The Auto-Tuning PID Controller for Interacting Water Level Process

Transcription

1 World Aademy of See, Egeerg ad Tehology Iteratoal Joural of Eletral ad Iformato Egeerg Vol:, No:, 7 The Auto-Tug PID Cotroller for Iteratg Water Level Proe Satea Tuyarrut, Taha Sukr, Arj Numomra, Supa Gulpah, ad tt Traeth Iteratoal See Idex, Eletral ad Iformato Egeerg Vol:, No:, 7 waet.org/publato/949 Abtrat Th paper preet the approah to deg the Auto- Tug PID otroller for teratve Water Level Proe ug tegral tep repoe. The Itegral Step Repoe (ISR) the method to model a dyam proe whh a be doe ealy, oveetly ad very effetly. Therefore th method advatage for deg the auto tue PID otroller. Our heme ue the root lou tehque to deg PID otroller. I th paper MATLAB ued for modelg ad tetg of the otrol ytem. The expermetal reult of the teratg water level proe a be atfygly llutrated the traet repoe ad the teady tate repoe. eyword Coupled-Tak, Iteratg water level proe, PID Cotroller, Auto-tug. I. INTRODUCTION MPORTANTLY, to model the dutral proe I eeary to deg the lear otroller uh a PI, PID. There are may method to model uh proe for example J.G. Zegler ad N.B. Nhol approah [] a well a.j Atrom ad T. Hugglud approah [] whh are famou ad better tha other tehque. Beaue of thee method are eay ad atfyg to model ytem by obtag the frequey ad ga at the rtal pot of the proe. Thee frequey ad ga a be employed to model the proe. However, th modelg[,3] ha a dver error wth the real proe, o that t brg about degg the better method amed Itegral Sytem Repoe (ISR) [4]. The ISR method ug the tep put gal employ to the proe ad meaure the repoe from the proe for ahevg the proe parameter. Th paper preet the deg of the Auto-Tug PID otroller for teratve Water Level Proe by root lou tehque ad the ytem modelg a be obtaed by tegral tep repoe method. II. THE INTERACTIVE COUPLED-TAN PROCESS Aordg to Fg., the put u the put preure wh h take to the pump, ad the output h the water level t ak. The olear equato a be obtaed by ma equval et equato ad Berury law gve by. dh () t β a k g h( t) h ( t) + u( t) ( ) dt A A dh () t β a β a gh ( t) + g h( t) h ( t) ( ) dt A A q Pump q o h Tak Tak h β Water β q o Fg. The teratve oupled-tak proe A the ro eto area of tak () ( m ), a the ro eto area of outlet of tak ( m ), a the ro eto area of joted ppe betwee tak ad tak ( m ), β the value rato at the outlet of tak, β the value rato betwee tak ad tak, g the gravty ( m / ) ad 3 k the ga of pump ( m / V ) aordg to equato learzed a equato. Satea Tuyarrut, Taha Sukr are wth Faulty of Egeerg, Pathumwa Ittute of Tehology, Bagkok 33, Thalad Arj Numomra, Supa Gulpah ad tt Traeth are wth Faulty of Egeerg, g Mogkut Ittute of Tehology Ladkrabag, Bagkok 5, Thalad (karj@kmtl.a.th). dh() t k ( H ( t ) + H ( t )) + U ( t ) dt T A dh() t + H () t + ( H () t H ()) t dt T T. () Iteratoal Sholarly ad Setf Reearh & Iovato () holar.waet.org/37-689/949

