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1 F U ZZY A Control of S upply D uct Outlet A ir T emperature in P ers on al Env ironm ent M odule u s in g PID an d F U ZZY Controller ( )

2 F U ZZY A Control of S upply D uct Outlet A ir T emperature in P ers on al Env ironm ent M odule u s in g PID an d F U ZZY Controller ( )

3 2002 8

4 i.,..... PID FUZZY..

5 ii Abs t ra c t T he PEM (Per sonal Environment Module) is the air conditioning module to control the thermal condition s of the task space, w hich is narr ow area defined near the occupant s. Previous studies show ed that PEM w as better than the conventional air conditioning sy stem in term s of ener gy saving and therm al comfort. Since the PEM is to control the narr ow space, the air flow r ate is u sually sm all. Also it s v elocity has a limit ation to pr ev ent the draft effect and the inlet temper ature should be controlled quickly and accurately within the oper ating range. T he objectiv e of w ork is to control the supply duct outlet air temper ature effectively. A linear model is dev eloped to describe the heat tran sfer phenomena accur ately and the properties included in the equations are also determined properly. From the results, a mathematical model of the heating process is obtained. T he heating device similar to the equipment using electric heater in PEM is prepar ed and the contr oller based on the governing equation s is designed to control the heat flux of the electric heater. Numerical analy sis is done to find the air flow and temper ature distribution at the task space for a given supply condition of PEM. With the r esult s obtained fr om the calculation, the control sy stem to r egulat e the supply duct outlet air temper ature is designed and implemented. PID and FUZZY contr ol sy stem s are u sed to pr ovide the fast respon se w ithout over shoot and m aintain the giv en temper atur e range precisely. Experimental data show that the control sy stem

Since the PEM is to control the narr ow space, the air flow r ate is u sually sm all.

6 iii satisfies the design criteria and w ork s properly in contr olling the supply duct outlet air temper atur e and the performance is impr ov ed in term s of thermal comfort and ener gy saving.

7 iv no me nc lature A w : [m 2 ] A s : [m 2 ] A h : [m 2 ] m : [m 2 ] m ah C a : [J/ K] m s C a : [J/ K] m h C h : [J/ K] m w C w : [J/ K] m d C d : [J/ K] T : [ ] T rh : [ ] T rs : [ ] T a : [ ] T i : ( ) [ ] U w : [W/ m 2 K] U s : [W/ m 2 K] U h : [W/ m 2 K] h o. w : [W/ m 2 K] h o. d : [W/ m 2 K] K P : (proportion al g ain ) K I : (int egral gain ) K D : (deriv ativ e gain ) u : [V] e :

8 v L : T : (sam plin g period) [sec] G re e k S y m bo ls : (T ime constant ) [sec] S ubs c ripts p : i : d : f : 1 3 :

9 v i Lis t o f Fig ure s F ig. 1 T he calculation dom ain 32 F ig. 2 Dim en sion s of in door area 32 F ig. 3 Velocity v ect or distribution s for differ ent operatin g condition s 33 F ig. 4 T em perature distribution for different operatin g condition s 34 F ig. 5 S chem atic diagram of ex perim ent al apparatu s 35 F ig. 6 Control v olum e of h eat er and supply du ct 35 F ig. 7 Ex perim ent al dat a v s sim ulation data 36 F ig. 8 Control sy stem block diagram 36 F ig. 9 Sy st em respon se w hen K p = F ig. 10 Sy st em respon se w hen K p =0.2, K D = F ig. 11 Sy st em respon se w hen K P =0.7, K D =2.19, K I = F ig. 12 Block diagram of fuzzy controller 39 F ig. 13 Input m em ber ship fun ction 39 F ig. 14 Output m emb er ship fun ction 39 F ig. 15 Sy st em respon se of fu zzy P ID controller w hen L = F ig. 16 Sy st em respon se of simple fuzzy controller w hen L =1.0 40

7 Ex perim ent al dat a v s sim ulation data 36 F ig. 8 Control sy stem block diagram 36 F ig. 9 Sy st em respon se w hen K p =0.08 37 F ig. 10 Sy st em respon se w hen K p =0.2, K D =1.0 37 F ig.

