Nonlinear optimal control of washing machine based on approximate solution of HJB equation

Rasoul M. Milasi, Mohammad Javad Yazdanpanah, Caro Lucas

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Performance of a washing machine depends on different parameters, namely water temperature, degree of soiling, water volume, and motor speed. In this paper, firstly, a nonlinear model is derived based on the empirical data. In addition, validity of the proposed model is also verified. Secondly, to optimize the performance, a quadratic energy function is considered, which is minimized subject tcj'the nonlinear model of the Washing Machine. Finding the corresponding control law requires solving a partial differential equation called Hamiltonian-Jacobi-Bellman (HJB) equation. An approximate solution for HJB equation using the second-, third-, and fourth-order terms of Taylor's series expansion is utilized. Simulation results reveal that the higher-order controller leads not only to a lower cost function but also to a better performance.

Original languageEnglish (US)
Pages (from-to)1-18
Number of pages18
JournalOptimal Control Applications and Methods
Issue number1
StatePublished - Jan 2008

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Software
  • Control and Optimization
  • Applied Mathematics


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