2 World Aademy of See, Egeerg ad Tehology Iteratoal Joural of Eletral ad Iformato Egeerg Vol:, No:, 7 Iteratoal See Idex, Eletral ad Iformato Egeerg Vol:, No:, 7 waet.org/publato/949 T A ( h ) h, T A h, βa g βa g h ad h the water level at operatg pot of th proe, T the tme otat betwee tak ad tak,ad T the tme otat of tak ad. For the equato a be modeled a the equato 3. Th the trafer futo for degg th otroller. H () G () U() TT + ( T + T ) + kt, m/ V A III. CONTROL SYSTEM STRUCTURE The otrol ytem truture ot of 3 part a how Fg.. The frt part the Iteratve oupled-tak proe; the eod part to defe the mathemat model of the proe ad the two degree of freedom otroller. Spefed %P.O. ad t RootLou Deg Pule Geerator Tug Model Etmator SP Forward PID Auto MV PV Plat Cotroller Cotroller Maual Fg. The otrol ytem truture I the part of modelg ytem, the Itegral Sytem Repoe (ISR) [4] ued for the Iteratve oupled-tak proe. Aordg to equato (3), t able to llutrate the eod order ytem wth two pole ad wthout zero thu, the modelg method by ISR wll be putted the tep gal for three tme. For the part of two degree of freedom otroller ot of the feedbak PID otroller ad feed forward pre-flter otroller. The mathematal model of otroller that obtaed by ISR deged the otroller by root lou tehque. [5] Feedbak otroller ( + z )( + z) d + p + G (4) Feed forward otroller z G f (5) ( + z ) (3) IV. INTEGRAL SYSTEM RESPONSE The Itegral Sytem Repoe (ISR) [4] a effetve approah to model the dutral proe beaue th method able to model uh proe ealy, ad the aheved model very loe to the atual proe. Formulate the trafer futo of the proe follow a. G () ( + γ ) ( + τ ) [ + ( γ+ γ + + γ ) + + ( γγ γ ) ] [ + ( τ + τ + L+ τ) + L+ ( ττ Lτ) [ + a + La ] [ b L b ] L L L b ( γ + γ + L+ γ ) a ( τ + τ + L+ τ ) M b ( γγ Lγ ) a ( ττ Lτ ) Iput the tep gal to the proe. M (6) y () t g( tτ )( τ) dτ (7) y ( t) Fg. 3 The proe repoe whe put tep gal order to defe value for Aordg to Fg. 3, the teady tate repoe a be aheved ad the fte tate elemet a be obtaed the equato (7) a followg. G () [ + b + Lb ] lm y ( t) lm lm t [ + a+ L a ] (8) Defe by y () t [ y ( τ )] dτ (9) y () t the tegral area betwee ad y () t to take Laplae to equato (9) a. Y() [ G()] () Defe by G() [ G()] ( a b) + ( a b) + L+ a + a+ La t () Iteratoal Sholarly ad Setf Reearh & Iovato () holar.waet.org/37-689/949

3 World Aademy of See, Egeerg ad Tehology Iteratoal Joural of Eletral ad Iformato Egeerg Vol:, No:, 7 The fte tate elemet a be obtaed the equato () a followg. [ G( )] lm y( t) lm [ G( )] ab t () Defe by y () t [ y ( τ )] dτ (3) y () t the tegral area betwee ad y () t y ( t ) Step 3. Fdg the ga of the otroller by ug the root lou tehque. d G ( d) H ( d) (7) Step 4. Subttuto all of the parameter the equato of otroller. Step 5. Plot the root lou of G() Gp() order to ofrm that the root lou pae the defed pot d. Step 6. To obta the atfyg repoe by puttg tep gal therefore, addg the feed forward otroller a how equato (8). z Gf () (8) ( + z ) Iteratoal See Idex, Eletral ad Iformato Egeerg Vol:, No:, 7 waet.org/publato/949 t Fg. 4 The proe repoe whe put tep gal order to defe value for From thee equato are able to derbe that the hgh order ytem mut take tep gal for may tme. The umber of takg tep put up to the order of eah proe whh oluded a the equato below. a a 3a3 ( ) + + L + a + ( ) b,,, (4) V. THE ROOT LOCUS TECHNIQUE To deg the otroller mut be defed the haratert of traet repoe ad teady tate repoe that a be explaed a. [5] ) The haratert of traet repoe a be derbed form of peret overhoot (P.O.) ) The haratert of teady tate repoe a be derbed form of ettlg tme t The method to deg for atfyg repoe at the traet tate ad teady tate a be appled a followg tep. Step. Fdg the dampg rato:ζ ad uder damped atural frequey: ω by oderg the haratert of traet repoe ad teady tate repoe from the equato (5). ζπ / ζ ( ± %) PO.. * e %, t 4 / ζω (5) d ζω ± jω ζ Step. Fdg the ummato of agle at d of the ope loop ytem G() Gp() by graphal method or arthmetal method ad the oder the eetal agle of ( d + z) order to the ummato of agle wll be beg aordg to the ytem odto.(6) ( θ z + θ z) + θ p (k+ ) π, k,,, (6) VI. EXPERIMENT RESULTS I th paper MATLAB ued for modelg ad tetg of the otrol ytem. The deg of the Auto-Tug PID otroller for teratve Water Level Proe by root lou tehque ad the ytem modelg a be obtaed by tegral tep repoe method. The expermetal reult of the teratg water level proe a be llutrated the repoe of otrol ytem ad the parameter ludg the operatg pot of the proe a how Table I ad Table II. TABLE I THE PARAMETERS OF THE PROCESS A, A; m a, a; m β β TABLE II THE OPERATING POINT OF THE PROCESS h; m h ; m u; V 3 k; m / V Aordg to the parameter ad the operatg pot of th proe a be tead to the equato (3). It wll be obtaed the trafer futo a equato (9) G () (9) VII. THE MODELED PROCESS BY USING ISR METHOD I the part of modelg ytem, after omparg the aheved model wth the o lear proe that a be modeled the proe followg the ISR method. Aordg to equato (3), the Iteratve oupled-tak proe, able to llutrate the eod order ytem wth two pole ad wthout zero thu, the modelg method by ISR wll be putted the tep gal for three tme order to get value of, ad a how fgure 5,6 ad 7 repetvely. Iteratoal Sholarly ad Setf Reearh & Iovato () holar.waet.org/37-689/949