10 v ii Lis t o f Ta b le s T able. 1 V alu es of the con stant s in th e k - m odel 30 T able. 2 Boun dary con dition s 30 T able. 3 F u zzy control rules for u 31

11 v iii Abstract Nomenclature Greek Symbols Subscripts List of Figures List of T ables

12 ix PID P ( ) PD( - ) PID ( - - ) PID PID

3.3 PID ( - - ) 19 3.3.4 PID 20 3.4 22 3.4.1 PID 23 3.

13 , [1]. (PEM : Pe rs o na l Enviro nme nt Mod ule)

14 2., (Tas k a re a) (Ambie nt a re a).,,,, [1].

15 3 1.2 (Pe rs o na l Air Cod itio ning). [2] [3 ]. (Pe rs o na l Enviro nme nt Mod ule : PEM). ( ) [2 ]... (mixing c ha mbe r).,,.,.

16 4...,.,. PID. PID..

17 (UFAC : Unde r Floo r Air Co nd itio ning) [4 ]. Fig m, m 4, m 4 (UFAC : Unde r Floo r Air Cond itio ning) [5] m PEM. Fig. 2 PEM 4 4 [5].,, 2 0. k -. x, y, z , Vo lume Method) [6] [7].. (Finite

3 m 4 (UFAC : Unde r Floo r Air Cond itio ning) [5]. 0.25 0.

18 6 : U i x i = 0 (1) : U j U i x j = + 1 r x j p x i ( U i - u x i u j j ) + g i - r r (2) : U i T x i = x i ( T - u x i i ) (3) : U i k x i = x i ( t k k x i ) + P + G - (4) : U i x i = x i ( t x i ) + c 1 ( P + G) k ( G 1 - c 3 P + G ) - c 2 2 k (5)

19 7 P = t ( U i x j + U j x i ) U i x j (6) G = g i t t T x i (7) - u i u j = t( U i x j + U j x i ) k ij (8) - u i = t t T x i (9) t = c k 2 (10) Ta ble. 1, Ta ble 2 [4 ] [8 ].

j x i ) - 2 3 k ij (8) - u i = t t T x i (9)

20 8 2.2 Fig. 3. Ca s e A, Cas e B, C, D PEM. xz Ca s e A PEM. Ca s e B, C, D PEM,. PEM. Ca s e B, C, D Ca s e B Ca s e D. Ca s e D. PEM. Ca s e B PEM. Fig. 4. Ca s e A xz xy. Cas e B, C, D xz PEM. PEM Ca s e D

21 9.. PEM. PEM Ca s e A. Ca s e B, C, D.. Ca s e B, C, D xy PEM.. Ca s e A B 23, Ca s e A 26, Ca s e B PEM Cas e B A , (z) 1.1 m,. Cas e B. C, D xy.

22 PEM...

23 ,. Fig. 5.. lumpe d he at c a pa c ity [9 ]. Fig. 6.. (11) (13). (11) (12), T h,. m ah C a d T a d t + m h C h d T h d t = q - m C a ( T a - T ) - U w A w ( T a - T rh ) (11)

24 12 U h A h ( T h - T a ) = m ah C a d T a d t + m C a ( T a - T ) + U w A w ( T a - T rh ) (12) m w C w d T rh d t = U w A w ( T a - T rh ) - h o. w A w ( T rh - T ) (13) (14) (15). m s C a d T i dt = m C a ( T a - T i ) - U s A s ( T i - T rs ) (14) m d C d d T rs d t = U s A s ( T i - T rs ) - h o. d A s ( T rs - T ) (15) (11) (15) La pla c e. T a ( s) = G 1 ( s) q( s) + G 2 ( s) T rh ( s) (16) G 1 ( s) = + 1 m h C h m ah C a s 2 m h C h + [ m U h A h C h + m ah C a ( m C h U h A a + U w A w ) ]s h 1 + m C a + U w A w (17) G 2 ( s) = U w A w G 1 ( s) (18)

25 13 T rh ( s) = G 3 ( s) T a ( s) (19) G 3 ( s) = U w A w m w C w s + U w A w + h o. w A s (20) T i ( s) = G 4 ( s) T a ( s) + G 5 ( s) T rs ( s) (21) G 4 ( s) = m C a m s C a s + m C a + U s A s (22) G 5 ( s) = U s A s m s C a s + m C a + U s A s (23) T rs ( s) = G 6 ( s) T i ( s) (24) G 6 ( s) = U s A s m d C d s + U s A s + h o. d A s (25) T a ( s) = T a - T T i ( s) = T i - T T rh ( s) = T rh - T T rs ( s) = T rs - T (Tra nsfe r func rio n) ( G h ) ( G s ). G h = G G 2 G 3 G s = G G 5 G 6 (26)

