American Institute of Mathematical Sciences

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March  2021, 11(1): 117-126. doi: 10.3934/naco.2020019

A PID control method based on optimal control strategy

Hong Niu 1,, , Zhijiang Feng 1, , Qijin Xiao 1, and  Yajun Zhang 2,

1. 

College of Science, Liaoning Shihua University, Fushun Liaoning, 113001, China
2. 

State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang Liaoning 110819, China

* Corresponding author: Hong Niu

Received  May 2019 Revised  October 2019 Published  March 2021 Early access  March 2020

Fund Project: This paper is supported by the National Natural Science Foundation of China (61603168, 61773107, 61866021, 61890923) and CSC (201808210410)

A PID control method which combined optimal control strategy is proposed in this paper. The posterior unmodeled dynamics measurement data information are made full use to compensate the unknown nonlinearity of the system, and the unknown increment of the unmodeled dynamics is estimated. Then, a nonlinear PID controller with compensation of the posterior unmodeled dynamics measurement data and the estimation of the increment of the unmodeled dynamics is designed. Finally, through the numerical simulation, the effectiveness of the proposed method is vertified.

Keywords: Nonlinear system, PID, Unmodeled dynamics, Data.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.
Citation: Hong Niu, Zhijiang Feng, Qijin Xiao, Yajun Zhang. A PID control method based on optimal control strategy. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 117-126. doi: 10.3934/naco.2020019
References:
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T. Y. Chai, Y. J. Zhang, H. Wang, C. Y. Su and J. Sun, Data based virtual un-modeled dynamics driven multivariable nonlinear adaptive switching control, IEEE Transactions on Neural Networks, 22 (2011), 2154-2171.   Google Scholar

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L. J. Chen and K. S. Narendra, Nonlinear adaptive control using neural networks and multiple models, Automatica, 37 (2001), 1245-1255.  doi: 10.1016/S0005-1098(01)00072-3.  Google Scholar

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Y. Fu and T. Y. Chai, Nonlinear multivariable adaptive control using multiple models and neural networks, Automatica, 43 (2017), 1101-1110.  doi: 10.1016/j.automatica.2006.12.010.  Google Scholar

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H. Y. Li, Y. N. Pan, P. Shi and Y. Shi, Switched fuzzy output feedback control and its application to a mass Cspring Cdamping system, IEEE Trans. Fuzzy Syst., 24 (2016), 1259-1269.   Google Scholar

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H. Y. Li, P. Shi and D. Y. Yao, Adaptive sliding-mode control of markov jump nonlinear systems with actuator faults, IEEE Trans. Autom. Control, 62 (2017), 1933-1939.  doi: 10.1109/TAC.2016.2588885.  Google Scholar

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Y. M. Li, S. Sui and S. C. Tong, Adaptive fuzzy control design for stochastic nonlinear switched systems with arbitrary switching and unmodeled dynamics, IEEE Trans. Cybern, 47 (2017), 403-414.  doi: 10.1007/s00034-015-0196-0.  Google Scholar

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Y. M. Li and S. C. Tong, Adaptive fuzzy output-feedback stabilization control for a class of switched nonstrict-feedback nonlinear systems, IEEE Trans. Cybern, 47 (2017), 1007-1016.  doi: 10.1007/s00034-015-0196-0.  Google Scholar

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Y. J. Liu, S. C. Tong and C. L. Philip Chen, Adaptive fuzzy control via observer design for uncertain nonlinear systems with unmodeled dynamics, IEEE Trans. Fuzzy Syst., 21 (2013), 275-288.   Google Scholar

[11]

S. C. Tong, T. Wang and Y. M. Li, Fuzzy adaptive actuator failure compensation control of uncertain stochastic nonlinear systems with un-modeled dynamics, IEEE Trans. Cybern, 44 (2014), 910-921.  doi: 10.1109/TAC.2013.2287115.  Google Scholar

[12]

L. X. Wang, A Course in Fuzzy Systems and Control [M], Pearson Education, 2003. doi: 10.1007/978-1-4612-0873-0.  Google Scholar

[13]

L. X. Wang, Fuzzy systems are universal approximators, , IEEE International Conference on Fuzzy Systems, San Diego, (1992), 1163–1170. Google Scholar

[14]

Y. G. Wang, T. Y. Chai, J. Fu, J. Sun and H. Wang, Adaptive decoupling switching control of the forced-circulation evaporation system using neural networks, IEEE Transactions on Control Systems Technology, 21 (2013), 964-974.   Google Scholar

