A control approach for PDE dynamics in Li-ion batteries using differential flatness theory

It is proven that the PDE dynamics in Li-ion batteries satisfies differential flatness properties and this enables to solve the associate state estimation problem and to design a stabilizing feedback controller. First, by applying semi-discretization and the finite differences method the particles' diffusion PDE model is decomposed into an equivalent set of nonlinear coupled ODEs and a state-space description is obtained. Next, by defining specific state variables as virtual control inputs it is shown that each row of the state-space model is a differentially flat subsystem for which a feedback control law can be found that eliminates the output's tracking error. Moreover, by exploiting differential flatness properties the state estimation problem for the diffusion PDE model can be solved which consequently means that feedback control can be implemented with the use of a small number of measurements. It is shown that, being differentially flat, the state-space model of the PDE can be transformed to the canonical form and that state-estimation can be performed with the use of the Derivative-free nonlinear Kalman Filter.