Enhanced Adaptive Neuro Sliding Mode Controller Parameter Optimization for Coupled Tank System
DOI:
https://doi.org/10.18196/jrc.v6i3.25992Keywords:
Improved Difference Evolution (MDE) Method, Adaptive Neuro Sliding Mode Control (ANSMC), Coupled Tank System (CTS), Radial Basis Function Neural Network (RBFNN), Nonlinear Control, System Stability, Optimization AlgorithmAbstract
This paper proposes the EANSMC-MDE method for the coupled tank system (CTS) liquid level control, which consists of the Improved Difference Evolution (MDE) optimizing method optimized parameters for the Adaptive Neuro Sliding Mode Controller (ANSMC). The CTS system represents a nonlinear object with delay and uncertainties, including varying parameters, sensor and output valve noises, etc. The suggested controller contains a direct adaptive controller directly approximated by a Radial Basis Function (RBF) neural network combined with a sliding mode controller used to compensate for the approximation errors of the RBF network and ensure system stability. The stability Lyapunov criterion is used to construct the sliding-mode control system and adaptive rule. The proposed algorithm delivers good control performance right from the start-up phase thanks to the use of pre-optimized parameters, which is an advantage compared to conventional adaptive control algorithms. Simulations are conducted to demonstrate the effectiveness of the proposed optimization method compared to different optimization methods using identical beginning conditions and objective function values to establish equitable comparisons. Furthermore, to demonstrate the superiority of the suggested control method, it is contrasted with the optimal SMC and the traditional ANSMC method. Additionally, the simulations evaluate the response capability of the proposed algorithm under the influence of significantly varying sensor noise levels across different magnitudes, changes in the reference signal, and substantial variations in system parameters. The proposed algorithm has the potential to be applied to other uncertain nonlinear systems. However, it has not yet been validated on systems with fast dynamic responses.
References
K. R. A. Govind, S. Mahapatra, and S. R. Mahapatro, “Design of an Optimal Control Strategy for Coupled Tank Systems Using Nonlinear Constraint Optimization With Kharitonov-Hurwitz Stability Analysis,” IEEE Access, vol. 11, pp. 72618-72629, 2023.
K. R. A. Govind and S. J. S. Mahapatra, “Frequency domain specifications-based robust decentralized PI/PID control algorithm for benchmark variable-area coupled tank systems,” Sensors, vol. 22, no. 23, p. 9165, 2022.
J. Sánchez-Palma and J. L. Ordoñez-Ávila, “A PID Control Algorithm With Adaptive Tuning Using Continuous Artificial Hydrocarbon Networks for a Two-Tank System,” IEEE Access, vol. 10, pp. 114694-114710, 2022.
S. A. Al-Samarraie and I. I. Gorial, “Assessment of FLC, PID, Nonlinear PID, and SMC controllers for level stabilization in mechatronic systems,” Journal of Robotics and Control, vol. 5, no. 6, pp. 1845-1861, 2024.
T. R. D. Kumar and S. J. Mija, “Boundary Logic-Based Hybrid PID-SMC Scheme for a Class of Underactuated Nonlinear Systems-Design and Real-Time Testing,” IEEE Transactions on Industrial Electronics, vol. 72, no. 5, pp. 5257-5267, 2025.
T. R. D. Kumar and S. J. Mija, “Synthesis and experimental demonstration of a hybrid adaptive PID-SMC algorithm for a class of underactuated nonlinear systems,” Nonlinear Nonlinear Dynamics, vol. 113, no. 12, pp. 15037–15056, 2025.
K. D. Wahyuadnyana, K. Indriawati, P. A. Darwito, A. N. Aufa, and H. Tnunay, “Performance analysis of PID and SMC control algorithms on AUV under the influence of internal solitary wave in the Bali Deep Sea,” Journal of Robotics and Control, vol. 5, no. 6, pp. 1957–1972, 2024.
A. Ardjal, M. Bettayeb, R. Mansouri, and B. Zouak, “Design and implementation of a model-free fractional order intelligent PI fractional order sliding mode controller for water level tank system,” ISA Transactions, vol. 127, pp. 501–510, 2022.
B. Gurjar, V. Chaudhari, and S. Kurode, “Parameter estimation-based robust liquid level control of quadruple tank system—Second-order sliding mode approach,” Journal of Process Control, vol. 104, pp. 1–10, 2021.