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Y. J. Zhang, Y. Jia, T. Y. Chai, D. H. Wang and W. Dai, Data-driven PID controller and its application to pulp neutralization process, IEEE Transactions on Control Systems Technology, 26 (2018), 828-841.   Google Scholar

show all references

References:
[1]

T. Y. Chai and Y. J. Zhang, Nonlinear adaptive switching control method based on un-modeled dynamics compensation, Acta Automatica Sinica, 37 (2010), 773-786.   Google Scholar

[2]

T. Y. Chai, Y. J. Zhang, H. Wang, C. Y. Su and J. Sun, Data based virtual un-modeled dynamics driven multivariable nonlinear adaptive switching control, IEEE Transactions on Neural Networks, 22 (2011), 2154-2171.   Google Scholar

[3]

L. J. Chen and K. S. Narendra, Nonlinear adaptive control using neural networks and multiple models, Automatica, 37 (2001), 1245-1255.  doi: 10.1016/S0005-1098(01)00072-3.  Google Scholar

[4]

Y. Fu and T. Y. Chai, Nonlinear multivariable adaptive control using multiple models and neural networks, Automatica, 43 (2017), 1101-1110.  doi: 10.1016/j.automatica.2006.12.010.  Google Scholar

[5]

J. S. R. JANG, ANFIS: Adaptive-network-based fuzzy inference system, IEEE Trans on System, Man, Cybernetics, 23 (1993), 665-685.  doi: 10.1109/TSMC.1972.5408561.  Google Scholar

[6]

H. Y. Li, Y. N. Pan, P. Shi and Y. Shi, Switched fuzzy output feedback control and its application to a mass Cspring Cdamping system, IEEE Trans. Fuzzy Syst., 24 (2016), 1259-1269.   Google Scholar

[7]

H. Y. Li, P. Shi and D. Y. Yao, Adaptive sliding-mode control of markov jump nonlinear systems with actuator faults, IEEE Trans. Autom. Control, 62 (2017), 1933-1939.  doi: 10.1109/TAC.2016.2588885.  Google Scholar

[8]

Y. M. Li, S. Sui and S. C. Tong, Adaptive fuzzy control design for stochastic nonlinear switched systems with arbitrary switching and unmodeled dynamics, IEEE Trans. Cybern, 47 (2017), 403-414.  doi: 10.1007/s00034-015-0196-0.  Google Scholar

[9]

Y. M. Li and S. C. Tong, Adaptive fuzzy output-feedback stabilization control for a class of switched nonstrict-feedback nonlinear systems, IEEE Trans. Cybern, 47 (2017), 1007-1016.  doi: 10.1007/s00034-015-0196-0.  Google Scholar

[10]

Y. J. Liu, S. C. Tong and C. L. Philip Chen, Adaptive fuzzy control via observer design for uncertain nonlinear systems with unmodeled dynamics, IEEE Trans. Fuzzy Syst., 21 (2013), 275-288.   Google Scholar

[11]

S. C. Tong, T. Wang and Y. M. Li, Fuzzy adaptive actuator failure compensation control of uncertain stochastic nonlinear systems with un-modeled dynamics, IEEE Trans. Cybern, 44 (2014), 910-921.  doi: 10.1109/TAC.2013.2287115.  Google Scholar

[12]

L. X. Wang, A Course in Fuzzy Systems and Control [M], Pearson Education, 2003. doi: 10.1007/978-1-4612-0873-0.  Google Scholar

[13]

L. X. Wang, Fuzzy systems are universal approximators, , IEEE International Conference on Fuzzy Systems, San Diego, (1992), 1163–1170. Google Scholar

[14]

Y. G. Wang, T. Y. Chai, J. Fu, J. Sun and H. Wang, Adaptive decoupling switching control of the forced-circulation evaporation system using neural networks, IEEE Transactions on Control Systems Technology, 21 (2013), 964-974.   Google Scholar

[15]

Y. J. Zhang, Y. Jia, T. Y. Chai, D. H. Wang and W. Dai, Data-driven PID controller and its application to pulp neutralization process, IEEE Transactions on Control Systems Technology, 26 (2018), 828-841.   Google Scholar

Figure 1.  Performance of proposed PID control mehtod (Output $ y $, Reference Input $ w $)
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Figure 2.  The controller $ u $
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Figure 3.  The estimation of unmodelled dynamics
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Figure 4.  The estimation error
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