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 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.