On observer performance for an electrochemical supercapacitor model

In this paper, the implementation of an observer with an electrochemical supercapacitor model is discussed. Using Lie derivatives, the model was shown to be locally nonlinear observable. When the two transference numbers, related to ion mobility, were selected to be equal, the model became linear and the states relating to ionic concentration became unobservable. These unobservable states were shown to not satisfy the weaker detectability condition. The energy storage characteristic of supercapacitors meant that they incorporated integrator dynamics and this led to random walk trajectories with a Kalman filter implementation. This problem could be corrected by using a more suitable observer or by introducing a control system such that the model becomes asymptotically stable. The comments on observer performance made in this paper could be applied to more complex electrochemical models, such as those for Lithium ion batteries, as they use many similar physical relationships.