Amercan J. of Engneerng and Appled Scences (4): 669-675, 009 ISSN 94-700 009 Scence Publcaons Improved Coupled Tan Lqud Levels Sysem Based on Swarm Adapve Tunng of Hybrd Proporonal-Inegral Neural Newor Conroller M.S. Raml, RM.T. Raa Ismal, M.A. Ahmad, S. Mohamad Naw and M.A. Ma Hussn Faculy of Elecrcal and Elecroncs Engneerng, Unversy Malaysa Pahang, Malaysa Absrac: Problem saemen: Accuracy and sably of many sysems n chemcal and process ndusres whch has Two-Inpu Two-Oupu (TITO) s one of he ey facors of process whch have cross couplng beween process npu and oupu. Approach: Unle radonal neural newor wegh adapaon usng graden descen mehod, Parcles Swarm Opmzaon (PSO) echnque was ulzed for adapve unng of neural newor weghs adusmen and fne unng he conroller s parameers. Desgn approach for conrollng lqud levels of Coupled Tan TITO sysem by usng hybrd PI-Neural Newor (hybrd PI-NN) conrollers. Resuls: Tunng mehod for parameers of mproved hybrd PI- NN conroller was also dscussed. Concluson: Performances of proposed mehod also compared wh PID-NN conrollers, was shown ha hybrd PI-NN conroller exhbed beer performance n erms of ransen response analyss. Key words: NN, PSO, level conrol, waer an INTRODUCTION Lqud an sysems play mporan role n ndusral applcaon such as n food processng, beverage, dary, flraon, effluen reamen, pharmaceucal ndusry, waer purfcaon sysem, ndusral chemcal processng and spray coang. A ypcal suaon s one ha requres flud o be suppled o a chemcal reacor a a consan rae. An upper an can be used for flerng he varaons n he upsream supply flow. Many mes he lqud wll be processed by chemcal or mxng reamen n he ans, bu always he level of he flud n he ans mus be conrolled. Val ndusres where lqud level and flow conrol are essenal nclude perochemcal ndusres, paper mang ndusres, waer reamen ndusres []. In order o acheve hgh performance, feedbac conrol sysem s adoped. Classcal PID conroller s wdely appled n ndusry conrol such as emperaure conrol, speed conrol, poson conrol, bu s dffcul for PID regulaon o reach he am of hgh speed and shor ranson me and small overshoo []. Advanced conrol mehods also have been proposed by several researchers such as sldng mode conrol [3] and nonlnear bac seppng conrol [4], unng mehods based on opmzaon approaches wh he am of ensurng good sably robusness have receved aenon n he leraure [5,6]. Accurae model and s parameers whch capure he characersc of he coupled an sysem s requred for desgnng s conroller for achevng a good performance. The specfc pon acled n he sudy s abou he advanages of usng a new hybrd PI-NN nsead of a PID-NN conroller, conssng of PSO, Neural Newor (NN) and PI conroller. From a generc unng rule he opmum sengs from an Inegral Squared Error creron pon of vew are derved. The valdaon resul shows ha hybrd PI-NN conroller much faser han PID-NN and also good robusness and small overshoo. Process plan descrpon: The schemac dagram of he coupled an sysem consdered n hs sudy s shown n Fg. where Q {Q, Q } are he nle flow rae o an and, Q s he lqud flow rae from an o an hrough orfce, Q o {Q o, Q o } are he oule flow rae of an and and h {h, h } denoes he lqud level of an and, respecvely. In hs smulaon, he arge s o conrol he level n wo ans by he nle lqud flow from wo pumps. The process npu are u {u (), u ()} (volage npu o pumps) and he oupu are h {h (), h ()} lqud level n an and respecvely. Correspondng Auhor: M.S. Raml, Faculy of Elecrcal and Elecroncs Engneerng, Unversy Malaysa Pahang, Malaysa 669
