approach to mathematical modelling of integer order and fractional order fuzzy PID controllers using one-dimensional input space and their experimental realization |
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| Authors: | Debdoot Sain BM Mohan |
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| Institution: | 1. Graduate School of Mechanical and Aerospace Engineering, Gyeongsang National University, 501 Jinjudaero, Jinju 52828, Republic of Korea;2. Department of Electrical Engineering, Hanyang University, 222 Wangsimniro, Seoul 04763, Republic of Korea;1. College of Science, Hebei Agricultural University, Baoding 071001, China;2. School of Science, Nanjing University of Science and Technology, Nanjing 210094, China;3. School of Information Technology, Jiangxi University of Finance and Economics, Nanchang 330013, China;4. School of Mathematics and Physics, Anhui Polytechnic University, Wuhu 241000, China;1. Smart Energy Systems Research Group, School of Engineering, Edith Cowan University, Australia;2. Department of Mechanical Engineering, School of Engineering, The University of Melbourne, Australia;1. School of Control Science and Engineering, Dalian University of Technology, Dalian 116023, China;2. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110004, China |
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| Abstract: | Though over the years, mathematical modelling of fuzzy PID controllers is carried out extensively with two-dimensional and three-dimensional input spaces, the modelling is rarely attempted using one-dimensional input space. In this paper, this gap is reduced by proposing a simple approach where each of the fuzzy P, fuzzy I, and fuzzy D components is modelled using one-dimensional input space and merged to provide the complete PID action. Another speciality of the proposed approach is that it does not require any AND or OR operator for obtaining the mathematical models of individual PID components. To the best of author’s knowledge, such a modelling approach is completely new. This newly introduced idea of modelling is further extended to fractional order fuzzy PID controllers. Applicability of the proposed fuzzy controllers is delineated with four simulation examples and one real-time experimentation case study. To understand the usefulness of the proposed control schemes, performances of the newly obtained controllers are compared with the results available in literature. As the proposed controllers are model-free controllers, they can easily be implemented for other control applications also. |
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