To address the challenge of achieving unified control across diverse nonlinear systems, a comprehensive control theory spanning from PID (Proportional-Integral-Derivative) to ACPID (Auto-Coupling PID) has been proposed. The primary concept is to unify all intricate factors, including internal dynamics and external bounded disturbance, into a single total disturbance. This enables the mapping of various nonlinear systems onto a linear disturbance system. Based on the theory of PID control and the characteristic equation of a critically damping system, Zeng’s stabilization rules (ZSR) and an ACPID control force based on a single speed factor have been designed. ACPID control theory is both simple and practical, with significant scientific significance and application value in the field of control engineering.
Ziegler, J.G. and Nichols, N.B. (1942) Optimum Settings for Automatic Controllers. Transaction of ASME , 64, 759-765. https://doi.org/10.1115/1.4019264
Ho, W.K., Lim, K.W. and Xu, W. (1998) Optimal Gain and Phase Margin Tuning for PID Controllers. Automatica , 34, 1009-1014. https://doi.org/10.1016/s0005-1098(98)00032-6
Wang, Q., Zou, B., Lee, T. and Bi, Q. (1997) Auto-Tuning of Multivariable PID Controllers from Decentralized Relay Feedback. Automatica , 33, 319-330. https://doi.org/10.1016/s0005-1098(96)00177-x
Shen, J., Xin, B., Cui, H. and Gao, W. (2017) Control of Single-Axis Rotation INS by Tracking Differentiator Based Fuzzy PID. IEEE Transactions on Aerospace and Electronic Systems , 53, 2976-2986. https://doi.org/10.1109/taes.2017.2722558
Wu, X., Qin, G., Sun, M., Yu, H. and Xu, Q. (2017) Using Improved Particle Swarm Optimization to Tune PID Controllers in Cooperative Collision Avoidance Systems. Frontiers of Information Technology & Electronic Engineering , 18, 1385-1395. https://doi.org/10.1631/fitee.1601427
Hanifah, R.A., Toha, S.F., Ahmad, S. and Hassan, M.K. (2018) Swarm-Intelligence Tuned Current Reduction for Power-Assisted Steering Control in Electric Vehicles. IEEE Transactions on Industrial Electronics , 65, 7202-7210. https://doi.org/10.1109/tie.2017.2784344
Marin, A., Hernandez R., J.A. and Jimenez, J.A. (2018) Tuning Multivariable Optimal PID Controller for a Continuous Stirred Tank Reactor Using an Evolutionary Algorithm. IEEE Latin America Transactions , 16, 422-427. https://doi.org/10.1109/tla.2018.8327395
Zeng, Z.Z., Xiao, Y.F. and Hao, Y.X. (2012) Nonlinear PID-Like Neuron Network Controller. Journal of University of Science and Technology Beijing , 34, 12-15.
Li, G.M. and Zeng, Z.Z. (2010) A Nonlinear PID Controller Based on Neural Net-Work Algorithm. Journal of Central South University , 41, 1865-1870.
Guo, C. (2018) Mold Level Control of Large Size Ingot Based on Fuzzy Self-Tuning PID. Journal of Mechanical Engineering , 54, 212.
Dong, L.H. and Zhao, P.B. (2013) Grey Predictive PID Control of the Tensioning Device System in Belt Conveyor. Journal of China Coal Society , 38, 342-347.
Zhao, J.S., Zhang, Y., Cao, X.M., et al . (2016) Multi-PID Controller Parameters Optimization of Fast Forging Hydraulic Press Based on GA. Journal of Central South University , 47, 2650-2660.
Chen, L.Q., Tan, Y.D., Wu, R., et al . (2017) Torque Distribution Control Strategy of Electronically Controlled Four-Wheel Drive Axle Based on Genetic Algorithm. Journal of Agricultural Machinery , 48, 361-367.
Wang, J. and Kumbasar, T. (2020) Optimal PID Control of Spatial Inverted Pendulum with Big Bang-Big Crunch Optimization. IEEE / CAA Journal of Automatica S i nica , 7, 822-832. https://doi.org/10.1109/jas.2018.7511267
Zeng, Z.Z. and Chen, Z.Y. (2020) On Control Theory of PID and Auto-Coupling PID. Control Theory & Applications , 37, 2654-2662.
