Hi All,
Just wondering if I have done this correctly. To write the system below into a state space form with a unit step.
100(s+5)/ (s+2)(s+3)
100s+500/s^2+5s+6
d^2y/dt^2 + 5dy/dt + 6y = 100du/dt+500u
Y(s) = 100s^-1+500s^-2/ 1+5s^-1+6s^2
Y(s) = (100s^-1+500s^-2)E(s)
E(s)= U(s)/1+5s^-1+6s^-2 therefore
E(s) = U(s) - 5s^-1E(s)-6s^-2E(s)
dx1/dt=x2
dx2/dt2=x3
dx3/dt3= -6x3-5x2+u
y= 500x1 +100x2
d/dt
:x1: :0, 1, 0: :x1: :0:
:x2:=:0, 0, 1: :x2:+:0: u(t)
:x3: :0,-6,-5: :x3: :1:
y=:500, 100, 0:
I would also like to know where I can find the information to write the above in correct equations so it make more sence to the reader.
Thanks
Just wondering if I have done this correctly. To write the system below into a state space form with a unit step.
100(s+5)/ (s+2)(s+3)
100s+500/s^2+5s+6
d^2y/dt^2 + 5dy/dt + 6y = 100du/dt+500u
Y(s) = 100s^-1+500s^-2/ 1+5s^-1+6s^2
Y(s) = (100s^-1+500s^-2)E(s)
E(s)= U(s)/1+5s^-1+6s^-2 therefore
E(s) = U(s) - 5s^-1E(s)-6s^-2E(s)
dx1/dt=x2
dx2/dt2=x3
dx3/dt3= -6x3-5x2+u
y= 500x1 +100x2
d/dt
:x1: :0, 1, 0: :x1: :0:
:x2:=:0, 0, 1: :x2:+:0: u(t)
:x3: :0,-6,-5: :x3: :1:
y=:500, 100, 0:
I would also like to know where I can find the information to write the above in correct equations so it make more sence to the reader.
Thanks
Last edited: