A New Method of Parameter Estimation and PID-Controller Tuning Based on the Inflectional Tangent. Prof. Dr.-Ing. Herbert M.

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1 A New Metho of aamete Estimation an ID-ontolle nin Base on the Inflectional anent of. D.-In. Hebet M. Schaeel Faclty of Infomation, Meia an Electical Enineein Innovative Diital Sinal ocessin an Applications (DiSA) esente at the Wokshop ocess Atomation 0th Novembe 008 in öln, Gemany of. D. H.M. Schaeel, olone Univesity of Applie Sciences Wokshop ocess Atomation 0 th Novembe 008 in öln /6

Schaeel Faclty of Infomation, Meia an Electical Enineein Innovative Diital Sinal ocessin an

2 Step esponse of a la pocess an fist oe pls ea-time appoximation (FOD) with ientical an h(t) inflection tan en t h G S ( s) e s s : ea-tim e : bil-p time t/s of. D. H.M. Schaeel, olone Univesity of Applie Sciences Wokshop ocess Atomation 0 th Novembe 008 in öln /6

3 nin les by Ziele n Nichols (94) - contolle I- contolle 0,9 ID- contolle, 4,0 0,5 of. D. H.M. Schaeel, olone Univesity of Applie Sciences Wokshop ocess Atomation 0 th Novembe 008 in öln 3/6

4 nin les by hien, Hones an Reswick fo optimal set-point contol (95) apeioic - contolle 0,3 I- contolle ID- contolle 0,35,, 0 0,5 0% oveshoot 0,7 0,60 0,6, 0 0,95, 35 0, 47 of. D. H.M. Schaeel, olone Univesity of Applie Sciences Wokshop ocess Atomation 0 th Novembe 008 in öln 4/6

oveshoot 0,7 0,60 0,6, 0 0,95, 35 0, 47 of. D. H.M.

5 Sm of time constants as a fnction of = / fo typical plants.8 G.6 tan sitio n G to G 4 G G G G / ansfe fnction of typical plants s st G s e G 4 s s n G G s 5 s t G3 s s s s n i s i i e whee = 0... s s of. D. H.M. Schaeel, olone Univesity of Applie Sciences Wokshop ocess Atomation 0 th Novembe 008 in öln 5/6

9 / ansfe fnction of typical plants s st G s e G 4 s s n G G s 5 s t G3 s s s s n i s i i

6 nin les by hn sin the sm of time-constants (995) -contolle D- contolle I- contolle ID- contolle nomal 0,33 0,5 0,5 0,66 0,67 fast 0,7 R n v S 0,8 0,94 of. D. H.M. Schaeel, olone Univesity of Applie Sciences Wokshop ocess Atomation 0 th Novembe 008 in öln 6/6

7 aamete estimation thoh the inflectional tanent aamete estimation # aamete estimation # 0, 48, 33 0, 37, 4 > 0,: , 6 036,, > 0,: , 6 037,, 0, : , : ; whee h 0,5 H 0,4 contibtion of bil-p time to sm of time-constants Hh e,7 h La-time (appaent ea-time) bil-p time / h h ( + ) bil-p vale. of. D. H.M. Schaeel, olone Univesity of Applie Sciences Wokshop ocess Atomation 0 th Novembe 008 in öln 7/6

bil-p time to sm of time-constants Hh e,7 h La-time (appaent ea-time) bil-p time / h h ( + ) bil-p vale.