26 ,, [10]..,.,., Dittus - Boe lte r. (the rma l c ond uctivity ta ble) [8 ]... V h m 3 V s m 3 m kg/ s m ah C a J / K U w W/ m 2 K A w m 2

27 15 m s C a J / K U s W/ m 2 K A s m 2 m h C h J / K U h W/ m 2 K A h m 2 m w C w J / K h o. w W/ m 2 K m d C d J / K h o. d W/ m 2 K G 1 = G 2 = ( s )( s ) ( s )( s ) G 3 = s G 4 = G 5 = G 6 = G h = G s = s s s (s ) ( s )( s )( s ) ( s ) ( s )( s )

28 Fig. 7 s imulation. [10 ]. Fig. 7. PEM,.,.

29 Fig. 8, PC Vis ua l C++.,, a ir tra ns mitte r LAN PC. G c, V ss PC 12 D/A (TPR) ( 5 V). V ss (11) (15) 0 (27), K h [W/ V]. q ss = V ss K h = ( T i + 273) ( T + 273) (27) 23 43, (ove rs hoot), (s aturatio n).

30 P ID ( - - ) P( ). (P ) Fig. 10 G c G c ( s) = K P (28),,., (Sa turatio n) K P Fig. 9, PD( - ). - (PD ) G c ( s) = K P + K D s (29) -

31 19,. Fig %. -, - (ze ro) s PID( - - ) - - (PID ). G c ( s) = K P + K D s + K I s (30) PID P PD (ste a dy- state e rro r). PID,. Fig. 11 (Root- loc us) K P 0.7, K D 2.19, K I PID. PID s, P PD.

32 20 Fig. 11 (ove rs hoot),. PID, Fig. 11,,.,., PID.., (type numbe r).,

33 21., -.

34 PID [11]. Fig. 12 (me mbe rs hip functio n) (fuzz ific atio n) (fuzzy rule ba s e) (infe re nc e) (defuzz ific ation). [12]. [1] ( ) [2] [3] ( PID ) PID [3]. Fuzzy PID. PID PID.

35 23 [1] PID PID PID [13] [14 ]. U( t) = K P e( t) + K I e( t)d t + K D e( t) (31), e ( t), e( t). (3 1) La pla c e. U( s) = K P E ( s) + K I E ( s) s + K D se ( s) (32) z- Tra pezo id s = 2 T 1 - z z - 1 se ( s) = E ( z ) [15] [16]. U( z )( 1 - z - 1 ) = K P E ( z )( 1 - z - 1 ) + K I T 2 ( 1 + z - 1 )E ( z ) + K D E ( z )( 1 - z - 1 ) (33)

36 24 (33) (34). u ( n T ) - u ( n T - T ) = K P e( n T ) - K I T 2 e( n T ) + 2 K I T 2 e( n T ) - ( K P e( n T - T ) - K I T 2 e( n T - T )) + K D ( e( n T ) - e( n T - T )) (, e( n T ) = e( n T ) - e( n T - T ) T ) (34) (34) PID. z- (35) PID PID s a mpling [16]. U( z ) = K P E ( z ) + K I 1 - z - 1 E ( z ) + K D 1-2 z z z - 1 E ( z ) (35) (, K P = K P - TK I 2, K I = K I T, K D = K D T ), PID PID (36). s a mpling 1.

37 25 e P ( n T ) = K P e( n T ) e I ( n T ) = e I ( n T - T ) + K I e( n T ) (36) e D ( n T ) = K D ( e( n T ) - e ( n T - T )) Fig. 13 (me mbe rs hip g ra de) (me mbe rs hip functio n). (d isturba nc e). (ro bot) [17 ]. p (pos itive) n(ne gative) L. Fig. 14 p (pos itive), n(ne gative), pl(pos itive la rge), nl (ne gative la rge) (fuzzy la be l), 1-5 [V}. Ta ble (u). [18 ].