Am. J. Engg. & Appled Sc., (4): 669-675, 009 Fg. : Schemac of coupled an process The nonlnear plan equaons can be obaned by mass balance equaons and Bernoull s law. Afer lnearzaon process, he lnear plan equaons can be obaned as: a g a g h ɺ () U () H () + A A h A h h H () H () x [ ] a g a g h ɺ () U () H () + A A h A h h H () H () x [ ] () A The cross seconal area of an and (cm ) a The cross seconal area of oule hole of an, and he cross seconal area of oned openng beween an and (cm ) The valve rao a he oule of an The valve rao a he oule of an x The valve rao beween an and, h, h are he seady-sae waer level of an and g The gravy (cm sec ), The gan of pump and pump (cm 3 Vsec ), respecvely From he lnear plan Eq., can be ransformed o yeld a nomnal bloc ransfer funcon of he form (): h (s) (s) (s) u (s) h (s) (s) (s) u (s) () 670 Fg. : Neuron form Through smple algebrac manpulaon, he ransfer marx (s) yelds o: Tx + T s + A TTx A Tx (s) (s) Tx + T s + A Tx A T T x (s) (s) T T + T T + T T x x x s + s + + + T TTx T T T Tx TTx (3) provded ha T s he me consan of an, T s he me consan of an and T x s he me consan neracon beween an and. Accordng o ransfer marx (s) n () and (3), he ransfer funcons of coupled-an process are second order form whch have cross couplng beween process npu and oupus. The decouplng conrollers are requred for mnmzng he effecs from cross couplng and ransform TITO plan ransfer funcon no SISO form. Ths s where neural newor srucure s nroduced a whch can be funconng as he decoupler conroller. PID neural newor conroller: A conrol srucure for conrollng he lqud level an usng PID neural newor conroller as shown n Fg. where has an npu s and an oupu θ. The propery of a neuron s decded by he npu-oupu acvaon funcon (f) whereby he P-neuron, I-neuron and D-neuron are represenng he Proporonal (P) funcon, Inegral (I) funcon and Dervaves (D) funcon, respecvely. For any neuron (namely he h neuron) n he newor whch has n- npus, a any me, he npu of he neuron s gven by:
Am. J. Engg. & Appled Sc., (4): 669-675, 009 n wx () (4) s () x () The oupus of n- conneced neurons n foregong layer and The conneced weghs w The oupu of hs neuron wll depend on s acvaon funcon whch can be Proporonal (P), Inegral (I) or Dervave (D) funcons. The neuron s oupu for each funcon s shown n Table. As a rule, a basc PID-NN consss of wo npu neurons and one oupu neurons whereby he hdden layer of hs newor srucure s made of hree neurons whch each represenng P, I and D acvaon funcon respecvely. The basc PID-NN s as shown n Fg. 3. Through connecve wegh adapaon beween layers, he PID-NN s acually acng as a convenonal PID conroller. Snce PID conrollers have been wdely used n ndusry, ha s o say here are much experence o choose P, I and D parameers n order o su he sysem s sably whou changng one s plan. The conrol sysem for conrollng he coupled an level sysem consss of several basc PID-NN whereby every basc PID-NN s a sub-ne. The mul PID-NN conrol sysem s shown n Fg. 4. The srucure of mul PID-NN s specal. If suable connecve weghs are obaned, each sub-ne of PID-NN s comparavely equal o a PID conroller. By referrng o Fg. 3 of he basc PID-NN, le say ha: w +, w, w o K P, w o K I, w 3o K D Table : Acvaon funcon for each ype of neuron Type of neuron P I D Oupu, θ () s () 0 s ()d ds () d Then, he npu o he newor srucure wll be: s w x r y e (5) Meanwhle, he newor oupu (dependng on he ype of neuron) of he hdden layer for each neuron s obaned as: θ f (s ) (6) Therefore, we derved he oal oupu for he basc PID-NN as shown n Fg. 3 as: (7) o w ox de K Pe K I ed KD θ + + d A any rae, he manpulaed varable sgnals neced no he plan as shown n Fg. 4 s obaned as: U θ (8) Hybrd PI-neural newor conroller: A combnaonal PI conroller wh neural newor srucure for conrollng he lqud level sysem of he coupled an as follows. Proporonal-Inegral (PI) conroller s a feedbac conroller whch drves he plan o be conrolled wh a weghed sum of error (dfference beween oupu and desred response) and he negral of ha value. The general model for a PI conroller s gven n Eq. 9: PI (s) H E H (s) E (s) P I (9) sk + K s The process varable The dfference beween he oupu and he desred response K P and K I The proporonal and negral gans respecvely Fg. 3: Basc PID-NN 67 Fg. 4: (TITO) process wh mul PID-NN conrol sysem
