Hello,
in a SISO LQR tracking control ,the input command computed is :
u(k) = us -G(x-xs)
us represents the steady state input directly computed from my desired reference trajectory y(k) = r. it's the feedforward part of my control
y(k) = C*x(k) and r = C*xs
I'm stucked with the feedbackward part of my input command because i don't know how to compute xs which represents the steady state target.
my vector C is equal to (0,0,a,b,0,0).
i don't really care of the state of x as long as y(k) follows my reference.
I use xs = 0 (as if I regulate my plant to the equilibrium point) but i think it's not good
do i have to reformulate in an another way my state space model?
Thank you
If you regulate the state variables to zero (xs = 0), the your output will be also zero becuase C*xs = r = 0. This makes sense only if the reference is zero. You can redefine your model in terms of the control error, such that when state "error" is regulated to zero, actually you have r - ys = r - C xs = 0, i.e. ys = r.
thank you adrian,
even if i do this this translation, i always have to explicit all my final & desired state in the feedback control, i mean a final value to reach for each x (xs(1),xs(2),...xs(N)). which i don't care and even can't handle it : i don't know how to compute them, my objective is only to reach y(k) = a*x(2) + b*x(4) to a set point. I don't meet this problem with a MPC algorithm because the state x is only used for prediction and my criterion to minimize is based only on y(k), reference point and command u.
Mmmm... you can modify the control law as u(k) = K r(k) - G x(k)
i.e. us = K r (k), where
K = inv(C * inv(I - A + B * G) * B)
I is the unit matrix with the dimension of A.
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