Logic Controllers 1. normally open contact normally closed contact. George Boole, ( ), Irish mathematician, Analysis of Logic).

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1 Logi Controllers Logil ontrol Exmples of equipments for logil ontrol A simple ON-OFF swith with two terminls normll open ontt normll losed ontt rel ontts oil rmture ontts Contts push utton oil oke A oil of wire is wrpped round soft iron ore, el A rel is swith whih is operted eletrill. Mn rels use oil s n eletromgnet to t swithing mehnism. Normll-open ontts onnet the iruit when the rel is tivted; nd disonnet when the rels is detivted. Tpes of logi : omintionl logi sequentil logi. Boolen lger George Boole, (85-864), Irish mthemtiin, Anlsis of Logi).: Two vlues of logil vriles: true / flse, logil / logil, high / low. A logil funtion is s follows f (,,,... ) where,, re independent vriles nd is dependent vrile Digrm desriing three logil funtions of the three independent vriles Comintionl logi CL Definition of logil funtions Verl desription Truth tles Krnugh mps Boolen expressions Let k e numer of logil vriles then the numer of the possile omintions of vlues etween them, nd there re N 2 k ws of ssigning n output vlue to eh of these k-input vlues

2 Truth tle (for 3 vriles there re 8 ws of ssigning the output vlue of to the input vlues of the 3 independent vriles) Krnugh mps Index Independent vrile Dependent vrile vrile: 2 vriles: 3 vriles: 4 vriles: d 5 vriles: d e

3 Logi Controllers 3 3 Bsi logil opertions (elementr funtions) Not funtion Logil disjuntion NOT opertion Opertor: (see exmples elow) Formul: ( NOT, x ) Truth tle: O opertion Opertor: Formul: Truth tle: logil dd (join), ( O ) Logil onjuntion Exlusive O AND opertion logil multipl Opertor:, Formul: ( AND ) Truth tle: XO opertion onl one out of n Opertor: Formul: Truth tle: heffer funtion (AND-NOT opertion) Piere funtion (O-NOT opertion) NAND Formul: Truth tle: heffer stroke opertion ( NAND ) NO Formul: Truth tle: ( NO )

4 Equivlene Non-equivlene E Formul: Truth tle: E NE Formul: Truth tle: NE Implition elongs to the logil elementr funtions. Opertor, formul Gtes of the retngulr shpe NOT (invertor) AND gte O gte XO gte NAND gte NO gte E gte E Distintive shpe NOT (invertor) AND gte O gte XO gte NAND gte NO gte A Venn digrm or set digrm is digrm tht shows ll possile logil reltions etween finite olletion of sets (ggregtion of things).

5 Logi Controllers 5 4 Lws nd theorems of Boolen lger Commuttive lw,, Assoitive lw ( ) ( ), ( ) ( ) Distriutive lw ( ), ( ) ( ). Involution lw. Dulit lws nd theorems explins dulit in mth s smmetr within mthemtil sstem suh tht theorem remins vlid if ertin ojets, reltions, or opertions re interhnged. The dul form of lw nd theorem n e otined replement of logil logil nd vie vers nd simultneousl replement of disjuntion onjuntion nd vie vers. The logil is the dul vlue of the logil nd disjuntion is the dul opertion of onjuntion: nd Dul forms of lws nd theorems Nme Logil disjuntion Logil onjuntion Lws of omplementr Opertion with nd Opertion with nd Idempotent lw implifition Theorem ( ) DeMorgn s lw ( ) Prove of lws nd theorems A) Algerill B) Using the truth tle

6 De Morgn equivlents De Morgn lw 5 Cnonil form of logil funtions In Boolen lger, n oolen funtion n e expressed in nonil form using the dul onepts of minterms (miniml terms) nd mxterms. Minterms re lled produts euse the re the AND of set of vriles, nd mxterms re lled sums euse the re the O of set of vriles. The set of vriles differs from eh other in suset of vriles, whih re inverted the NOT funtion. We n s tht the minterm is produt term in whih eh of the vriles ppers one (in either its omplemented or unomplemented form). Thus, minterm is logil expression of n vriles tht emplos onl the omplement opertor nd the onjuntion opertor. For three vriles (n 3) ll the minterms re s follows,,,,,,,. These onepts re lled duls euse of their omplementr-smmetr reltionship s expressed De Morgn's lws, whih stte tht AND( x,, z,... ) NO( x,, z,... ) nd O x,, z,... NAND x,, z,.... ( ) ( ) Note: AND ( x, ) x, NAND ( x, ) x, O ( x, ) x nd ( x, ) x NO. The dul nonil forms of n oolen funtion re "sum of minterms" nd "produt of mxterms." The term "um of Produts" or "op" is widel used for the nonil (in simplest or stndrd) form tht is disjuntion (O) of minterms. Its De Morgn dul is "Produt of ums" or "Po" for the nonil form tht is onjuntion (AND) of mxterms. These forms llow for greter nlsis into the simplifition of these funtions, whih is of gret importne in the minimiztion or other optimiztion of digitl iruits. Let truth tle e given

