(3) Consider a Single Particle electrochemical model that predicts a battery cell voltage by including Li-ion diffusion dynamics in the positive and negative electrodes¹. The model is based on the following

paper: Di Domenico, D., Stefanopoulou, A. and Fiengo, G.; Lithium-ion battery state of charge and critical charge estimation using an electrochemical model-based extended Kalman filter, Journal of Dynamic Systems, Measurement and Control, vol. 132, no. 6, 2010. (i) Plot the positive and the negative equilibrium potentials, Up and Un, respectively, for the en- tire range of 0 ≤ SOC ≤ 1 using 0% and 100% normalized concentration values provided in run_model_skeleton.m. Un = 8.0029+ 5.0647x12.5782-0.5 8.632210-4-¹+2.176510-5³/2 -0.46016 exp(15.0(0.06 - x)) - 0.55364 exp(-2.4326(x - 0.92)) Up = -18.6000y³ +31.1854y² - 17.9895y + 7.4810 Cse.n Cs,max,n and y = Cse.p Cs,max.p where z = respectively. The figure should consist of two subplots; the first for Up and the second for Un, both plotted against SOC. Include your name in the title. are normalized concentration at negative and positive electrodes (ii) Fill in the blank system matrix equations in run_model_skeleton.m. Submit your code. (iii) Simulate the model using the input already in the HW3SP_model.mdl. Submit a plot of the resulting Cse,n and Csep in the following format. One figure with two subplots; first subplot charts Csep vs. time (in seconds), and the second plots Cse,n vs. time (in seconds). Include your name in the title.