.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 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) arrow to (Obs.e,Here) ] with .nw at last [].sw+(0,-0.5) ') # . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . # ifelse(0,1,` 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$" at S1.s+(0,-boxht/2) ljust ] with .nw at Observer.sw + (0,-0.3) "(c) A multiblock example" below ljust at last [].sw+(0,-3pt__) ') # . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . # Nonlinear: [boxwid = boxwid*3/2; boxht = boxht*3/2 thicklines_ scale = 0.8 circlerad = 0.3/2 R: box "reference" "$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,-0.25) "(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