Zeng, Z.Z. (2022) Necessity of Correcting Dimensionless Proportional Gain and Its Improvement Strategy. Control Engineering of China , 29, 1387-1394.
Zeng, Z.Z. (2023) ACPI Control Theory. International Journal of Engineering and Science Invention , 12, 39-47.
Zeng, Z.Z. and Liu W.J. (2019) Wisdom PI Control for First-Order Systems with Time-Delay. Control Theory & Applications , 36, 1322-1328.
Cheng T., Zeng, Z.Z., Du X.F., et al . (2019) Predictive Self-Coupling PI Control Method for Large Time-Delay Systems. Information and Control , 48, 672-677.
Wang W., Zeng, Z.Z. and Zhang Z.H. (2023) Auto-Coupling PID Control Method for Delay Weakening of First Order Systems with Large Time Delays. Control E n gineering of China .
Wang, F.Q., Zeng, Z.Z., Cheng, T., et al . (2021) Auto-Coupling PID Control Method for Strict Feedback Nonlinear Uncertain Systems. Control Engineering of China , 28, 971-978.
Su, J. and Zeng, Z.Z. (2021) Maximum Power Point Tracking Based on Auto-Coupling PI Control for a Wind Power Generation System. Power System Pr o tection and Control , 49, 119-127.
Su, J. and Zeng, Z.Z. (2022) Auto-Coupling PID Control Method for Nonlinear Time Varying Systems. Control Theory & Applications , 39, 299-306.
Bai, J.Z. and Zeng, Z.Z. (2022) States Adjust of Continuous Stirred Tank Reactor by Auto-Coupling Proportional-Integral-Differential Control. Control Theory & A p plications , 39, 1065-1070.
Chen, L.Q. and Zeng, Z.Z. (2022) Trajectory Tracking Control of Three-Link Manipulator Based on Auto-Coupling PID. Aerospace Control and Application , 48, 70-77.
Xu, H.Q., Zeng, Z.Z. and Chen, Z.Y. (2022) An ACPI Control Method for High-Order Nonlinear Unknown System. Electronics Optics ＆ Control , 29, 42-46.
Cheng, Q.Z., Zeng, Z.Z., Cheng, T., et al . (2022) Auto-Coupling PD Cooperative Control Method for Unknown Nonlinear Systems. Control Engineering of China , 29, 1437-1442.
Liu, W.J. and Zeng, Z.Z. (2022) Auto-Coupling PID Control of Non-Affine Pure-Feedback Nonlinear System. Control Engineering of China , 29, 1264-1270.
Su, J., Zeng, Z.Z. and Xiong, Y.L. (2022) Auto-Coupling PID Cooperative Control Method for Synchronization of Uncertain Chaotic Systems. Control Engineering of China , 29, 1464-1472.
Ren, S.R. and Zeng, Z.Z. (2022) Auto-Coupling PI Guidance Law with Precision Terminal Guidance. Fire Control & Command Control , 47, 83-86.
Huang, D., Xu, H.Q., Zhuang, L., et al . (2022) ACPID Control Method of Unmatched Nonlinear Systems. Journal of Electric Power Science and Technology , 37, 222-228.
Xiong, Y.L., Zeng, Z.Z. and Wang, W. (2023) Auto-Coupling PID Control Method for Nonlinear Underactuated Unstable Systems. Aerospace Control and Applic a tion , 49, 82-89.
Zeng, P., Zeng, Z.Z. and Xiong, Y.L. (2023) Auto-Coupling PD Control of Chaotic Oscillation in a Seven-Dimensional Power System. Power System Protection and Con trol , 51, 13-20.
Zeng, P. and Zeng, Z.Z. (2023) Auto-Coupling PID Control of Flexible Transmission System with Sandwich Structure. Aerospace Control and Application , 49, 73-79.
Huang, L.R., Zeng, Z.Z. and Zeng, P. (2023) Auto-Coupling PID Control Method for Hydraulic Turbine Regulation System. Journal of Hydroelectric Engineering , 42, 80-88.