7 Logi Controllers 7 A) The formul is omposed s sum of logil produts (minterms), whih re omposed of 3 vriles in the form, resulting in the logil ee tht,, ontriutes to the sum funtion vlue of the logil. B) The formul is omposed s produt of logil sums (mxterms), whih re omposed of 3 vriles, resulting in the logil (...)... ( )... (...) ee tht,, ontriutes to the produt funtion vlue of the logil. Exmple: A) um of onjuntions (op) B) Produt of disjuntions (Po) ( ) ( ) Proof tht oth the results give the sme result Ad A) ( ) ( ) ( ) Ad B) (( ) ) ( ) ( ) 6 The use of Krnugh mps to retion logil funtion A Krnugh mp is grphil w of minimizing Boolen expression sed on the rule of omplementtion. It works well if there re 2, 3, or 4 vriles, ut gets mess or impossile to use for expressions with more vriles thn tht. A Krnugh mp uses new term lled minterm. For oolen funtion of n vriles x, x 2,, x n, the minterm is produt term in whih eh of the n vriles ppers one (in either its omplemented or unomplemented form). Thus, minterm is logil expression of n vriles tht emplos onl the omplement opertor nd the onjuntion opertor. The ide ehind Krnugh mp (Krnugh, 953) is to drw n expression s truth tle s mtrixes in suh w tht eh row nd eh olumn of the mtrix puts minterms tht differ in the vlue of single vrile djent to eh other. Then, grouping djent ells of the mtrix, ou n identif produt terms tht eliminte ll omplemented literls, resulting in minimized version of the expression. The Krnugh mp is used to produe miniml sum of produts implementtion of n expression drwing retngles round groups of djent minterms in the mp; eh retngle will orrespond to one produt term, nd the full expression will e onstruted s the O (sum) of ll the produt

8 terms. The gol is to hve s few produt terms s possile, whih implies tht eh produt term will ount for s mn minterms s possile. Exmple Let truth tle e speifing the logil funtion of the form The Krnugh mp n e reted on the se of this funtion. Now the solution of the prolem strts. It is required to design the miniml form of this funtion using the Krnugh mp. 3 2 : ( ) 2: ( ) 3: ( ) Notie tht two minterms omposed of 3 vriles gives one minterm omposed of 2 vriles, whih simplified onsiderl the resulting formul. The finl minimized formul is s follows ere re the rules for lotion the irles enlosing prt of the Krnugh mp of the retngle shpe: Ever minterm must e inside t lest one irle, ut there must not e n zeros inside n irle. Ever retngle hs to e s lrge s possile. Cirles m wrp round to inlude ells in oth the leftmost nd rightmost olumns. likewise for the top nd ottom rows. The numer of minterms enlosed in irle must e power of two (, 2, 4, 8, or 6 minterms for 4-vrile mps). ome funtions hve "don t re" onditions, whih re omintions of inputs tht will never our, resulting in ses where it doesn t mtter whether the output is zero or one. Where these don t re onditions pper in Krnugh Mp (usull indited X s insted of ones or zeros), the m e inluded inside irles or not depending on wht will mke the irles s few nd s lrge s possile.. Pirs

9 Logi Controllers 9 d d d d d d d d There re omintions of the possile vlues of the independent vriles, whih nnot exist in the rel world (for instne the lift nnot e simultneousl in two different floors). In this se the output vlue is sustituted X. The dependent vlue is repled the vlue, whih is profitle for minimizing the resulting formul. X 7 Design of the logil ontrol sstems el Integrted iruits Progrm ode. el logi Logil funtions nd ontt(s) rel oil V V V Logil funtions nd V V V V V

10 Exmple V V Ldder digrm Funtion Blok digrms Integrted iruits (IC) 5V input T T 2 v E K T 3 output nother gtes V NAND gte with 2 inputs N 74N NAND nd NO logil gtes re the two pillrs of logi, in tht ll other tpes of Boolen logil gtes (i.e., AND, O, NOT, XO, XNO) n e reted from suitle network of just NAND or just NO gte(s). The n e uilt from rels or trnsistors, or n other tehnolog tht n rete n inverter nd two-input AND or O gte. ene the NAND nd NO gtes re lled the universl gtes. Min triks The design of the logil AND using onl NAND gtes ( ) The design of the logil O using onl NAND gtes The design of the logil AND using onl NO gtes The design of the logil O using onl NO gtes ( )