4 World Aademy of See, Egeerg ad Tehology Iteratoal Joural of Eletral ad Iformato Egeerg Vol:, No:, 7 Aordg to Fg. 8, t llutrate the omparo of the tep put repoe betwee the modeled ytem from ISR ad olear model. I th artle, the traet repoe of the modeled ytem from ISR very mlar to the modeled ytem of olear model, but there ome error ot more tha 5 peret for ISR method. Iteratoal See Idex, Eletral ad Iformato Egeerg Vol:, No:, 7 waet.org/publato/949 Fg. 5 The proe repoe whe put tep gal for fdg Fg. 6 The proe repoe whe put tep gal for fdg Fg. 7 The proe repoe whe put tep gal for fdg A a reult, t wll be obtaed, ad a repetvely , 8.4 ad 779. Ad the the trafer futo a be formulated a a followg G () () Fg. 8 Comparo the tep put repoe betwee the modeled ytem from ISR ad olear model VIII. THE STEP INPUT RESPONSE I th top, The PID otroller deg by ug root lou tehque wll be explaed. The proe model whh aheved by ISR a the equato () employed to deg the otroller uder th odto. ( ± %) PO.. 5%, t 3e, e ( t) From the odtoal requremet, t to be. ζ.69, ω.93, d.33± j.4 Ad the t obtaed. θ 8.484, z.55, z.885, 8.5 Therefore, the feedbak otroller ad feed forward otroller are able to be how a followg. G G f Fg. 9 The root lou of otrol ytem Fg. The tep repoe of otrol ytem A a reult, the traet repoe of the modeled ytem from ISR ha the peret overhoot ot more tha 5 peret ad the ettg tme ot more tha 3 m. that uder the odto of otrol ytem deg. Iteratoal Sholarly ad Setf Reearh & Iovato () holar.waet.org/37-689/949

5 World Aademy of See, Egeerg ad Tehology Iteratoal Joural of Eletral ad Iformato Egeerg Vol:, No:, 7 IX. CONCLUSION Th paper preet the deg of Auto-tug PID otroller by ug Itegral Sytem Repoe method order to model the proe. The teratve Water Level Proe ued a a ae tudy ad the MATLAB to be a tool for modelg ad tetg the ytem. I th artle, the traet repoe of the modeled ytem from ISR very mlar to the modeled ytem of olear model, but there ome error ot more tha 5 peret that uder the odto of otrol ytem deg. Iteratoal See Idex, Eletral ad Iformato Egeerg Vol:, No:, 7 waet.org/publato/949 REFERENCES [] L, Ljug, Sytem Idetfato Theory for the Uer, Eglewood Clff, NJ, Prete-Hall 987. [] J.G. Zegler ad N.B. Nhol, Optmum ettg for automat otroller, Tra. ASME, vol.65, 943, pp [3].J. Atrom ad T. Hagglud, Automat tug of mple regulator, Proeedg of IFAC 9 th World Coger.,Budapet, Hugary, 984, [4] J. Dorey, Cotuou ad Drete Cotrol Sytem, MGraw Hll,. [5] Numomra A., -DOF Cotrol Sytem Deged by Root Lou Tehque, Proeedg of ACC otrol 5 th,orea, Otober. Iteratoal Sholarly ad Setf Reearh & Iovato () holar.waet.org/37-689/949