(1) In this problem, you will implement Kalman filters to estimate the core-temperature of cylindrical batteries under unknown cooling conditions. As show in Fig. 1, three estimation approaches (an open-loop observer, a Kalman filter, and a dual Kalman filter) are included in DEKF_h_est_sin 2020.51x. Unzip the provided file Estimation_HW7.zip. The thermal dynamics of the considered cylindrical cell are based on the two-state thermal model as given by: dr -Az + Bu, y-Cx+Du where x = 5, u — [ġ T…]³ and y = (T. T.] are states, inputs and outputs respectively. System matrices A, B, C, and D are defined as follows: -48ah R(24k+ Rh) -150h 24k+Rh A- -320ah -120a(4k+Rh) R²(24k+ Rh) 48ah R²(24k+ Rh) a B- kVR(24k+Rh) 320ah 0 C- 24k+Rh R²(24k+ Rh) 24k-3Rh 120Rk,+15R²h 8(24k+ Rh) 24k 24k+Rh 15Rk 48k +2Rh 4Rh 0 D- 24k+ Rh Rh 0 24ks + Rh Since Kalman filters are to be implemented in the discrete-time domain, the dynamics are discretized via the forward Euler approxiamtion, resulting in the following system: 2+1 - Ash + Belt -Cz + Du where A-I+AAt and B₁ - BAt with a sampling time At. Using the Kalman filter algorithm provided in lecture slides, fill the blanks in the two Matlab function blocks: Thermal DEKF and Thermal KF. The file HW5 DEKF_init.m initializes the simulation including the thermal parameters of the considered battery, the initial values of state and parameter estimates, and loading measurement data. Submit a figure with three subplots showing the convection coefficient, core and surface temperature trajectories (vs. time) obtained from the submodules and actual data.

Fig: 1