11 Logi Controllers NOT AND O NAND NO Integrted monolithi iruits on the mrket re produed with the ertin numer of inputs, for exmple 2, 4, 8. The design of the logil iruit hs to respet this ft. The importnt prt of tsk to e solved is the numer of the gte inputs. In the other word it is needed to design the ontrol sstem flowhrt using onl gtes with given numer of inputs. The design of the ontrol sstem flowhrt for the logil disjuntion or onjuntion omposed of 3 vriles using NAND gtes with onl 2 inputs ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) The smol n designtes gte, indexed n, with 2 inputs. When the hrt for the logil produt of 3 vriles (,, ) is drwn, ou should strt t the gte 4 hving s n input the output of the gte 3, nd then ou should ontinue onneting the output of the gte 2 nd the vrile to the input of the gte 3. The design of the ontrol sstem flowhrt for the logil disjuntion or onjuntion omposed of 3 vriles using NOD gtes with onl 2 inputs ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

12 Progrmmle Logi Controllers - PLC Computer tools supporting the design of logi ontrol sstems re sed on Ldder Digrm LAD, Kontktpln KOP in Germn Control stem Flowhrt CF, Funktions pln FUP in Germn ttement list TL, Anweisungsliste AWL in Germn trutured Text (T) 8 Exmple The first prt of the truth tle The seond prt of the truth tle d A d Krnugh mp X X d The minimized form of the logil formul d Ldder digrm d To rete lok digrm the formul hs to e dpted to the gtes whih re emploed For NAND gtes V V ( ) d d d d d d ( )

13 Logi Controllers 3 For NO gtes ( ) d ( ) d ( ) d d d d d d 9 equentil logi Let logil funtion e defined formul f (,,,,... ) P 3P CL Memor 2 3 where P is the pst vlue of the oolen vrile Clok Exmple of liquid level ontrol sstem sed on logil ontroller Fill vlve Tnk Vlve for drining Two liquid level guges h high level h 2 low level z Controlled sstem Vlves re onsidered to e either full opened ( or z ) or ompletel losed ( or z ). The drin vlve is ontrolled independentl of the inlet (fill) vlve. The liquid level guge provides logil signl if the liquid level is ove ertin level or logil signl if the level is elow mentioned level. A tnk whih is filled with ondutive liquid h 2 h ON-OFF sensors sed on eletril ondutivit The Krnugh mp for the output logil vrile of the logil ontrol sstem. P h 2 X X h

14 Logil funtion for the omintionl logi h 2 P h Adpting for using NAND gtes h 2 h2 P h h2 P h h h P h Flip-flops ; A flip-flop or lth is iruit tht hs two stle sttes nd n e used to store stte informtion. Flip-flops nd lthes re fundmentl uilding lok of digitl eletronis sstems used in omputers, ommunitions, nd mn other tpes of sstems. Flip-flops n e either simple (trnsprent or opque) or loked (snhronous or edge-triggered); the simple ones re ommonl lled lthes. The word lth is minl used for storge elements, while loked devies re desried s flip-flops. Logi iruits re divided into snhronous nd snhronous tpes. In snhronous sequentil iruits, the stte hnges onl t disrete times in response to lok signl. In snhronous iruits the stte of the devie n hnge t n time in response to hnging inputs. Mehnil flip-flop tpe whih hnges its stte snhronousl set output reset - high L - low time Timing digrm Truth tle Krnugh mp for the output logil vrile Previous output X X? P P X X The logil funtion for design Ldder Digrm ( ) P P Where P is the pst vlue of P The output is energized even when the input eses. This is lled lth iruits. V V

15 Logi Controllers 5 The use of the NO nd NAND gtes to uild the flip-flops of the tpe Gtes NO: ( ) ( ) Gtes NAND: ( ) P P P P D tpe whih hnge its stte snhronousl with lok signl The D flip-flop n e viewed s memor ell, whih is set or reset snhronousl with lok signl D Clok Clok D Timing digrm time JK tpe whih hnge its stte snhronousl with lok signl nhr. Clok Asnhr. J K C Truth tle: J K n n n Using flip-flop iruits in sequentil iruits The use of the tpe flip-flops The prolem is to design two logil funtion generting the set nd reset signls: f f ( h, h2 ) ( h, h ) 2 h h 2 f f A liquid level ontrol sstem sed on logil ontroller X h 2 Funtion for setting the set input of the flip-flops h 2 X h 2 Funtion for setting the reset input of the flipflops h h h