8 haacteistic feqency paametes of a plant fo contolle tnin G e s s s... s s s... s t s 3 3 Seies-expansion of the ea-time tem e s 3 t 3 st s s... 6 sm of time constants inclin ea-time n i t i n n n i j t i t i ji i poct sm of time constants inclin ea-time It is not necessay to etemine the exact vale of the ea-time of the pocess fo a contolle tnin. of. D. H.M. Schaeel, olone Univesity of Applie Sciences Wokshop ocess Atomation 0 th Novembe 008 in öln 8/6

.. 6 sm of time constants inclin ea-time n i t i n n n i j t i t i ji i poct sm of time constants inclin ea-time

9 ontolle tnin sin feqency-omain infomation accoin to the pinciple of the cascae ampin atio I-contolle fo optimal set-point contol (Schaeel 995) nomal esin Bttewoth 0.5 shap esin schebyscheff 0.5 b ID-contolle fo optimal set-point contol (Schaeel 995) Boaban esin ; a ; v of. D. H.M. Schaeel, olone Univesity of Applie Sciences Wokshop ocess Atomation 0 th Novembe 008 in öln 9/6

10 I-contolle fo optimal istbance ejection (Schaeel 005) Bttewoth (nomal esin) 4 schebyscheff 0. b IAE ID-contolle fo optimal istbance ejection Bttewoth schebyscheff 0,b IAE ,464 0, , S 3 S 3 6 0,04 8 I 9 S 3 0,5 4 D 3 S 3 0, I 9 S 3 0,807 4 D 3 S 3 0,069 8 I 9 S 3 0,876 4 D 3 S 3 of. D. H.M. Schaeel, olone Univesity of Applie Sciences Wokshop ocess Atomation 0 th Novembe 008 in öln 0/6

46 ID-contolle fo optimal istbance ejection Bttewoth schebyscheff 0,b IAE 6 6 6 0,464 0,345 6 0,356 6 3 S 3

11 ontolle-tnin sin the extene metho of inflectional tanent -contolle D- contolle I- contolle I-Rele Optimal istbance ejection 3 0,586 0,353 0,7 0, 45,5 0, 6 0, I 3 0,33 0, 3 4, optimal set-point contol 3 0,586 0,353 0,7A 0, 45,5 0, 6 0, 0,5 0,5 I A S 3 0,375 0,88 3,4 3, 7 of. D. H.M. Schaeel, olone Univesity of Applie Sciences Wokshop ocess Atomation 0 th Novembe 008 in öln /6

set-point contol 3 0,586 0,353 0,7A 0, 45,5 0, 6 0, 0,5 0,5 I A S 3 0,375 0,88 3,4 3, 7 of. D.

12 ID- Rele, 3, 7 0,86 0,55,5 0, 5 0, 0,5 0, 7 0,08 : 0,08 0,08 : 4 0,5 0, 33 0, 9 0,333 0,3 with la-time an bil-p time = / ; h = h ( + ) bil-p vale H h e,7 h h 0,5 H 0,4 contibtion of to sm of time-constants of. D. H.M. Schaeel, olone Univesity of Applie Sciences Wokshop ocess Atomation 0 th Novembe 008 in öln /6

h 0,5 H 0,4 contibtion of to sm of time-constants of. D. H.M.

13 Simlation eslts n oe plant with non-minimm phase tem G s 7,5s 5s7,5s I-contolle fo optimal set-point contol,4, 0,8 0,6 0,4 0, 0-0, -0, Schaeel HR ape. HR 0% hn nomal hn schnell of. D. H.M. Schaeel, olone Univesity of Applie Sciences Wokshop ocess Atomation 0 th Novembe 008 in öln 3/6

50 00 Schaeel HR ape. HR 0% hn nomal hn schnell of. D. H.M.

14 3 oe plant with lea-tem G s 40s 58s6s6s I-contolle fo optimal set-point contol,4, 0,8 0,6 0,4 0, Schaeel HR ape. HR 0% hn nomal hn schnell of. D. H.M. Schaeel, olone Univesity of Applie Sciences Wokshop ocess Atomation 0 th Novembe 008 in öln 4/6

15 Expeimental eslts at a flow pocess Online Lab of Jim Heny, Univesity of ennessee at hattanooa, 7 6,5 Flowate/(lb/min) 6 5,5 5 4,5 4 3, ,5 6 6,5 7 7,5 8 otpt x(t) olyon so t/s of. D. H.M. Schaeel, olone Univesity of Applie Sciences Wokshop ocess Atomation 0 th Novembe 008 in öln 5/6

e 7 6,5 Flowate/(lb/min) 6 5,5 5 4,5 4 3,5 3 5 5,5 6 6,5 7 7,5 8 otpt x(t)

