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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 }
{ arrow up linewid then right ; box ht bh wid bw "$K_D s$"
arrow to (S2,Here) then to S2.n }
{ arrow down linewid then right ; box ht bh wid bw "$K_I/s$"
arrow to (S2,Here) then to S2.s }
arrow right from S2.e "$u(s)$" above
box "$G(s)$"
arrow right ; "$y(s)$" above rjust at Here+(0,2pt__)
arrow down boxht*5/4 from last arrow.c then left last arrow.c.x-S1.x \
then to S1.s
"$-\;$" below rjust
]
"(a) $PID$ control" below ljust at PID.sw+(0,-5pt__)
# . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . #
# https://tex.stackexchange.com/questions/575592/how-to-create-a-controls-system-diagram
Observer: [
define(`thickarrow',`arrow thick 3 wid 7bp__')
define(`thickline',`line thick 3')
fillval = 0.6
boxwid = 0.3
boxht = 0.4
circlerad = 0.1
{"$r$" above ljust}
R: arrow
S: circle fill
{"$-$" below ljust at S.s; "$+$" above rjust at S.w+(2bp__,0)}
{ OLP: box invis fill 0.9 wid 3.1 ht 1.4 with .nw at Here+(0.3,boxht*5/4)
"\sf plant" at OLP.sw above ljust }
U: arrow right 0.4
{"$u$" at last arrow+(2bp__,0) above }
Bp: box fill "$B$"
thickarrow right 0.4
Sp: circle fill
{"$\;+$" below ljust at Sp.s; "$+$" above rjust at Sp.w+(2bp__,2bp__)}
thickarrow right 0.4
{"`$\dot{\mathbf x}$'" at last arrow + (0,7bp__)}
Ip: box fill "$I/s$"
thickarrow right 1
{"$\mathbf x$" at last arrow + (0,7bp__) }
Cp: box fill "$C$"
# print Cp.e.x - Bp.w.x + 0.2
thickline right 0.4
Yp: thickarrow
{"$\mathbf y$" at last arrow + (0,7bp__) }
Ap: box fill "$A$" with .n at Ip.s+(0,-boxht/2)
thickarrow <- from Ap.e right 0.4 then up Ip.y-Ap.y
thickarrow from Ap.w to (Sp,Ap) then to Sp.s
# print OLP.n.y-Ap.s.y+0.1
#
K: box fill "$K$" at Ap + (0,-boxht*3/2)
arrow from K.w to (S,K) then to S.s
{OBS: box invis fill 0.9 wid 4.3 ht 1.8 with .nw at (S.w,K.s)-(0.1,0.1)
"\sf observer" at OBS.sw ljust above }
Io: box fill "$I/s$" at K + (0,-boxht*3/2)
thickarrow <- from Io.w left 0.4
{"`$\dot{\hat{\mathbf x}}$'" at last arrow + (0,7bp__)}
Sxo: circle fill
{"$\;+$" below ljust at Sxo.s; "$+$" above rjust at Sxo.w+(2bp__,2bp__)}
thickarrow <- left 0.4
SLo: circle fill
{"$\;+$" below ljust at SLo.s; "$+$" above rjust at SLo.w+(2bp__,2bp__)}
thickarrow <- left 0.4
Bo: box fill "$B$"
arrow from 1/4 between U.start and U.end up boxht \
then left 2*boxht then down Bp.y-Bo.y+boxht then to Bo.w
Ao: box fill "$A$" with .n at Io.s+(0,-boxht/2)
thickline from Io.e right 0.4
{thickarrow <-> from K.e to (Here,K.e) then to (Here,Ao) then to Ao.e
thickarrow from Ao.w to (Sxo,Ao.w) then to Sxo.s }
Xhat: Here
Co: box fill "$C$" at (Cp,Here)
thickarrow right 0.4
{"$\hat{\mathbf y}$" at last arrow + (0,7bp__) }
{ thickarrow from Xhat to Co.w }
{"$\hat{\mathbf x}$" at last arrow + (0,7bp__) }
Syo: circle fill
{"$\;+$" above ljust at Syo.n; "$-$" below rjust at Syo.w+(2bp__,-2bp__)}
thickarrow <- from Syo.n to (Syo,Cp)
Lo: box fill "$L$" with .n at Ao.s+(0,-boxht/2)
# print Io.n.y+0.1 - (Lo.s.y-0.1)
thickarrow from Syo.s down Syo.s.y-Lo.y then to Lo.e
thickarrow from Lo.w to (SLo,Lo.w) then to SLo.s
] with .nw at last [].sw+(0,-0.3)
"(b) Single-input plant with feedback from a full-order observer" \
below ljust at Observer.sw+(0,-5pt__)
# . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . #
ifelse(0,1,`
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 last [].sw+(0,-0.5)
')
# . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . #
ifelse(1,1,`
Multiblock: [
boxht = 0.4
boxwid = boxht
circlerad = boxht*0.4
define summer { [ C: circle
line from C.nw to C.se
line from C.sw to C.ne
"$$1$" at C.n+(0,1bp__) below
"$$2$" at C.s-(0,1bp__) above
"$$3$" at C.e+(1bp__,0) rjust
"$$4$" at C.w-(1bp__,0) 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$" at (T.x,T.y+boxht*5/4)
arrow from Y to (Y,R1) then to R1.e
arrow from R1.w to (S2,R1) then to S2.n
"$n_1$" ljust at S2.n+(0,boxht/2)
left
Rf: doublebox(R_2,R_3) at ((S1.x+T.x)/2,T.y-boxht*5/4)
arrow from T to (T,Rf) then to Rf.e
arrow from Rf.w to (S1,Rf) then to S1.s
"$n_2$" at S1.s+(0,-boxht/2) ljust
] with .nw at Observer.sw + (0,-0.3)
"(c) A multiblock example" below ljust at Multiblock.sw+(0,-3pt__)
')
# . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . #
Nonlinear: [boxwid = boxwid*3/2; boxht = boxht*3/2
thicklines_
scale = 0.8
circlerad = 0.3/2
R: box "reference" "$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}}$" above; corner
arrow to D.n
arrow from D.e right "$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 last [].sw + (0,-0.2)
"(d) Nonlinear feedforward (for performance) and small-signal feedback
(for stability)" below ljust at Nonlinear.sw+(0,-5pt__)
#print PID.n.y - Nonlinear.s.y
.PE
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