38 PID PID PID. a na log PID c o ntro l PID tra pezo id [16] [19 ]. u P ( z ) = E ( z ), u I ( z ) = T z z - 1 E ( z ), u D ( z ) = 2 T 1 - z z - 1 E ( z ) (37). e 1 ( n T ) = e f ( n T ), e 2 ( n T ) = e 2 ( n T - T ) + T 2 ( e f ( n T ) + e f ( n T - T )) e 3 ( n T ) = - e 3 ( n T - T ) + 2 T ( e f ( n T ) - e f ( n T - T )) (38) PID,, PID.

39 Fig. 11 PID -. L Simulink Fuzzy log ic too lbox. L 1.0. L L L. Fig. 15. PID PID. L. L. L., L

40 28. Fig. 16 Fuzzy PID L. PID PID.

41 29 4. PID. (1). (2) PID,. (3) PID PID. (4). (5) PID. (6) PEM.

42 30 C C1 C2 C3 k T able 1 Valu es of the con st ant s in the k - m odel. P osition Condition W all V elocity u,v,w =0 T em perature adiabatic PA C diffu ser inlet V elocity Case B,C,D 0.4 m/ s Case B Case C Case D T em perature V elocity T em perature Case A Case A bott om m/ s 26.0 diffu ser inlet V elocity Case B,C,D m/ s Case B Case C Case D T em perature Outlet Pressure p =p a t m Out door T em perature 0 T able 2 Boun dary con dition s.

43 31 e P e I e D u Rule 1 n n n nl Rule 2 n n p n Rule 3 p n n n Rule 4 p n p p Rule 5 n p n n Rule 6 n p p p Rule 7 p p n p Rule 8 p p p pl T able 3. F uzzy control rules for u.

44 32 F ig. 1 T he calculation dom ain. F ig. 2 Dim en sion s of the in door area.

45 33 (a ) Ca se A (x z plane) (b ) Case A (xy plan e) (c ) Case B (x z plan e) (d ) Case B (x y plane) (e) Case C (x z plan e) (f) Case C (xy plan e) (g ) Case D (x z plan e) (h ) Case D (x y plane) F ig. 3 V elocity v ector distribution s for different operating con dition s. (x z plan e at y =1.8m, x y plane at z=1.1m )

46 34 (a ) Ca se A (x z plane) (b ) Case A (x y plan e) (c ) Case B (x z plan e) (d) Case B (xy plan e) (e) Case C (x z plan e) (f) Case C (x y plane ) (g ) Case D (x z plan e) (h ) Case D (x y plan e) F ig. 4 T em perature distribution for different operating con dition s. (x z plan e at y =1.8m, x y plane at z=1.1m )

47 35 F ig. 5 S ch em atic diagram of experim ental apparatu s. F ig. 6 Control v olum e of heater an d supply duct.

48 36 F ig. 7 Ex perim ent al dat a v s sim ulation dat a. F ig. 8 Control sy st em block diagram.

49 37 F ig. 9 Sy stem respon se w hen K p =0.08. F ig. 10 Sy st em respon se w hen K p =0.2, K D =1.0.

50 38 F ig. 11 Sy stem respon se w hen K P =0.7, K D =2.19, K I =0.013.

51 39 F ig. 12 Block diagram of fuzzy controller. F ig. 13 Input m em bership function F ig. 14 Output m em bership function.

52 40 F ig. 15 Sy st em r espon se of fuzzy PID controller w hen L=1.0. F ig. 16 Sy st em respon se of sim ple fuzzy controller w hen L =1.0

53 41 1. S. H. Cho, A Fundamental Study for Dev elopment of Per sonal Environment Module (PEM ) Sy stem, 1998, Report of LG- Honeyw ell Industrial Inc., pp S. H. Cho, W. T. Kim and M. Zaheer - uddin, 2001, T hermal Char act eristics of A Per sonal Environment Module T ask Air Conditioning Sy stem : An Experimental Study, Energy Conv er sion and Management, Vol. 42 pp Koh and Hasegaw a, Per sonal Air - conditioning, 1991, Heating Piping and Air - conditioning, Vol. 65, No. 7, pp J. H. Cho, E. J. Cho, T. B. Seo and Y. C. Park, 2000, Air Flow and Heat T r an sfer Analy sis of Per sonal Envir onm ent Module Sy stem, Pr oceeding of SAREK Wint er Annual Conference, Vol. 1, pp C. O. Yoon, J. J. Yee, K. S. Chung, H. T. Han and Y. C Park, 2000, T he Experimental Study on T he T herm al Environmental Char act eristics of Per sonal Air - conditioning Sy stem, Pr oceeding of SAREK Summer Annual Confer ence, Vol. 1 pp B. Griefahn, C. Kunemund and V. Gehring, 2000, T he Significance of Air Velocity and T urbulence Inten sity for Respon ses to Horizontal Draft s in a Con stant Air T emper ature of 23, Int ernational Journal of Indu strial Er gonomics, Vol. 26, pp S. H. Cho, C. Y. Jang, and C. S. T ae, 2000, T he experimental study on thermal char acteristics of PEM sy stem,

