Hi, my current code is written for time responses using the lsim function but it needs to be converted to ode45 and i have no idea where to start. Here's my current code with lsim, andy help would be appreciated!
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% Elevator deflection code
A=[-.045 .036 0 -32.2;-.369 -2.02 176 0;.0019 -.0396 -2.948 0;0 0 1 0];
B=[0;-28.17;-11.88;0];
C=eye(4);
D=[0;0;0;0];
values=eig(A);
T = 0:1:200;
U = ones(size(T));
sys = ss(A,B,C,D);
[Y, Tsim, X] = lsim(sys,U,T);
plot(Tsim,Y)
Y1=(Y(:,1)./176.)/57.7
Y2=Y(:,2)./176
newY= [Y1 Y2 Y(:,3) Y(:,4)]
subplot(2,2,1)
plot(Tsim,Y1)
ylabel('delta(u)/V')
xlabel('Time (s)')
subplot(2,2,2)
plot(Tsim,Y2)
ylabel('delta(alpha)(deg)')
xlabel('Time (s)')
subplot(2,2,3)
plot(Tsim,Y(:,3))
ylabel('q(deg/s)')
xlabel('Time (s)')
subplot(2,2,4)
plot(Tsim,Y(:,4))
ylabel('delta(theta)(deg)')
xlabel('Time (s)')
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Accepted Answer
Star Strider
on 15 Sep 2014
Use the: Y = C*exp(A*t)*D*U representation of a linear control system:
A=[-.045 .036 0 -32.2;-.369 -2.02 176 0;.0019 -.0396 -2.948 0;0 0 1 0];
B=[0;-28.17;-11.88;0];
C=eye(4);
T = 0:1:200;
U = ones(size(T));
for k1 = 1:length(T)
Y(:,k1) = C*expm(A*T(k1))*B*U(k1);
end
figure(1)
plot(T, Y)
producing:
<<www-mathworks-com-matlabcentral-answers-uploaded_files-18154-Hi--20my-20current-20code-20is-20written-20for-20time-20responses-20using-20the-20lsim-20function-20but-20it-20needs-20to-20be-20converted-20to-20ode45-20and-20i-20have-20no-20idea-20where-20to-20start-20--202014-2009-2014.png>>
2 Comments
Star Strider
on 16 Sep 2014
My pleasure!
I apologise — I didn’t realise you were required to use ode45.
In recompense, this should get you started:
A=[-.045 .036 0 -32.2;-.369 -2.02 176 0;.0019 -.0396 -2.948 0;0 0 1 0];
B=[0;-28.17;-11.88;0];
C=eye(4);
T = 0:1:200;
odelin = @(t,x) [-.045 .036 0 -32.2;-.369 -2.02 176 0;.0019 -.0396 -2.948 0;0 0 1 0]*[x(1); x(2); x(3); x(4)] + [0;-28.17;-11.88;0];
[t,y] = ode45(odelin, T, zeros(4,1));
It’s not perfect compared to the expm result (if it is correct as I believe it is). But then I can’t let you miss out on all the fun!
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