Adaptive Nonlinear Proportional–Integral–Derivative Control of a Continuous Stirred Tank Reactor Process Using a Radial Basis Function Neural Network
Temperature control in a continuous stirred tank reactor (CSTR) poses significant challenges due to the process’s inherent nonlinearities and uncertain parameters. This study proposes an innovative solution by developing an adaptive nonlinear proportional–integral–derivative (NPID) controller. The n...
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2025-07-01
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| author | Joo-Yeon Lee Gang-Gyoo Jin Gun-Baek So |
| author_facet | Joo-Yeon Lee Gang-Gyoo Jin Gun-Baek So |
| author_sort | Joo-Yeon Lee |
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| description | Temperature control in a continuous stirred tank reactor (CSTR) poses significant challenges due to the process’s inherent nonlinearities and uncertain parameters. This study proposes an innovative solution by developing an adaptive nonlinear proportional–integral–derivative (NPID) controller. The nonlinear gain that dynamically scales the error fed to the integrator is enhanced for optimized performance. The network’s ability to approximate nonlinear functions and its online learning capabilities are leveraged by effectively integrating an NPID control scheme with a radial basis function neural network (RBFNN). This synergistic approach provides a more robust and reliable control strategy for CSTRs. To assess the proposed method’s feasibility, a set of simulations was conducted for tracking, disturbance rejection, and parameter variations. These results were compared with those of an adaptive RBFNN-based PID (APID) controller under identical conditions. The simulations indicated that the proposed method achieved reductions in maximum overshoot of 33.7% and settling time of 54.2% for upward and downward setpoint changes and 27.2% and 5.3% for downward and upward setpoint changes compared to the APID controller. For disturbance changes, the proposed method reduced the peak magnitude (<i>M<sub>peak</sub></i>) by 4.9%, recovery time (<i>t<sub>rcy</sub></i>) by 23.6%, and integral absolute error by 16.2%. Similarly, for parameter changes, the reductions were 3.0% (<i>M<sub>peak</sub></i>), 26.4% (<i>t<sub>rcy</sub></i>), and 24.4% (<i>IAE</i>). |
| format | Article |
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| institution | Kabale University |
| issn | 1999-4893 |
| language | English |
| publishDate | 2025-07-01 |
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| spelling | doaj-art-75bbd986434b4252afd2b51957450dd02025-08-20T03:35:27ZengMDPI AGAlgorithms1999-48932025-07-0118744210.3390/a18070442Adaptive Nonlinear Proportional–Integral–Derivative Control of a Continuous Stirred Tank Reactor Process Using a Radial Basis Function Neural NetworkJoo-Yeon Lee0Gang-Gyoo Jin1Gun-Baek So2Ocean Space Development & Energy Research Department, Korea Institute of Ocean Science and Technology, Busan 49111, Republic of KoreaDepartment of Electrical Power and Control Engineering, Adama Science and Technology University, Adama 1888, EthiopiaDepartment of Maritime Industry Convergence, Mokpo National Maritime University, Mokpo 58628, Republic of KoreaTemperature control in a continuous stirred tank reactor (CSTR) poses significant challenges due to the process’s inherent nonlinearities and uncertain parameters. This study proposes an innovative solution by developing an adaptive nonlinear proportional–integral–derivative (NPID) controller. The nonlinear gain that dynamically scales the error fed to the integrator is enhanced for optimized performance. The network’s ability to approximate nonlinear functions and its online learning capabilities are leveraged by effectively integrating an NPID control scheme with a radial basis function neural network (RBFNN). This synergistic approach provides a more robust and reliable control strategy for CSTRs. To assess the proposed method’s feasibility, a set of simulations was conducted for tracking, disturbance rejection, and parameter variations. These results were compared with those of an adaptive RBFNN-based PID (APID) controller under identical conditions. The simulations indicated that the proposed method achieved reductions in maximum overshoot of 33.7% and settling time of 54.2% for upward and downward setpoint changes and 27.2% and 5.3% for downward and upward setpoint changes compared to the APID controller. For disturbance changes, the proposed method reduced the peak magnitude (<i>M<sub>peak</sub></i>) by 4.9%, recovery time (<i>t<sub>rcy</sub></i>) by 23.6%, and integral absolute error by 16.2%. Similarly, for parameter changes, the reductions were 3.0% (<i>M<sub>peak</sub></i>), 26.4% (<i>t<sub>rcy</sub></i>), and 24.4% (<i>IAE</i>).https://www.mdpi.com/1999-4893/18/7/442CSTRadaptive controlnonlinear PID controllerRBFNNsystem identification |
| spellingShingle | Joo-Yeon Lee Gang-Gyoo Jin Gun-Baek So Adaptive Nonlinear Proportional–Integral–Derivative Control of a Continuous Stirred Tank Reactor Process Using a Radial Basis Function Neural Network Algorithms CSTR adaptive control nonlinear PID controller RBFNN system identification |
| title | Adaptive Nonlinear Proportional–Integral–Derivative Control of a Continuous Stirred Tank Reactor Process Using a Radial Basis Function Neural Network |
| title_full | Adaptive Nonlinear Proportional–Integral–Derivative Control of a Continuous Stirred Tank Reactor Process Using a Radial Basis Function Neural Network |
| title_fullStr | Adaptive Nonlinear Proportional–Integral–Derivative Control of a Continuous Stirred Tank Reactor Process Using a Radial Basis Function Neural Network |
| title_full_unstemmed | Adaptive Nonlinear Proportional–Integral–Derivative Control of a Continuous Stirred Tank Reactor Process Using a Radial Basis Function Neural Network |
| title_short | Adaptive Nonlinear Proportional–Integral–Derivative Control of a Continuous Stirred Tank Reactor Process Using a Radial Basis Function Neural Network |
| title_sort | adaptive nonlinear proportional integral derivative control of a continuous stirred tank reactor process using a radial basis function neural network |
| topic | CSTR adaptive control nonlinear PID controller RBFNN system identification |
| url | https://www.mdpi.com/1999-4893/18/7/442 |
| work_keys_str_mv | AT jooyeonlee adaptivenonlinearproportionalintegralderivativecontrolofacontinuousstirredtankreactorprocessusingaradialbasisfunctionneuralnetwork AT ganggyoojin adaptivenonlinearproportionalintegralderivativecontrolofacontinuousstirredtankreactorprocessusingaradialbasisfunctionneuralnetwork AT gunbaekso adaptivenonlinearproportionalintegralderivativecontrolofacontinuousstirredtankreactorprocessusingaradialbasisfunctionneuralnetwork |