% problem 3 of the mini project
% Prabir Barooah, March 20, 2009

clear all
%conversion: 
mph2mpersec = 0.44704; %m/sec

m = 1300; %kg
b = 42926.2; %N/volt
a = 150.91; %30.17; % N/m^2 s^2 

v_0 = 60*mph2mpersec;
theta_0 = a*v_0^2/b;


%% Linear plant
p= 2*a*v_0/m;
k = b/m;

P = tf(k,[1 p]);
time = [0:0.01:20]';
higherthan_tensec_points = find(time>=10);
tensec_point  =higherthan_tensec_points (1);
u = zeros(length(time),1);
u(tensec_point:end) = 0.3;

y = lsim(P,u,time);
v_linear_predict = v_0 + y;

%for running simulink model 'car_nonlinear'
theta_1 = theta_0;
theta_2 = theta_0+0.3;
% step time is already specified as 10 sec, so...
sim('car_nonlinear');

figure
ph = plot(tout,v,'r'); hold on;
ph2 = plot(time,v_linear_predict);
set(ph,'linewidth',2);
set(gca,'fontsize',18);
xlabel('t (sec)');
ylabel('v(m/s)');