Question

What is P-I-D control? (Control system, PID controller)

Answer 1

A proportional integral derivative controller is a control loop mechanism working on feedback that is used in industrial control systems and has other applications requiring continuously modulated control. A PID controller continuously calculates an error value (difference between a desired setpoint (SP) and a measured process variable (PV) )and applies a correction based on proportional, integral, and derivative terms (denoted P, I, and D respectively).
Eg.
In a container there is incoming flow of water having qi (variable) flow rate and outgoing flow of water with constant flow rate.
There is need to maintain the the height of water filled to be 1metre.
h(t)=1m
hm(t)=variable distance of water filled which is continuously measure by transducer.
Error =h(t)-hm(t). Is set differently for all three cases explained below-
Group of perform a specific task Ilt) target [h(t) = Lm C. Controller homxt) konkt) 1 Pransducer 2:1) &LT im har(t) shm(t) at if Ilt=ų d E(A) future Control system components connected together to (desired task) forms control tlm. e set point am TANK 19; (4) dhm (t) the (t)- Ai (A) it q;lt) > 9(t) at value Kilt) =K1 (d) it Q2 = 1 Thant) Sensor - Present past Ilt) = kg Jets Lipntegral controller qi(t) - 9o (t)=A. d het) 9; (d) c Ilt) + dhm t (t ta hm (t)=q qi (t) at a,=1 11t) Ihm (t) Elt) Controller < [h(t)- hm (A) 164) = f(EU) brengen KI Elt). [(t) = it L Proportional Controller t Ew at dt Derivative controller

BLOCK DIAGRAMO of Control system- /p of control spy 3 Set peint ELA controller Elt) f< > Value KO ai Lt) Plant tank imit) target ht) hm Ct) Sensor I Mathematical a Analysis of above control &m- Tanks " dhm (t) at thom (t) = q (t) (if R=4 Valver dilt) =k. Ilt) then q;(t) = 1(t) Ihm (A) at thm (t) =ILA) Tlt) = f <[Elt)]> ohn Lt thm (t) = f<Elk) at Elt- allthet It kee by proportional Controller 14t) = ķ Elt) Sit te It ke k Elt) dhm ln thalt) ILA) = Kp E(A) at -(1tket (itkee dhm (1) dt s(t) = \ Itke hm (d) = kp [ h (d) - hm (d) b if (&p=9 dhm (t) at + (it kp) hm (t) = kp -(It kelt hmit) = ke It ke [neuvot shim (t)=,0.921- e lot EW) = 0.1(1+ gēlot) IL) = 0.9 (1+ gelot) e(t)e Chult)

K Elt) t t Elt) Ilt) hult) ga 0 om GI оч 31 м 3,874 0.56gm Oiga olm ogm esteady state) Note's proportional controller strategy is a simplest will not be equals to but the steady state essor strategy zero, By Integral Controller - £(t) = Kejectat thm (t) = = KI / Elt) dt dhm (A) dt AOKメリット ď hm (A) t dem Lt) dt dt² d (ht) hin (t) b 1 - dhults + ochin (A) at + Kehm (tl =kc dt anost hm (t) = -ė I hk sin ( JK - Yu + 0 Slow But Reach to alm. at tro him Ct) n hom (o)= lm n E Cool = om (w .. Note. The speed of integral controller strategy is But ultimately steady state essor will be equals to less t Pero

By Derivative controller- Ilt) = kod ECA) at othm (t) dt thm (t) = kode(t) dt dhmt dt thm (t) = kod at [1-hm (4) (tko ) dan (A) hm (t =o at (ikkelt hom (t) = ko Itko All aut t=oo) im ogn hm (00) h(at) = at t=ot ko Itko Ko=9 hot) = 0.gm and then if fast, reach to o.gm om i falls to t I ELA I(A)= K ELA) & Kale (t) at tko PE (t) at it to it o + + is much agressi but steady Zero state essor may not called as universal controller. Note & Derivative controller too equals to PLD) controller is (PO commonly used strategy in industrial applicat?