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

A PID control method based on optimal control strategy

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.

Citation: Hong Niu, Zhijiang Feng, Qijin Xiao, Yajun Zhang. A PID control method based on optimal control strategy. Numerical Algebra, Control and Optimization, 2021, 11 (1) : 117-126. doi: 10.3934/naco.2020019
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. 

[2]

T. Y. ChaiY. J. ZhangH. WangC. 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. 

[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.

[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.

[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.

[6]

H. Y. LiY. N. PanP. 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. 

[7]

H. Y. LiP. 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.

[8]

Y. M. LiS. 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.

[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.

[10]

Y. J. LiuS. 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. 

[11]

S. C. TongT. 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.

[12]

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

[13]

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

[14]

Y. G. WangT. Y. ChaiJ. FuJ. 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. 

[15]

Y. J. ZhangY. JiaT. Y. ChaiD. 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. 

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. 

[2]

T. Y. ChaiY. J. ZhangH. WangC. 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. 

[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.

[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.

[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.

[6]

H. Y. LiY. N. PanP. 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. 

[7]

H. Y. LiP. 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.

[8]

Y. M. LiS. 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.

[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.

[10]

Y. J. LiuS. 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. 

[11]

S. C. TongT. 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.

[12]

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

[13]

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

[14]

Y. G. WangT. Y. ChaiJ. FuJ. 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. 

[15]

Y. J. ZhangY. JiaT. Y. ChaiD. 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. 

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