Differential equation approximation and enhancing control method for finding the PID gain of a quarter-car suspension model with state-dependent ODE

H. W.J. Lee; Y. C.E. Lee; Kar Hung Wong; Kok Lay Teo

doi:10.3934/JIMO.2019055

Differential equation approximation and enhancing control method for finding the PID gain of a quarter-car suspension model with state-dependent ODE

H. W.J. Lee, Y. C.E. Lee, Kar Hung Wong, Kok Lay Teo

Research output: Journal article publication › Journal article › Academic research › peer-review

2 Citations (Scopus)

Abstract

Active suspension control strategy design in vehicle suspension systems has been a popular issue in road vehicle applications. In this paper, we consider a quarter-car suspension problem. A nonlinear objective function together with a system of state-dependent ODEs is involved in the model. A differential equation approximation method, together with the control parametrization enhancing transform (CPET), is used to find the optimal proportional-integral-derivative (PID) feedback gains of the above model. Hence, an approximated optimal control problem is obtained. Proofs of convergences of the state and the optimal control of the approximated problem to those of the original optimal control problem are provided. A numerical example is solved to illustrate the efficiency of our method.

Original language	English
Pages (from-to)	2305-2330
Number of pages	26
Journal	Journal of Industrial and Management Optimization
Volume	16
Issue number	5
DOIs	https://doi.org/10.3934/JIMO.2019055
Publication status	Published - Sep 2020

Keywords

Car suspension
Control parametrization enhancing technique
Differential equation approximations
Optimal control
PID controllers
Time-varying feedback gains

ASJC Scopus subject areas

Business and International Management
Strategy and Management
Control and Optimization
Applied Mathematics

More information

10.3934/JIMO.2019055

Cite this

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title = "Differential equation approximation and enhancing control method for finding the PID gain of a quarter-car suspension model with state-dependent ODE",

abstract = "Active suspension control strategy design in vehicle suspension systems has been a popular issue in road vehicle applications. In this paper, we consider a quarter-car suspension problem. A nonlinear objective function together with a system of state-dependent ODEs is involved in the model. A differential equation approximation method, together with the control parametrization enhancing transform (CPET), is used to find the optimal proportional-integral-derivative (PID) feedback gains of the above model. Hence, an approximated optimal control problem is obtained. Proofs of convergences of the state and the optimal control of the approximated problem to those of the original optimal control problem are provided. A numerical example is solved to illustrate the efficiency of our method.",

keywords = "Car suspension, Control parametrization enhancing technique, Differential equation approximations, Optimal control, PID controllers, Time-varying feedback gains",

author = "Lee, {H. W.J.} and Lee, {Y. C.E.} and Wong, {Kar Hung} and Teo, {Kok Lay}",

note = "Funding Information: Acknowledgments. The authors would like to thank three referees for their valuable comments and suggestions. This research was supported by the General Research Fund (Project no. G. YBCM) of the Research Grants Council, Hong Kong. Funding Information: The authors would like to thank three referees for their valuable comments and suggestions. This research was supported by the General Research Fund (Project no. G. YBCM) of the Research Grants Council, Hong Kong. Publisher Copyright: {\textcopyright} 2020 American Institute of Mathematical Sciences.",

year = "2020",

month = sep,

doi = "10.3934/JIMO.2019055",

language = "English",

volume = "16",

pages = "2305--2330",

journal = "Journal of Industrial and Management Optimization",

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publisher = "American Institute of Mathematical Sciences",

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Differential equation approximation and enhancing control method for finding the PID gain of a quarter-car suspension model with state-dependent ODE. / Lee, H. W.J.; Lee, Y. C.E.; Wong, Kar Hung; Teo, Kok Lay.

In: Journal of Industrial and Management Optimization, Vol. 16, No. 5, 09.2020, p. 2305-2330.

Research output: Journal article publication › Journal article › Academic research › peer-review

TY - JOUR

T1 - Differential equation approximation and enhancing control method for finding the PID gain of a quarter-car suspension model with state-dependent ODE

AU - Lee, H. W.J.

AU - Lee, Y. C.E.

AU - Wong, Kar Hung

AU - Teo, Kok Lay

N1 - Funding Information: Acknowledgments. The authors would like to thank three referees for their valuable comments and suggestions. This research was supported by the General Research Fund (Project no. G. YBCM) of the Research Grants Council, Hong Kong. Funding Information: The authors would like to thank three referees for their valuable comments and suggestions. This research was supported by the General Research Fund (Project no. G. YBCM) of the Research Grants Council, Hong Kong. Publisher Copyright: © 2020 American Institute of Mathematical Sciences.

PY - 2020/9

Y1 - 2020/9

N2 - Active suspension control strategy design in vehicle suspension systems has been a popular issue in road vehicle applications. In this paper, we consider a quarter-car suspension problem. A nonlinear objective function together with a system of state-dependent ODEs is involved in the model. A differential equation approximation method, together with the control parametrization enhancing transform (CPET), is used to find the optimal proportional-integral-derivative (PID) feedback gains of the above model. Hence, an approximated optimal control problem is obtained. Proofs of convergences of the state and the optimal control of the approximated problem to those of the original optimal control problem are provided. A numerical example is solved to illustrate the efficiency of our method.

AB - Active suspension control strategy design in vehicle suspension systems has been a popular issue in road vehicle applications. In this paper, we consider a quarter-car suspension problem. A nonlinear objective function together with a system of state-dependent ODEs is involved in the model. A differential equation approximation method, together with the control parametrization enhancing transform (CPET), is used to find the optimal proportional-integral-derivative (PID) feedback gains of the above model. Hence, an approximated optimal control problem is obtained. Proofs of convergences of the state and the optimal control of the approximated problem to those of the original optimal control problem are provided. A numerical example is solved to illustrate the efficiency of our method.

KW - Car suspension

KW - Control parametrization enhancing technique

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KW - Time-varying feedback gains

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Differential equation approximation and enhancing control method for finding the PID gain of a quarter-car suspension model with state-dependent ODE

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