Zhang, C.Q., Zeng, Z.Z. and Wang, W. (2024) Control Method of Magnetic Levitation Ball System Based on ACPI. Journal of Railway Science and Engineering , 21, 1180-1188.
Zhang, Z.H., Zeng, Z.Z., Wang, W., et al . (2023) Auto-Coupling PID Anti-Swing Control Strategy for Underactuated Bridge Crane. Mechanical Science and Tec h nology for Aerospace Engineering .
Huang, L.R., Zeng, Z.Z. and Zhang, Z.H. (2023) Research on Auto-Coupling PID Control Strategy of Permanent Magnet Synchronous Motor Governing System. Mechanical Science and Technology for Aerospace Engineering .
Lu, Y.X., Zeng, Z.Z., Tang, L.J., et al . (2023) Research on a Self-Coupling PID Control Strategy for Reactor Core Power. Journal of Chinese Society of Power Eng i neering , 43, 1494-1499
Xiong, Y.L. and Zeng, Z.Z. (2024) Research on a Self-Coupling PID Control Strategy for an Underactuated TORA System. Control and Decision , 39, 853-860.
Zeng, Z.Z. and Zhang, Z.H. (2023) Auto-Coupling PID Control Method for Underactuated VTOL Aircraft. Aerospace Control and Application , 49, 38-46.
Zeng, P., Zeng, Z.Z. and Huang, L.R. (2024) Cascaded Self-Coupling PID Control of SCR Denitration System. Journal of Chinese Society of Power Engineering , 44, 84-90.
Huang, L.R., Zeng, Z.Z. and Zeng, P. (2024) Auto-Coupling PD Attitude Control Method for Flexible Spacecraft. Aerospace Control and Application , 50, 75-83.
Bechlioulis, C.P. and Rovithakis, G.A. (2009) Adaptive Control with Guaranteed Transient and Steady State Tracking Error Bounds for Strict Feedback Systems. Automatica , 45, 532-538. https://doi.org/10.1016/j.automatica.2008.08.012
Huang, X., Song, Y. and Lai, J. (2019) Neuro-Adaptive Control with Given Performance Specifications for Strict Feedback Systems under Full-State Constraints. IEEE Transactions on Neural Networks and Learning Systems , 30, 25-34. https://doi.org/10.1109/tnnls.2018.2821668
Wu, J.W., Liu, Y.H., Su, C.Y., et al . (2021) Adaptive Command Filtered Control of Strict Feedback Systems with Uncertain Control Gains. Acta Automatica Sinica , 50, 1015-1023.
Tong, S., Min, X. and Li, Y. (2020) Observer-Based Adaptive Fuzzy Tracking Control for Strict-Feedback Nonlinear Systems with Unknown Control Gain Functions. IEEE Transactions on Cybernetics , 50, 3903-3913. https://doi.org/10.1109/tcyb.2020.2977175
Qiu, J., Sun, K., Wang, T. and Gao, H. (2019) Observer-Based Fuzzy Adaptive Event-Triggered Control for Pure-Feedback Nonlinear Systems with Prescribed Performance. IEEE Transactions on Fuzzy Systems , 27, 2152-2162. https://doi.org/10.1109/tfuzz.2019.2895560
Fan, B., Yang, Q., Jagannathan, S. and Sun, Y. (2019) Output-Constrained Control of Nonaffine Multiagent Systems with Partially Unknown Control Directions. IEEE Transactions on Automatic Control , 64, 3936-3942. https://doi.org/10.1109/tac.2019.2892391
Zhang, Y., Wen, C.Y. and Soh, Y.C. (2000) Discrete-Time Robust Backstepping Adaptive Control for Nonlinear Time-Varying Systems. IEEE Transactions on A u tomatic Control , 45, 1749-1755. https://doi.org/10.1109/9.880641
Zeng, Z.Z., Wu, L.D., Yang, Z.Y., et al . (2016) Self-Learning Sliding-Mode Disturbance Rejection Control for Non-Affine Systems. Control Theory & Applications , 33, 980-987.