S. Kamal, T. Haque, and L. Chen, “Discrete-time control with application to coupled tank system: A ceiling function approach,” SSRN, 2023.
V. K. Singh, S. Kamal, B. Bandyopadhyay, S. Ghosh, and T. N. Dinh, “Prescribed-Time Optimal Control of Nonlinear Dynamical Systems With Application to a Coupled Tank System,” IEEE Transactions on Automation Science and Engineering, vol. 22, pp. 191-201, 2025.
X. Meng, H. Yu, J. Zhang, T. Xu, and H. Wu, “Liquid level control of four-tank system based on active disturbance rejection technology,” Measurement, vol. 175, p. 109146, 2021.
X. Meng, H. Yu, J. Zhang, T. Xu, H. Wu, and K. Yan, “Disturbance observer-based feedback linearization control for a quadruple-tank liquid level system,” ISA Transactions, vol. 122, pp. 146–162, 2022.
X. Meng, H. Yu, T. Xu, and H. Wu, “Disturbance observer and L2-gain-based state error feedback linearization control for the quadruple-tank liquid-level system,” Energies, vol. 13, no. 20, p. 5500, 2020.
X. Meng, H. Yu, H. Wu, and T. Xu, “Disturbance observer‐based integral backstepping control for a two‐tank liquid level system subject to external disturbances,” Mathematical Problems in Engineering, vol. 2020, no. 1, pp. 1-22, 2020.
B. Tacal and L. Ucun, “Bernstein polynomials-based compensator design for coupled tank system with saturation nonlinearity,” Proceedings of the Institution of Mechanical Engineers, Part I, vol. 236, no. 7, pp. 1274–1284, 2022.
R. Raj, A. Kumar, D. Sharma, and S. Khan, “TS fuzzy controller with S- and Z-type MFs to control a coupled-tank system,” Materialstoday: Proceedings, vol. 80, pp. A8–A13, 2023.
D. S. Bhandare, N. R. Kulkarni, and M. V. Bakshi, “Hardware implementation of a novel intelligent fuzzy fractional order proportional-integral (FFOPI) controller for a coupled tank liquid level control system,” Sādhanā, vol. 49, no. 4, p. 296, 2024.
Q. N. Duong and N. T. Dang, “Model-free optimal control for underactuated quadrotor aircraft via reinforcement learning,” Journal of Robotics and Control, vol. 5, no. 6, pp. 1827–1835, 2024.
K. Phothongkum and S. Kuntanapreeda, “Stability-constrained reinforcement learning for level control of nonlinear coupled tank system: An experimental study,” Neural Computing and Applications, vol. 37, no. 6, pp. 4277–4290, 2025.
L. N. Tan, T. P. Cong, and D. P. Cong, “Neural Network Observers and Sensorless Robust Optimal Control for Partially Unknown PMSM With Disturbances and Saturating Voltages,” IEEE Transactions on Power Electronics, vol. 36, no. 10, pp. 12045-12056, 2021.
L. N. Tan and T. C. Pham, “Optimal Tracking Control for PMSM With Partially Unknown Dynamics, Saturation Voltages, Torque, and Voltage Disturbances,” IEEE Transactions on Industrial Electronics, vol. 69, no. 4, pp. 3481-3491, 2022.
L. N. Tan, N. Gupta, and M. Derawi, “H∞ Control for Oscillator Systems With Event-Triggering Signal Transmission of Internet of Things,” IEEE Access, vol. 11, pp. 8938-8949, 2023.
L. N. Tan, H. -T. Tran, and T. -T. Tran, “Event-Triggered Observers and Distributed H∞ Control of Physically Interconnected Nonholonomic Mechanical Agents in Harsh Conditions,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 52, no. 12, pp. 7871-7884, 2022.
S. Zeghlache, M. Z. Ghellab, A. Djerioui, B. Bouderah, and M. F. Benkhoris, “Adaptive fuzzy fast terminal sliding mode control for inverted pendulum-cart system with actuator faults,” Mathematics and Computers in Simulation, vol. 210, pp. 207–234, 2023.
X. Su, X. Yang, and Y. Xu, “Fuzzy adaptive terminal sliding mode control based on recurrent neural network compensation for a maglev system,” Engineering Applications of Artificial Intelligence, vol. 124, p. 106588, 2023.
