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 publicationJournal articleAcademic researchpeer-review

2 Citations (Scopus)


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 languageEnglish
Pages (from-to)2305-2330
Number of pages26
JournalJournal of Industrial and Management Optimization
Issue number5
Publication statusPublished - Sep 2020


  • 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

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