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

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 to 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. Copyright © 2007 John Wiley & Sons, Ltd.