Z. Wu, B. Jiang, and Q. Gao, “State estimation and fuzzy sliding mode control of nonlinear Markovian jump systems via adaptive neural network,” Journal of the Franklin Institute, vol. 359, no. 16, pp. 8974–8990, 2022.
B. Jiang, H. R. Karimi, X. Zhang, and Z. Wu, “Adaptive neural-network-based sliding mode control of switching distributed delay systems with Markov jump parameters,” Neural Networks, vol. 165, pp. 846-859, 2023.
M. S. Mahmoud, M. Maaruf, and S. El-Ferik, “Neuro-adaptive output feedback control of the continuous polymerization reactor subjected to parametric uncertainties and external disturbances,” ISA Transactions, vol. 112, pp. 1-11, 2021.
S. Ullah, Q. Khan, A. Mehmood, S. A. M. Kirmani, O. Mechali, R. Ahmed, and K. Hussain, “Neuro-adaptive fast integral terminal sliding mode control design with variable gain robust exact differentiator for under-actuated quadcopter UAV,” ISA Transactions, vol. 120, pp. 293-304, 2022.
B. Gao, Y.-J. Liu, and L. Liu, “Adaptive neural fault-tolerant control of a quadrotor UAV via fast terminal sliding mode,” Aerospace Science and Technology, vol. 129, p. 107818, 2022.
J. Hu, D. Zhang, Z. Wu, and H. Li, “Neural network-based adaptive second-order sliding mode control for uncertain manipulator systems with input saturation,” ISA Transactions, vol. 136, pp. 126-138, 2023.
J. Wang, T. P. Zhu, B. He, G. Deng, C. Zhang, and X. Huang, “An adaptive neural sliding mode control with ESO for uncertain nonlinear systems,” International Journal of Control, Automation and Systems, vol. 19, pp. 687–697, 2021.
D. T. Tran, H. N. Tong, and K. K. Ahn, “An extended state observer-based on the terminal sliding mode control for 6-DOF manipulator against lumped uncertainties,” International Journal of Control, Automation and Systems, vol. 23, no. 3, pp. 810-823, 2025.
S. Choueikh, M. Kermani, and F. M’sahli, “A comparative study of nonsingular terminal sliding mode and backstepping schemes for the coupled two‐tank system,” Complexity, vol. 2021, no. 1, pp. 1–18, 2021.
M. Tao, X. He, S. Xie, and Q. Chen, “RBFNN-based singularity-free terminal sliding mode control for uncertain quadrotor UAVs,” Computational Intelligence and Neuroscience, vol. 2021, no. 1, pp. 1-10, 2021.
Z. Liu, X. Gong, and J. Fei, “Nonsingular fast terminal sliding mode control of DC–DC buck converter using fuzzy neural network and disturbance observer,” Nonlinear Dynamics, vol. 113, no. 11, pp. 13389–13414, 2025.
I. U. Haq et al., “Neural network-based adaptive global sliding mode MPPT controller design for stand-alone photovoltaic systems,” PloS ONE, vol. 17, no. 1, p. e0260480, 2022.
Z. Han, S. Li, and H. Liu, “Composite learning sliding mode synchronization of chaotic fractional-order neural networks,” Journal of Advanced Research, vol. 25, pp. 87–96, 2020.
B. Li, X. Zhao, and M. Wu, “Adaptive neural network sliding mode control for a class of SISO nonlinear systems,” Mathematics, vol. 10, no. 7, p. 1182, 2022.
M. Yang, X. Zhang, Y. Xia, Q. Liu, and Q. Zhu, “Adaptive neural network-based sliding mode control for a hydraulic rotary drive joint,” Computers and Electrical Engineering, vol. 102, p. 108189, 2022.
S. Chaudhuri, R. Saha, A. Chatterjee, S. Mookherjee, and D. Sanyal, “Adaptive neural-bias-sliding mode control of rugged electrohydraulic system motion by recurrent Hermite neural network,” Control Engineering Practice, vol. 103, p. 104588, 2020.
J. Fu, F. Huang, and Z. Chen, “Optimization-based adaptive neural sliding mode control for nonlinear systems with fast and accurate response under state and input constraints,” Journal of the Franklin Institute, vol. 359, no. 13, pp. 6735–6758, 2022.