Am. J. Engg. & Appled Sc., (4): 669-675, 009 Fg. 5: (TITO) process wh hybrd PI-NN conrol sysem The hybrd PI-NN s consruced by seres cascadng he PI conrollers wh a neural newor srucure as shown n Fg. 5 Throughou he newor, he lnear acvaon funcon s used n all neurons. Fgure 5 shows he plan ransfer funcon (s) ha has he cross couplng beween process npus and oupus. Because of neracon beween processes, he neural newor srucures wll bascally ac as a decoupler conroller for mnmzng he cross couplng effecs va s connecve wegh adapaon. In conras o he PID-NN, he manpulaed varable sgnals neced no he plan for he hybrd PI- NN s obaned as: U O (0) where we have: and O W O appled n many research and applcaon areas. I has been demonsraed ha PSO ges beer resuls n a faser and cheaper way as compared wh oher mehods. Frs nroduced by Eberhar and Kennedy [8], PSO, le oher evoluonary compuaons, can ypcally nalze a pool of parcles wh random brd posons (called agen) n wo-dmensonal space [9] where each s represened by a pon n he X-Y coordnaes and he velocy s smlarly defned. Brd flocng s assumed o opmze a ceran fness funcon. Each agen nows s bes value so far (pbes) and s curren poson. Ths nformaon s an analogy of personal experence of an agen. Each agen res o modfy s poson usng he concep of velocy. The velocy of each agen can be updaed by he followng equaon: ψ ωψ + η Γ (pbes Ω ) + η Γ (gbes Ω ) () + Ψ ω η and η The velocy of agen a eraon Weghng funcon Weghng facors Γ and Γ The cognve and socal learnng parameers whch generaed randomly beween 0 and Ω p bes g bes The curren poson of agen a eraon The p bes of agen The bes value so far n he group among he p bess of all agens The followng weghng funcon s normally used n Eq. : O W O The ne oupu O on he oher hand, comes from Eq. 9 whch yeld o O (s)e (s) PI Parcles swarm opmzaon: Overvew of he PSO: PSO s a mehod for opmzng hard numercal funcon on meaphor of socal behavor of flocs of brds and schools of fsh. Ths echnque has been wdely used n across wde range of applcaon such as n communcaon, bomedcal [`]. I also has, very recenly, emerges as an mporan combnaoral meaheursc echnque for boh connuous-me and dscree-me opmzaon. In pas several years, PSO algorhms have been successfully 67 ω ω max mn ω ωmax ermax er ω max The nal wegh ω mn The fnal wegh er max The maxmum eraon number er The curren eraon number () Usng he prevous equaon, a ceran velocy, whch gradually brngs he agen close o pbes and gbes, can be calculaed. The curren poson (search pon n he soluon space) can be modfed by he followng equaon:
Am. J. Engg. & Appled Sc., (4): 669-675, 009 Ω Ω + Ψ (3) + + A some eraon, he poson of he agen based on Eq. 3 mgh be flyng-off from he nal lm. Hence, a fly-bac algorhm s mplemened o brng bac he agen o whn he lm. The fly-bac pseudocode used n he program s presened below: + If Ω less han Ω mn Ω + Ω mn +(Ω max -Ω mn)x r and else f Ω + more han Ω max Ω + Ω mn +(Ω max -Ω mn )X r and end Model reference adapve unng usng PSO: In boh PID-NN and hybrd PI-NN conrol sysems; he am of he conrollers algorhm s o mnmze he followng fness funcon (f ): n n m f E { R }(q) H (q) [ ] (4) ref m q R The desred se-pons and H The oupus of he sysem as shown n Fg. 4 