Re: ? PID control
"vee vee vee vee" <ccos.bbs@bbs.cis.nctu.edu.tw> 撰寫於郵件新聞:4NaHWX$vfs@bbs.cis.nctu.edu.tw...
> System eqn: du/dt = -a*u+q
> P-feedback control: q = a*u_desired
> I-feedback control: q = ?
> D-feedback control: q = ?
> thanks,
> by Cheng Cosine
> Apr/17/2k6 NC
If you know "a" precisely and you can feedback "u",
then a better controller can be designed as
q = a*u + du_d/dt - k*(u - u_d)
where u_d is the desired trajectory and k>0 is a constant.
With this control law, the closed loop system becomes
de/dt + ke =0 (1)
where e = u - u_d is the tracking error between the actual
trajectory and desired trajectory. Since (1) is a stable linear
time invariant (LTI) system, the tracking error will converge
to zero asymptotically.
You might ask me why not using the PID controller.
Don't forget that you are having a first order LTI system,
and its stabilization is fairly simple. You don't have to go
to PID to push your cost.
Hope this works! Have fun!
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