(2) In this problem, you are asked to develop two battery models based on the given data. The test data available to you are in the file: HW2_P2_Data.mat including two data

sets: Chg1_1 (denoting test data during a charging event) and Dis1_1 (denoting test data during a discharging event). Each set has 4 columns: time (sec), current (A), terminal voltage (V) and SOC (between 0 and 1). The sign convention of the current signal follows standard industry practice, and a positive current denotes a discharging event. (i) Build the "battery voltage model" in the form of Vt.k = Ko - Rolk where Vt, and I denote the battery voltage and the battery current at time step k. You need to identify the two battery model parameters Ko and Ro. The identification should be done in the sense of least square (for the whole test data). The least square solution can be solved using pseudo inverse. • Report your identified model parameters {Ko Ro} for charging and discharging, separately. • Provide a figure with two subplots showing the measured and estimated (by your model) battery voltage vs. time in the top subplot and the error between the measured and estimated voltages in the bottom subplot. • Attach your Matlab codes (ii) Repeat part (i), except that you use a more complicated model structure: V = Ko-K₁/2k - K2²k + K3 ln (zk) + K4 ln (1 – zk) — R₂Ik • Report your identified model parameters Ko,..., K4, R.} for charging and discharging, sepa- rately. • Provide a plot showing the measured and estimated (by your model) battery voltage vs. time. • Attach your Matlab codes