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.PS
# control.m4
gen_init
linewid = linewid*0.8
circlerad = 0.35/2
bw = boxwid/2
bh = boxht/2
# . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . #
PID: [
{"$r(s)$" above ljust}
arrow
S1: circle
line right "$e(s)$" above
{ arrow right ; box ht bh wid bw "$K_p$"
arrow right linewid-circlerad ; S2: circle }
{ line up linewid ; arrow right ; box ht bh wid bw "$K_D s$"
line to (S2,Here) ; arrow to S2.n }
{ line down linewid ; arrow right ; box ht bh wid bw "$K_I/s$"
line to (S2,Here) ; arrow to S2.s }
arrow right from S2.e "$u(s)$" above
box "$G(s)$"
arrow right ; "$y(s)$" above rjust at Here+(0,2pt__)
line down boxht*3/2 from last arrow.c then left last arrow.c.x-S1.x
arrow to S1.s
"$-\;$" below rjust
]
"(a) $PID$ control" below ljust at PID.sw+(0,-5pt__)
# . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . #
Observer: [ {"$r$" above ljust}
arrow
S: circle
"$-\;$" below rjust at S.s
arrow <- down linewid/2 from S.s
box ht bh wid bw "$K$"
arrow <- down linewid/2
line right linewid "$\hat x$" above
Obs:box wid linewid*5 ht boxht*5/4 \
"$\frac{d}{dt}\hat x = (A{-}LC)\hat x + B u + L y$"
"\sl Observer" above ljust at Obs.sw
arrow <- right linewid/2 from 3/4<Obs.se,Obs.ne>
line to (Here,S)
{"$u$" above at Here+(linewid/2,0)}
arrow from S.e to Here+(linewid,0)
Plant: box wid boxwid*3/2 ht boxht*5/4 \
"$\frac{d}{dt} x=Ax+Bu$" "$\quad y=Cx$\hfill\hbox{}"
"\sl Plant" above ljust at Plant.sw
arrow right from Plant.e
"$y$" above rjust at Here+(0,2pt__)
move to last arrow.c
line to (Here, 1/4<Obs.se,Obs.ne>)
arrow to (Obs.e,Here)
] with .nw at PID.sw+(0,-0.5)
"(b) Output feedback with a full-order observer" below ljust \
at Observer.sw+(0,-5pt__)
# . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . #
Multiblock: [
boxwid = boxht
circlerad = boxht*0.4
define summer { circle
{line from last circle.nw to last circle.se
line from last circle.sw to last circle.ne
"$$1$" at last circle.n below
"$$2$" at last circle.s above
"$$3$" at last circle.e rjust
"$$4$" at last circle.w ljust}
}
define doublebox {[box "$$1$"; arrow; box "$$2$"]}
arrow "$E_1$" above
S1: summer(,-,,+)
linewid = boxwid/2
arrow "$\epsilon$" above
doublebox(H_1,H_2)
arrow
S2: summer(-,,,+)
arrow
T: doublebox(H_3,H_4)
line
Y: Here
arrow
"$S_1$" above
R1: box "$R_1$" at (T.x,T.y+boxht*3/2)
arrow from Y to (Y,R1) then to R1.e
arrow from R1.w to (S2,R1) then to S2.n
"$n_1$" ljust at S2.n+(0,boxht/2)
left
Rf: doublebox(R_2,R_3) at ((S1.x+T.x)/2,T.y-boxht*3/2)
arrow from T to (T,Rf) then to Rf.e
arrow from Rf.w to (S1,Rf) then to S1.s
"$n_2$" at S1.s+(0,-boxht/2) ljust
] with .nw at Observer.sw + (0,-0.5)
"(c) A multiblock example" below ljust at Multiblock.sw+(0,-5pt__)
# . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . #
Nonlinear: [boxwid = boxwid*3/2; boxht = boxht*3/2
thicklines_
scale = 0.8
circlerad = 0.3/2
R: box "reference" "$R$"
arrow right linewid*4/3 "${y_c}_{\hbox{\scriptsize ref}}$" above
Gh: box "```inverse'''" "$\hat G$"
arrow from Gh.s down "${y_m}_{\hbox{\scriptsize ref}}$" ljust
E: circle
arrow from E.e right "$e$" above
box "stabilizer" "$K$"
arrow "$\delta u$" above
D: circle
line from Gh.e to (D,Gh.e) "$u_{\hbox{\scriptsize ref}}$" above
arrow to D.n
arrow from D.e right "$u$" above
G: box "plant" "$G$"
arrow <- from G.n up boxht/2
"disturbance $z$" above
arrow right from G.e + (0,boxht/4)
"$y_c$" ljust
arrow right from G.e + (0,-boxht/4)
"$y_m$" ljust
move to last arrow.c
arrow down Here.y-G.s.y+boxht*2/3 then left Here.x-E.x then to E.s
"$-$" at Here + (-0.15,-0.1)
arrow <- down from R.s
"$W$ control input" at Here - (0,0.1)
UL:R.nw +(-boxht/2,boxht/2)
UR:(D.e,UL) + (0.1,0)
line dashed from UL to UR then to (UR,G.s+(0,-boxht*3/2))
line dashed to (Gh.w,Here) "Controller" above
line dashed to (Here,Gh.s+(0,-boxht/2))
line dashed to (UL,Here) then to UL
] with .nw at Multiblock.sw + (0,-0.5)
"(d) Nonlinear feedforward (for performance) and small-signal feedback (for stability)" \
below ljust at Nonlinear.sw+(0,-5pt__)
.PE
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