state_space_1_vars.asv

% 1 RC parameters
R0 = .05;
R1 = .005;
C = 500;
Q = 3600;

% polynomail OCV linearization from homework
p_0 = 3.4707;
p_1 = 1.6112;
p_2 = -2.6287; 
p_3 = 1.7175;

% from project OCV(SOC) fit
p_0_2 = 3.64021760674922;
p_1_2 = 0.168800688918405;
p_2_2 = 0.951263116462285;
p_3_2 = -0.547527330994019;

% linearization test
z_vec = linspace(0, 1, 100);
ocv_nl = p_0 + p_1 * z_vec + p_2 * z_vec.^2 + p_3 * z_vec.^3;
ocv_nl_2 = p_0_2 + p_1_2 * z_vec + p_2_2 * z_vec.^2 + p_3_2 * z_vec.^3;
y_eq = (p_0 + .5 * p_1 + .25 * p_2 + .125 * p_3);
dy_dz_mult = (p_1 + p_2 + 3/4 * p_3) * -0.5;
ocv_lin = (p_1 + p_2 + 3/4 * p_3) .* z_vec + y_eq + dy_dz_mult;

plot(z_vec, ocv_nl, 'DisplayName', 'nl homework');
hold on
%plot(z_vec, ocv_nl_2, 'DisplayName', 'nl curve fit');
%hold on
plot(z_vec, ocv_lin, 'DisplayName', 'lin');
legend;

A_mat = [0, 0; 0, - 1 / (C*R1)];

B_mat = [1/Q; 1/C];

%C_mat = [1, 0; 0, 1; p_1 + p_2 + 3*p_3 / 4, 0];

C_mat = [1, 0; 0, 1; p_1 + p_2 + 3*p_3 / 4, 0; p_1 + p_2 + 3*p_3 / 4, 1];

D_dummy = [0; 0; 0; R0];

%C_mat = eye(2);

%D_dummy = [0;0];

% initial conditions
z0 = 0.5;
V_c0 = 0;
x0 = [z0, V_c0]; 

% 5th order poly
%p_5 = 20.9865358625928;
%p_4 = -52.9516197704481;
%p_3 = 48.7434451832868;
%p_2 = -19.7495647885364;
%p_1 = 3.74878321288425;
%p_0 = 3.28229043218463;