A. Merabet, S. Kanukollu, A. Al-Durra, and E. F. El-Saadany, “Adaptive recurrent neural network for uncertainties estimation in feedback control system,” Journal of Automation and Intelligence, vol. 2, no. 3, pp. 119–129, 2023.
S. C. Yogi, V. K. Tripathi, and L. Behera, “Adaptive Integral Sliding Mode Control Using Fully Connected Recurrent Neural Network for Position and Attitude Control of Quadrotor,” IEEE Transactions on Neural Networks and Learning Systems, vol. 32, no. 12, pp. 5595-5609, 2021.
T. Kang, H. Peng, F. Zhou, X. Tian, and X. Peng, “Robust predictive control of coupled water tank plant,” Applied Intelligence, vol. 51, pp. 5726–5744, 2021.
P. Singh, D. K. Giri, and A. K. Ghosh, “Robust backstepping sliding mode aircraft attitude and altitude control based on adaptive neural network using symmetric BLF,” Aerospace Science and Technology, vol. 126, p. 107653, 2022.
A. Baraean et al., “Physics-informed NN-based adaptive backstepping terminal sliding mode control of buck converter for PEM electrolyzer,” Heliyon, vol. 10, no. 7, p. e29254, 2024.
W. Ruan, Q. Dong, X. Zhang, and Z. Li, “Friction compensation control of electromechanical actuator based on neural network adaptive sliding mode,” Sensors, vol. 21, no. 4, p. 1508, 2021.
Z. Zhu, Z. Duan, H. Qin, and Y. Xue, “Adaptive neural network fixed-time sliding mode control for trajectory tracking of underwater vehicle,” Ocean Engineering, vol. 287, p. 115864, 2023.
V. B. V. Nghia, T. V. Thien, N. N. Son, and M. T. Long, “Adaptive neural sliding mode control for two-wheel self-balancing robot,” International Journal of Dynamics and Control, vol. 10, no. 3, pp. 771–784, 2022.
Z. Zhao and X. Jin, “Adaptive neural network-based sliding mode tracking control for agricultural quadrotor with variable payload,” Computers and Electrical Engineering, vol. 103, p. 108336, 2022.
S. Liu, L. Zhang, B. Niu, X. Zhao, and A. M. Ahmad, “Adaptive neural finite-time hierarchical sliding mode control of uncertain under-actuated switched nonlinear systems with backlash-like hysteresis,” Information Sciences, vol. 599, pp. 147–169, 2022.
L. Shanmugam and Y. H. Joo, “Adaptive neural networks-based integral sliding mode control for TS fuzzy model of delayed nonlinear systems,” Applied Mathematics and Computation, vol. 450, p. 127983, 2023.
A. Zheng, Y. Huang, J. Na, and Q. Shi, “Adaptive neural identification and non-singular control of pure-feedback nonlinear systems,” ISA Transactions, vol. 144, pp. 409-418, 2024.
H. Feng et al., “A new adaptive sliding mode controller based on the RBF neural network for an electro-hydraulic servo system,” ISA Transactions, vol. 129, pp. 472–484, 2022.
N. V. Quan and N. N. Son, “Control of a DC–DC buck converter using adaptive neural network,” Electrical Engineering, 2024.
K. A. Sundari and P. Maruthupandi, “Optimal design of PID controller for the analysis of two-tank system using metaheuristic optimization algorithm,” Journal of Electrical Engineering & Technology, vol. 17, no. 1, pp. 627–640, 2022.
S. L. Narayanan, M. Kasiselvanathan, K. B. Gurumoorthy, and V. Kiruthika, “Particle swarm optimization based artificial neural network (PSO-ANN) model for effective k-barrier count intrusion detection system in WSN,” Measurement: Sensors, vol. 29, p. 100875, 2023.
T. Zong, J. Li, and G. Lu, “Auxiliary model-based multi-innovation PSO identification for Wiener–Hammerstein systems with scarce measurements,” Engineering Applications of Artificial Intelligence, vol. 106, p. 104470, 2021.
R. Cortez, R. Garrido, and E. Mezura-Montes, “Spectral richness PSO algorithm for parameter identification of dynamical systems under non-ideal excitation conditions,” Applied Soft Computing, vol. 128, p. 109490, 2022.
T. Zong, J. Li, and G. Lu, “Parameter estimation of multivariable Wiener nonlinear systems by the improved particle swarm optimization and coupling identification,” Information Sciences, vol. 661, p. 120192, 2024.