and 5 Sep : Evaluae he fness funcon values by f (Ω ) assgnng each Ω as he neural newor weghs and he conroller s parameers. Sep 3: Assgn he global and local bes posons: Se he local bes poson for each parcle usng pbes Ω and compare he evaluaed fness values and fnd he global bes poson gbes Ω, for some J N, such ha f ( Ω ) f ( Ω ) for I, N. Sep 4: Search for mnmum value of f : Updae he parcle veloces Ψ I accordng o Eq. Updae all posons Ω usng formula (3). Chec all posons o ensure ha Ω Ω Ω. If any mn max of he componens of he poson vecors go ou of bounds, hey can be called bac usng he fly-bac algorhm Evaluae f ( Ω ) (I,,,N) Updae he local bes poson: f f ( Ω ) < f (pbes ) Then pbes Ω Updae he global bes poson gbes, by leng gbes Ω, for some J N such ha f ( Ω ) < f ( Ω ) for (I,,,N) Meanwhle, q (,,,n) s he seral number. ref s he frs order model reference ransfer funcon and s represened as: ref (s) (5) τ s + where, τ he me consan for shapng he oupu ransen responses o be as desred. The connecve weghs of PID-NN and hybrd PI- NN as well as he PI parameers are changed and opmzed on each eraon of he PSO. Before begnnng he opmzaon, a populaon sze (.e., number of parcles) N and a maxmum number of eraons er max are chosen. The compuaon flow of PSO echnque can be descrbed n he followng seps: Sep 5: Repea Sep. 4 unl a goal s reached or he number of eraons s surpassed. RESULTS AND DISCUSSION The parameers of he coupled an sysem are aen as follows: Cross seconal area of an and, A 66.5 (cm ) Hegh of each an H 8.5 (cm) Area of he couplng orfce, a 0.963 (cm ) Valve rao a he oule of an, 0.35903 Valve rao a he oule of an, 0.345848 Valve raon of he oule beween an and, x 0.38705 ravaonal rae g 98 cm sec Sep : Randomly nalze he populaon: selec he (normalzed) parcle posons Ω Ω, Ω,, Ω N and veloces Ψ Ψ, Ψ,, Ψ N (,,,N) from unform dsrbuons wh Ω { Ω, Ω } and Ψ {0,0. ( Ω Ω )},,,,N. max mn mn max 673 The lqud levels of he coupled an sysem are requred o follow sep responses whn he range of 0~300 cm (0-00%). Sysem responses namely he lqud level for boh an and are observed. The mnmum and maxmum values of he conrolled manpulaed varables are capped o u mn 0 vol and u max 5 V.
Am. J. Engg. & Appled Sc., (4): 669-675, 009 In he ranng sage, nalze he parameers of PSO as followng. For hybrd PI-NN, here are addonal K P s and K I s for he PI conrollers. Populaon sze 0, nera wegh facor ω s se accordng o (0) where ω max 0.9 and ω mn 0.. Cognve and socal learnng consans are Γ Γ.4. The value n every poson can be clamped o he range [ Ω mn, Ω max ] usng flybac algorhm o reduce he lelhood of parcles leavng he search space. The number of eraons s er max 00. The me consan for he model reference s chosen as τ 0s. Fgure 6 and 7 shows he lqud level responses of coupled an sysem usng PID-NN and hybrd PI-NN conrollers for an and, respecvely. I s noed ha boh conrollers can rac he sep responses of 50 cm. However, he hybrd PI-NN shows a beer performance n erms of me response specfcaons and negral square error as compared o he PID-NN conroller. For he me response performance of he lqud level n an, he PID-NN produces selng me and rse me of 07 and 5.7 sec, whereas he hybrd PI-NN produces selng me and rse me of 8.3 and sec. In he mean me, PID-NN produces selng me and rse of 09 and 4 sec whereas he hybrd PI-NN produces selng me and rse me of 39.7 and. sec for he lqud level n an. I shows ha he PID-NN resuls n a slower response as compared o hybrd PI- NN. I can be sad ha wh hgher number of connecve weghs of neural newor srucure, he complexy o compue he requred manpulaed varables wll ncrease and affec he speed of he response. In erm of negral square error for lqud