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 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 & 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.   Google Scholar

[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.   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. 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.   Google Scholar

[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.  Google Scholar

[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.  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. 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.   Google Scholar

[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.  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. 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.   Google Scholar

[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.   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. 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.   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. 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.   Google Scholar

[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.  Google Scholar

[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.  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. 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.   Google Scholar

[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.  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. 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.   Google Scholar

[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.   Google Scholar

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
[1]

Shigui Ruan. Nonlinear dynamics in tumor-immune system interaction models with delays. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 541-602. doi: 10.3934/dcdsb.2020282

[2]

Neng Zhu, Zhengrong Liu, Fang Wang, Kun Zhao. Asymptotic dynamics of a system of conservation laws from chemotaxis. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 813-847. doi: 10.3934/dcds.2020301

[3]

Van Duong Dinh. Random data theory for the cubic fourth-order nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020284

[4]

Manil T. Mohan. First order necessary conditions of optimality for the two dimensional tidal dynamics system. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020045

[5]

Sze-Bi Hsu, Yu Jin. The dynamics of a two host-two virus system in a chemostat environment. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 415-441. doi: 10.3934/dcdsb.2020298

[6]

Abdelghafour Atlas, Mostafa Bendahmane, Fahd Karami, Driss Meskine, Omar Oubbih. A nonlinear fractional reaction-diffusion system applied to image denoising and decomposition. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020321

[7]

Riadh Chteoui, Abdulrahman F. Aljohani, Anouar Ben Mabrouk. Classification and simulation of chaotic behaviour of the solutions of a mixed nonlinear Schrödinger system. Electronic Research Archive, , () : -. doi: 10.3934/era.2021002

[8]

José Luis López. A quantum approach to Keller-Segel dynamics via a dissipative nonlinear Schrödinger equation. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020376

[9]

Xin Zhao, Tao Feng, Liang Wang, Zhipeng Qiu. Threshold dynamics and sensitivity analysis of a stochastic semi-Markov switched SIRS epidemic model with nonlinear incidence and vaccination. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2021010

[10]

Youshan Tao, Michael Winkler. Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 439-454. doi: 10.3934/dcds.2020216

[11]

Karoline Disser. Global existence and uniqueness for a volume-surface reaction-nonlinear-diffusion system. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 321-330. doi: 10.3934/dcdss.2020326

[12]

Michiel Bertsch, Danielle Hilhorst, Hirofumi Izuhara, Masayasu Mimura, Tohru Wakasa. A nonlinear parabolic-hyperbolic system for contact inhibition and a degenerate parabolic fisher kpp equation. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3117-3142. doi: 10.3934/dcds.2019226

[13]

Masaru Hamano, Satoshi Masaki. A sharp scattering threshold level for mass-subcritical nonlinear Schrödinger system. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1415-1447. doi: 10.3934/dcds.2020323

[14]

Vo Van Au, Mokhtar Kirane, Nguyen Huy Tuan. On a terminal value problem for a system of parabolic equations with nonlinear-nonlocal diffusion terms. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1579-1613. doi: 10.3934/dcdsb.2020174

[15]

Paul E. Anderson, Timothy P. Chartier, Amy N. Langville, Kathryn E. Pedings-Behling. The rankability of weighted data from pairwise comparisons. Foundations of Data Science, 2021  doi: 10.3934/fods.2021002

[16]

Xin Guo, Lei Shi. Preface of the special issue on analysis in data science: Methods and applications. Mathematical Foundations of Computing, 2020, 3 (4) : i-ii. doi: 10.3934/mfc.2020026

[17]

Anna Anop, Robert Denk, Aleksandr Murach. Elliptic problems with rough boundary data in generalized Sobolev spaces. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020286

[18]

Haruki Umakoshi. A semilinear heat equation with initial data in negative Sobolev spaces. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 745-767. doi: 10.3934/dcdss.2020365

[19]

Marion Darbas, Jérémy Heleine, Stephanie Lohrengel. Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations. Inverse Problems & Imaging, 2020, 14 (6) : 1107-1133. doi: 10.3934/ipi.2020056

[20]

Bao Wang, Alex Lin, Penghang Yin, Wei Zhu, Andrea L. Bertozzi, Stanley J. Osher. Adversarial defense via the data-dependent activation, total variation minimization, and adversarial training. Inverse Problems & Imaging, 2021, 15 (1) : 129-145. doi: 10.3934/ipi.2020046

 Impact Factor: 

Metrics

  • PDF downloads (97)
  • HTML views (392)
  • Cited by (0)

Other articles
by authors

[Back to Top]