A. Tanveer and S. M. Ahmad, “High fidelity modeling and GA optimized control of yaw dynamics of a custom-built remotely operated unmanned underwater vehicle,” Ocean Engineering, vol. 266, p. 112836, 2022.
X.-Q. Zhang, Q. Cheng, W. Sun, Y. Zhao, and Z. Li, “Research on a TOPSIS energy efficiency evaluation system for crude oil gathering and transportation systems based on a GA-BP neural network,” Petroleum Science, vol. 21, no. 1, pp. 621–640, 2024.
Z. Ma, X. Li, and J. Sun, “A data-driven fault detection approach for unknown large-scale systems based on GA-SVM,” Information Sciences, vol. 658, p. 120023, 2024.
S. Chauhan, B. Singh, and M. Singh, “Modified ant colony optimization-based PID controller design for coupled tank system,” Engineering Research Express, vol. 3, no. 4, p. 045005, 2021.
A. G. K. R and S. Mahapatra, “Improving precision and robustness in level control of coupled tank systems: A tree seed optimization and μ-analysis approach,” Results in Control and Optimization, vol. 15, p. 100410, 2024.
R. V. Rao, “Rao algorithms: Three metaphor-less simple algorithms for solving optimization problems,” International Journal of Industrial Engineering Computations, vol. 11, no. 1, pp. 107–130, 2020.
S. Sahay, R. Upputuri, and N. Kumar, “Optimal power flow-based approach for grid dispatch problems through Rao algorithms,” Journal of Engineering Research, vol. 11, no. 2, p. 100032, 2023.
A. Farah, A. Belazi, F. Benabdallah, A. Almalaq, M. Chtourou, and M. A. Abido, “Parameter extraction of photovoltaic models using a comprehensive learning Rao-1 algorithm,” Energy Conversion and Management, vol. 252, p. 115057, 2022.
M. Ghasemi et al., “A new metaphor-less simple algorithm based on Rao algorithms: A fully informed search algorithm (FISA),” PeerJ Computer Science, vol. 9, p. e1431, 2023.
C. Van Kien, H. P. H. Anh, and N. N. Son, “Adaptive inverse multilayer fuzzy control for uncertain nonlinear system optimizing with differential evolution algorithm,” Applied Intelligence, vol. 51, no. 1, pp. 527–548, 2021.
C. D. Iweh and E. R. Akupan, “Control and optimization of a hybrid solar PV–hydro power system for off-grid applications using particle swarm optimization (PSO) and differential evolution (DE),” Energy Reports, vol. 10, pp. 4253–4270, 2023.
W. Deng, J. Xu, Y. Song, and H. Zhao, “Differential evolution algorithm with wavelet basis function and optimal mutation strategy for complex optimization problem,” Applied Soft Computing, vol. 100, p. 106724, 2021.
H. Zhang, Z. Gao, Y. Pan, G. Yang, W. J. (Chris) Zhang, and J. Wang, “A synergy of the adaptive whale optimization algorithm and differential evolution for abrupt motion tracking,” Applied Soft Computing, vol. 144, p. 110554, 2023.
S. Gao, K. Wang, S. Tao, T. Jin, H. Dai, and J. Cheng, “A state-of-the-art differential evolution algorithm for parameter estimation of solar photovoltaic models,” Energy Conversion and Management, vol. 230, p. 113784, 2021.
N. Li, H. Yang, W. Zhu, and C. Liu, “A novel grey decision-DE optimized internal model controller for vibration control of nonlinear uncertain aeroelastic blade system,” ISA Transactions, vol. 107, pp. 27–39, 2020.
N. N. Son, “Level control of quadruple tank system based on adaptive inverse evolutionary neural controller,” International Journal of Control, Automation and Systems, vol. 18, no. 9, pp. 2386–2397, 2020.
N. N. Son, H. P. H. Anh, and C. V. Kien, “Adaptive sliding mode control with hysteresis compensation-based neuro-evolution for motion tracking of piezoelectric actuator,” Applied Soft Computing, vol. 115, p. 108257, 2022.
M. Aicardi, A. Bozzi, S. Graffione, R. Sacile, and E. Zero, “Alternating direction method of multipliers in distributed control of a system of systems: Application to a quadruple tank plant,” Control Engineering Practice, vol. 149, p. 105972, 2024.
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