Not expecting a solution worked out for me... I'm stuck and need a hint. My prof is on vacation this week and is unreachable and the homework is due the day he returns...
given:
Servo-tracking control problem.
roots of error dynamics equation are:
-4, -2+2j, -2-2j
our physical model is for that of rocket control:
y" - k1 y = k2 B + k3 w,
where w = wind disturbance--an unknown and unmeasurable constant the only measurable physical things are y, ycmd and y'. k1 and k2 >0 and known (but not given--ie we are free to choose a value I assume)
We are to design B so that y approaches ycmd for all t.
ycmd is of the form
ycmd = c1 + c2t
now I know the error equation should look like:
e''' + a3 e" + a2 e' + a1 e = 0;
So....
I plug the roots given into matlab poly() and get a characteristic equation:
e''' + 8e'' + 24e' + 32e = 0;
which meets the hurwitz constraints:
all coeffs >0 and a3 * a2 > a1, 8*24 >32 check.
So now my confusion is:
How do I draw a math flow diagram for the physical model, when all I have is an equation in terms of 3rd order error, e?
He wants us to sim this in simulink and then vary/tweak the given roots to see how the servo-tracking changes.
In class he developed B as a PID algorithm, which I understand accounts for the unknown constant wind.
Can anyone give me some direction?
Thanks,
Bo