16 Conttors A onttor is n eletrill ontrolled swith used for swithing power iruit. The onttor is similr to rel exept with higher llowed urrent rtings to ontrol n equipment of the high power level. A onttor is ontrolled iruit whih hs muh lower power level thn the swithed iruit. Green utton el oil Conttor oil Min ontts Conttor Auxilr ontts ed utton P Auxilir ontt Lights Min ontts 22V~ V~ The onttors re used to ontrol eletri motors, lighting, heting, pitor nks, nd other eletril lods. Pushuttons re often olor-oded to ssoite them with their funtion. Commonl used olors re red for stopping the mhine or proess nd green for strting the mhine or proess. The use of JK flip-flop tpe for ounting pulses exdeiml ounter for N,, 5 Output Output Output 2 Output Input pulses T C C C C eset It is ssumed tht if the J nd K inputs re not onneted to the other outputs of gtes or flip-flops or re not grounded then J nd K 3 2 N

17 Logi Controllers 7 Timing digrm T time Binr-oded deiml ounter 2 3 Input pulses T eset exdeiml ounter 3 2 even-segment displ 2 3 Deoder CL A B G DP deiml point 2 IEC 3 equentil Funtion Chrts equentil funtion hrts re sed on teps with ssoited tions Trnsitions with ssoited logil onditions Direted links etween steps nd trnsitions FC equentil onfigurtion initil step trnsition step 2 trnsition 2 step 3 s s 2 ondition tion ondition 2 s 3 tion 2 s, s 2, internl logil vriles Trnsition is enled if the ondition rehes logil vlue equl to logil One of steps on the left digrm is tive while the others re intive.

18 FC imultneous Brnh In simultneous rnh, ll rnhes re exeuted until the trnsition eomes tive. FC eletion Brnh In seletion rnh, onl one rnh is exeuted depending on whih trnsition is tive. Divergent nd onvergent AND Divergent nd onvergent O Progrm ode tte vriles s, s 2,, trnsition onditions for trnsition p, p 2, nd tions, 2,, The initil vlue of ini fter power ON is zero s s p s s ini n n s2 s p s2 s3 s3 s2 p2 s3 s4... s2 2 s3... n sn ini 2 Cli hnging of sttes Assignment of the outputs ini Exmple of sequentil funtion hrt for the tpe flip-flops. s with OFF Button TAT s 2 with ON TAT TOP Button TOP

19 Logi Controllers 9 Funtionl digrm of tehnologil proess vlve vlve 2 tnk v v 3 h h 2 tnk 3 v 4 v 5 vlve 5 t temperture sensor with inr output h,, h 6 sensors of liquid level with inr output FC Ation ulifiers tnk 2 heting h 5 h 6 v 2 h 3 t h 4 p s 2 s 3 h equentil funtion hrt s v Witing for finishing heting the tnk 2 s 7 s 8 Initil step trt s 4 s 5 s 6 v 2 p - lws fulfills ondition v 3 v 4 h h4 v 5 h 6 2 h5 h 3 t Witing for finishing filling up the tnk s n ulifier Desription Vrile Ation Ation 2 2 N Non-stored Terminte when the step eomes intive. et (stored) Continue fter the step is detivted, until the tion is reset. eset Terminte the exeution of n tion previousl strted with the, D, L, or D qulifier. L Time Limited trt when step eomes tive nd ontinue until the step goes intive or set time psses. D Time Deled trt del timer when the step eomes tive. If the step is still tive fter the time del, the tion strts nd ontinues until detivted. P Pulse trt when the step eomes Ative/Detive nd exeute the tion onl one. D tored nd tored nd time Deled Ation strts fter time del, ontinues until reset. Time Deled D Deled If step is still tive, tion strts fter time del, ontinues until reset. L tored tored Time Limited Ation strts when step eomes tive, ontinues for set time or until reset.

