Fall 2001 6.3114-5 For purposes of scaling, define ass= T ≡Nars We would then implement the control in the new form u=Nr-K C=(Nu+KN)r-kx Nur+K(N-r-I +K( which can be visualized as XsS K A B C Use N to modify the reference command r to generate a feed- forward state command to the system Is Use N to modify the reference command r to generate a feed- forward control input uss Note that this development assumed that r was constant, but it could also be used if r is a slowly time-varving command But as we have seen, the architecture is designed to give good steady-state behavior, and it might give weird transient responses
Fall 2001 16.31 14–5 • For purposes of scaling, define: xss ≡ Nxrss uss ≡ Nurss • We would then implement the control in the new form u = Nr ¯ − Kx = (Nu + KNx)r − Kx = Nur + K(Nxr − x) = uss + K(xss − x) which can be visualized as: – Use Nx to modify the reference command r to generate a feedforward state command to the system xss. – Use Nu to modify the reference command r to generate a feedforward control input uss • Note that this development assumed that r was constant, but it could also be used if r is a slowly time-varying command. – But as we have seen, the architecture is designed to give good steady-state behavior, and it might give weird transient responses
Fall 2001 6.3114-6 ● For our example, a B 0.5 LL C 0 0.5 SO 0.5 =[-0.5] and N=N+KN2=-05+[1457/7 0.5 as we had before
Fall 2001 16.31 14–6 • For our example, xss uss = A B C 0 −1 0 1 = 1 −0.5 −0.5 so xss = 1 −0.5 , uss = −0.5 and N¯ = Nu + KNx = −0.5 + 14 57 1 −0.5 = −15 as we had before.