level n an, he hybrd PI-NN resuls n wce less of ISE as compared o he PID-NN wh he value of.45 0 5 and.567 0 5 respecvely. Smlarly for lqud level n an, he ISE of hybrd PI-NN and PID-NN were obaned as.09 0 5 and.567 0 5, respecvely. The comparave assessmen of boh conrollers s shown n Table Fgure 8 and 9 shows he lqud level responses n an and, respecvely, wh a sep dsurbance of 40 cm neced no he process varable of an durng he seady-sae response. Noed ha he PID-NN conroller produced maxmum percenage overshoos of 35 and 4% for lqud level n an and whereas hybrd PI-NN produces 7 and 8%, respecvely. Furhermore, could be seen ha hybrd PI-NN produce mnmum oscllaon as compared o PID-NN n response o dsurbance necon. I s proven ha he hybrd PI- NN conroller resuls n faser selng me and mnmum overshoo. Besdes ha hybrd PI-NN also exhbs good robusness n mnmzng he cross-couplng effec beween wo ans. Fg. 6: Smulaed response of he lqud level n an Fg. 8: Smulaed response of he lqud level n an wh dsurbance Fg. 7: Smulaed response of he lqud level n an 674 Table : Performance comparson of lqud level n an and Selng me Rse me Overshoo ISE (sec) (sec) (%) ( 0 5 ) --------------------- -------------------- ------------------ ------------------- Conroller Tan Tan Tan Tan Tan Tan Tan Tan PID-NN 07 09.0 5.7 4.0 7.78 5.4.39.567 Hybrd 383 39.7.0. 0.00 0.067.45.09 PI-NN
Am. J. Engg. & Appled Sc., (4): 669-675, 009 Fg. 9: Smulaed response of he lqud level n an wh dsurbance a an CONCLUSION Ths sudy nroduces an mproved hybrd PI-NN conroller for he coupled sysem. The NN weghs connecve and conroller parameers are opmzed by ulzng he PSO algorhm va model reference adapaon. The proposed mehod provdes a beer performance wh respec o PID-NN conroller even under dsurbance necon. The smulaons for boh PID-NN and hybrd PI-NN conrollers are also performed and compared. Based on he resuls, can be concluded ha hybrd PI-NN s more robus and can provde more sable responses han PID-NN. ACKNOWLEDEMENT 4. Pan, H., H. Wong, V. Kapla and M.S. De Queroz, 005. Expermenal valdaon of a nonlnear bac seppng lqud level conroller for a sae coupled wo an sysem. Con. Eng. Prac., 3: 7-40. hp://ca.ns.fr/?amodeleaffchen&cpsd60789 5. Xu, Z. and Q. Zhao, 00. A novel approach o faul deecon and solaon based on wavele analyss and neural newor. Proceedngs of he 00 IEEE Canadan Conference on Elecrcal and Compuer Engneerng, pp: 57-577. DOI: 0.09/CCECE.00.0590 6. Amnan, M. and F. Amnan, 007. A modular faul-dagnosc sysem for analog elecronc crcus usng neural newors wh wavele ransform as a preprocessor. IEEE Trans. Crc. Sys. Insrumen. Measur., 56: 546-554. DOI: 0.09/TIM.007.904549 7. Pol, R., 008. Analyss of he publcaons on he applcaons of parcles swarm opmzaon. J. Arf. Evolu. Appl., -0. DOI: 0.55/008/68575 8. Eberhar, R.C. and J. Kennedy, 995. A new opmzer employng parcles swarm heory. Proceedngs of 6h Inernaonal Symposum Mcro Machne and Human Scence, Oc. 4-6, Nagoya, Japan, Pscaaway, pp: 39-43. DOI: 0.09/MHS.995.4945 9. Reynolds, C., 987. Flocs, herds and schools: A dsrbued behavoral model. Compu. raph., : 5-34. Ths sudy was suppored by Faculy of Elecrcal and Elecroncs Engneerng, Unversy Malaysa Pahang, under Conrol and Insrumenaon (COINS) Research roup. REFERENCES. Vsol, 004. A new desgn for a PID plus feedforward conroller. J. Process Conrol, 4: 457-463. DOI: org/0.06/.procon.003.09.003\%0. Tan, K.K., S. Huang and R. Ferdous, 00. Robus self unng PID conroller for nonlnear sysems. J. Process Conrol, : 753-76. DOI: 0.06/S0959-54(0)00005-7 3. Almuar, N.B. and M. Zrb, 006. Sldng mode conrol of coupled ans. Mecharoncs, 6: 47-44. hp://ca.ns.fr/?amodeleaffchen&cpsd795 8798 675