54 42 Korean Journal of Air Conditioning and Refrigeration Engi neering, Vol. 12, No. 5, pp F. P. Incr opera and D. P. Dew itt, 1996, Fundamentals of Heat and Mass T ran sfer, published by John Wiley & Son s, 4th ed., pp Y. G. Shin, and Y. I. Kim., 1998, Modeling of electric heater contr ol dynamics, Proceeding of SAREK Summer Annual Conference, Vol. 3, pp Y. J. Chang, Y. C. Park, K. S. Chung, H. T. Han and J. J. Rhee, 2001, A PID control of electric heater for PEM, Korean Journal of Air Conditioning and Refriger ation Engi neering, Vol. 13, No. 1, pp T. T erano, K. A sai and M. Sugeno, 1992, Fuzzy Sy stem s T heory and It s Application s, 1st ed., Academic Pres s Inc. 12. L. W ang, 1997, A Cour se in Fuzzy Sy stem s and Control, 1st ed., Pr entice hall 13. D. Misir, H. Malki and G. Chen, 1996, Design and analy sis of a fuzzy pr oportional- integr al- derivative contr oller, Fuzzy Sets and Sy stem s, Vol. 79 pp J. Carv ajal, G. Chen and H. Ogmen, 2000, Fuzzy PID controller : Design, performance ev aluation, and stability analy sis, International Journal of Information Sciences, Vol. 123 pp J. G. Bollinger and N. A. Duffie, 1988, Computer Contr ol of Machines and Proces ses, 1st ed, A ddison - Wesley. 16. G. Fr anklin, J. Pow ell and M. Workman, 1997, Digital Control of Dynamic Sy stem s, 3rd ed., Addison - W esley.

55 P. Soor ak sa and G. Chen, 1998, Mathematical m odeling and fuzzy control of a flexible- link robot arm, Mathematical Computer Modeling, Vol. 27, No. 6, pp W. LI, 1998, Design of a Hybrid Fuzzy Logic Proportional Plu s Conventional Integral- Derivative Contr oller, IEEE T r an saction s on Fuzzy Sy stem, Vol. 6, No. 4, pp H. Malki, H. Li and G. Chen, 1994, New design and st ability analy sis of fuzzy pr oportional- derivative contr ol sy stem, IEEE T ransaction of Fuzzy Sy stem s, Vol. 2, No. 4, pp

334 退溪學 과 儒敎文化第 55 號角說 에서는 뿔이 난 말과 고양이라는 기형의 동물을 소재로 하여 당대 정치 상 황을 비판하였고, 白黑難 에서는 선과 악을 상징하는 색깔인 白 과 黑 이 서로 벌이 는 문답을 통하여 옳고 그름의 가치관이 전도된 현실세

334 退溪學 과 儒敎文化第 55 號角說 에서는 뿔이 난 말과 고양이라는 기형의 동물을 소재로 하여 당대 정치 상 황을 비판하였고, 白黑難 에서는 선과 악을 상징하는 색깔인 白 과 黑 이 서로 벌이 는 문답을 통하여 옳고 그름의 가치관이 전도된 현실세 南坡洪宇遠 의 논설류 산문 연구 禹芝英 *1) 차 례. 서론. 친근한 소재를 통한 공감의 확대. 문답의 서술방식을 통한 논리성의 강화. 우언의 서술방식을 통한 현실 비판. 결론 국문초록 南坡洪宇遠 은 仁祖 에서 肅宗 연간에 활동한 문인 관료이다. 홍우원의 문집인 南坡集 은 시와 상소문이 대부분의 비중을 차지하고, 記說序 등의 산문