20 3 PLC progrmming Lnguge tndrds IEC 3 is n interntionl stndrd for PLCs formulted the Interntionl Eletrotehnil Commission (IEC). As regrds PLC progrmming, it speifies the sntx, semntis nd grphis smols for the following PLC progrmming lnguges: Ldder digrm (LD) equentil Funtion Chrts (FC) Funtion Blok Digrm (FBD) trutured Text (T) Instrution List (IL) Ldder digrms Equivlen etween ldder digrm nd n eletril iruit Ldder ung ung ung 2 End rung Inputs: Contts Left hnd power ril onnetion End Outputs: Coils ight hnd power ril onnetion An eletril equivlent of the rung 24 V - Pressed utton The eletril iruit is losed Btter Power flow Lmp COM North Amerin stle of progrmming, U-tpe of eletril drwing stndrd A rung of the ldder digrm looks like s follows normll open ontt norml output normll losed ontt norml output n lterntive of drwing the norml output The end rung of the ldder digrm hs to e lerl denoted End end rung Internl rels do not exist s rel-world swithing devies ut re onl its in the PLC memor tht ehve in the sme w s rels. To distinguish internl rel outputs from externl rel outputs, the re given different tpes of ddresses. Different mnufturers tend to use different terms for internl rels nd different ws of expressing their ddresses. internl rels

21 Logi Controllers 2 Conventions whih re dopted for drwing ldder digrm The vertil lines of the digrm represent the power rils etween whih iruits re onneted. 2 Eh rung on the ldder defines one opertion in the ontrol proess. 3 A ldder digrm is exeuted from left to right nd from top to ottom. When the PLC is in its run mode, it goes through the entire ldder progrm to the end, the end rung of the progrm eing lerl denoted, nd then promptl resumes t the strt. This proedure of going through ll the rungs of the progrm is lled sn. 4 Eh rung must strt with n input or inputs nd must end with t lest one output. The term input is used for ontrol tion, suh s losing the ontts of swith, used s n input to the PLC. The term output is used for devie onneted to the output of PLC, e.g. motor. 5 Eletril devies re shown in their norml ondition. Thus swith whih is normll open until some ojet loses it, is shown s open on the ldder digrm. A swith tht is normll losed is shown losed. 6 A prtiulr devie n pper in more thn one rung of ldder. For exmple, we might hve rel whih swithes on one or more devies. The sme letters nd/or numers re used to lel the, devie in eh sitution. 7 The inputs nd outputs re ll identified their ddresses, the nottion used depending on the PLC mnufturer. (W. Bolton: Instrumenttion nd ontrol sstems, 24 Elsevier) The ldder digrm for ontrol of the liquid level in the tnk The liquid level ontrol sstem n e desried the ldder digrm. Low level igh level Fill vlve Both the level ontts re normll (ove the level of liquid) losed. Energizing the fill vlve tivtes the ontt designted Fill vlve. Fill vlve Timer In mn ontrol tsks it is neessr to del the onnetion or disonnetion of ontt for speified time intervl. For exmple, motor or pump might need to e ontrolled to operte for prtiulr intervl of time, or e swithed on fter some time intervl. PLCs re equipped uilt-in timers. Timers ount frtions of seonds or seonds using the internl CPU lok. Ldder progrm with del-on timer The Timer s n internl output swithes on the Timer s n internl rel fter del. etivtion of the Timer is ineffiient unless preset del hs not een rehed. Output On Off Time Input Timer Timer Output nning Proess ed Inputs to Input AM Exeute Progrm Dignostis nd Communition tsks Updte Outputs from Output AM epet sn

22 All input Terminls Input Imge Tle Controlled proess Exeute progrm solving the ldder digrm All output Terminls Output Imge Tle Modes of opertion un mode (the proessor egins the snning proess s previousl desried) Progrm mode (the proessor stops snning the ldder progrm nd (tpill) ll the outputs re turned off) Test mode (this mode is identil to the UN mode, exept ll outputs re disled (held in their off stte)) equentil Funtion Chrts nd ldder digrms The Ldder Digrm logi for tpil step tep n- tep n s n- s n Trns p n Previous step tep n- Trns p n tep n One the tep/trnsition logi hs een ompleted then the tions n written to Outputs. In simple sstem outputs n e driven diretl from the sttes tep Output tep 3 tep 5 Trnsition ondition Current step tep n- Previous step

23 Logi Controllers 23 4 Progrmmle Logi Controllers 24V E Progrmle Logi Controller Input inr signls PLC ts s n eletri swithord whih is devie tht direts eletriit from one soure to nother. Output inr signls rels vlves lmps, lights Glvni seprtion of PLC internl iruits nd externl iruits el nd opto-isoltor devies Externl iruits PLC Externl iruits PLC C filter optron PLC Externl iruits LED phototrnsistor mplifier Using rels Using optrons Progrmmle logi ontroller Input unit stem memor Opertionl memor Miroproessor Progrm memor Output unit input output Externl iruits us Allen-Brdle PLC instlled in ontrol pnel PLC IMATIC 7-3 Jiří Tům