16 haacteistic paametes of the step esponse fnction p = (lb/min)/% h / p = = 0.3s = 0.65s = / = 0.49 Reslts fo the contolle pocess to a setpoint chane ontolle ain (%/lb/min) =, Valve open (sec) 0 Inteal ime (sec) = 0,4 Valve close (sec) 30 Initial set-point (lb/min) = 4 Valve open (sec) 30 hane in set-point (lb/min) = 5 Valve close (sec) 0 ime fo chane in set-point (sec) = Flow/(lb/min) x(t) w(t) t/s Response of the contolle vaiable to a step chane of the efeence inpt of. D. H.M. Schaeel, olone Univesity of Applie Sciences Wokshop ocess Atomation 0 th Novembe 008 in öln 6/6

set-point (lb/min) = 4 Valve open (sec) 30 hane in set-point (lb/min) = 5 Valve close (sec) 0 ime fo chane in set-point (sec) = 5 30 9 8 Flow/(lb/min) 7 6

17 (t) / % Inpt sinal (maniplate vaiable) of the flow-pocess t/s of. D. H.M. Schaeel, olone Univesity of Applie Sciences Wokshop ocess Atomation 0 th Novembe 008 in öln 7/6

18 Refeences Ziele, J.G. an G.A. Nichols, (94). Optimm settins fo atomatic contolles, ans. ASME, 64, pp , New Yok. hien,.l., Hones, J.A. an Reswick, J.B., On the atomatic contol of enealize passive systems, ans. ASME, 74, (95), pp Schaeel, H.M. (997a). aameteschätzn übe ie Wenetanente n iekte Releentwf in en AE- Wekzeen Simool n SIMID.. VDI/VDE Asspacheta "Rechneestützte Entwf von Reelsystemen", 6./7.Sept., assel, GMA-Beicht 3, pp Schaeel, H.M. (997b). A new metho of iect ID contolle esin base on the pinciple of cascae ampin atios. oc. 4 th Eopean ontol onfeence, Bssels,.-4. Jly 997,, ape WE-A H4, BELWARE Infomation echnoloy, Wateloo. Schaeel, H.M. (998). Nee inzipien es iekten Entwfs paameteoptimiete Rele fü stabile, schwinnsfähie n instabile Stecken mit em AE-Wekze Simool. GMA-oness 98 Mess- n Atomatisienstechnik, Lwisb, VDI-Beichte 397, pp Schaeel, H.M. (003a). Speasheet ontol ozessientifikation, Releentwf n Reelkeissimlation mit MS - Excel. GMA-oness 003, Atomation n Infomation in Witschaft n Gesellschaft, Baen-Baen, VDI- Beichte 756, pp , (003). Schaeel, H.M.(003b). ocessientification, ontolle nin an ontol icit Simlation sin MS Excel. oc. 3 th IFA Symposim on System Ientification, Rotteam, Nethelans, Ast 003, ape SWR 43 (on D). of. D. H.M. Schaeel, olone Univesity of Applie Sciences Wokshop ocess Atomation 0 th Novembe 008 in öln 8/6

. VDI/VDE Asspacheta "Rechneestützte Entwf von Reelsystemen", 6./7.Sept., assel, GMA-Beicht 3, pp. 9-8. Schaeel, H.M. (997b).

A PID Tuning Method for Tracking Control of an Underactuated Gantry Crane

A PID Tuning Method for Tracking Control of an Underactuated Gantry Crane Univesal Jounal of Engineeing echanics 1 (13), 45-49 www.aesciences.com A PID Tuning etho fo Tacing Contol of an Uneactuate Ganty Cane. Nazemizaeh Deatment of echanics, Damavan Banch, Islamic Aza Univesity,