Problem Set-1 c Week 11Challenge : Transient Handling

%Passenger Car Values
M=2000*0.45;
Mf=0.65*M;
Mr=0.35*M;
Iz=1128;
L=8.33*0.304;
a=2.92*0.304;
b=L-a;

u=20;

Cf=13752*4.45; % Converting to N/rad
Cr=11460*4.45;

%Race Car Values
RM=1719*0.45;
RMf=0.4*RM;
RMr=0.6*RM;

RIz=865;
RL=9.52*0.304;
Ra=5.71*0.304;
Rb=RL-Ra;

RCf=62228*4.45; %Converting to N/rad
RCr=96608*4.45;

%Calculating Yaw and lateral force Terms for Passenger Car
Nd=Cf
Nr=(a^2*Cf+b^2*Cr)/u;
Nb=a*Cf-b*Cr;
Yd=Cf;
Yr=(a*Cf-b*Cr)/u;
Yb=Cf+Cr;

%Calculating Yaw and lateral force Terms for Race Car
RNdel=RCf
RNr=(Ra^2*RCf+Rb^2*RCr)/u;
RNb=Ra*RCf-Rb*RCr;
RYd=RCf;
RYr=(Ra*RCf-Rb*RCr)/u;
RYb=RCf+RCr;

%Passesger Car
A=[-(Cf+Cr)/(M*u), (b*Cr-a*Cf)/(M*u)-u
(b*Cr-a*Cf)/(Iz*u), -(a^2*Cf+b^2*Cr)/(Iz*u)];

B=[Cf/M; a*Cf/Iz];

C_lat=[1 0]; D_lat=0;
C_yaw=[0 1]; D_yaw=0;
C_acc=A(1,:)+u*[0,1]; D_acc=(1);

C=[C_lat;C_yaw;C_acc];
D=[D_lat;D_yaw;D_acc];

t=[0:0.01:6];
U=(5*pi/180)*sin(2*pi*7*t); % 5 degree steering at 7 Hz

sys=ss(A,B,C,D);

Y=lsim(sys,U,t);

sys.inputname={'Steering'};
sys.outputname={'Lateral';'Yaw';'Acceleration'};

(mag,W)=bodemag(sys({'Yaw'}, 'Steering'));

step(sys);

subplot(2,2,1)
plot(t,Y(:,1));
title('Lateral Speed')

subplot(2,2,2)
plot(t,Y(:,2));
title('Yaw Rate')

subplot(2,2,3)
plot(t,Y(:,3));
title('Lateral Acceleration')

%Race Car
RA=[-(RCf+RCr)/(RM*u), (Rb*Cr-Ra*Cf)/(RM*u)-u
(Rb*RCr-Ra*RCf)/(RIz*u), -(Ra^2*RCf+Rb^2*RCr)/(RIz*u)];

RB=[RCf/RM; Ra*RCf/RIz];

RC_lat=[1 0]; RD_lat=0;
RC_yaw=[0 1]; RD_yaw=0;
RC_acc=RA(1,:)+u*[0,1]; RD_acc=(1);

RC=[RC_lat;RC_yaw;RC_acc];
RD=[RD_lat;RD_yaw;RD_acc];

t=[0:0.01:6];
RU=(5*pi/180)*sin(2*pi*7*t); % 5 degree steering at 7 Hz

Rsys=ss(RA,RB,RC,RD);

RY=lsim(Rsys,RU,t);

Rsys.inputname={'Steering'};
Rsys.outputname={'Lateral';'Yaw';'Acceleration'};

(Rmag,RW)=bodemag(sys({'Yaw'}, 'Steering'));

step(Rsys);

subplot(2,2,1)
plot(t,RY(:,1));
title('Lateral Speed')

subplot(2,2,2)
plot(t,RY(:,2));
title('Yaw Rate')

subplot(2,2,3)
plot(t,RY(:,3));
title('Lateral Acceleration')