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 2002 8 ( )
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 2002 8 ( )
2002 8
i.,..... PID FUZZY..
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
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.
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 :
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 :
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 =0.08 37 F ig. 10 Sy st em respon se w hen K p =0.2, K D =1.0 37 F ig. 11 Sy st em respon se w hen K P =0.7, K D =2.19, K I =0.013 38 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 =1.0 40 F ig. 16 Sy st em respon se of simple fuzzy controller w hen L =1.0 40
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
v iii Abstract Nomenclature Greek Symbols Subscripts List of Figures List of T ables 1. 1 1.1 1 1.2 3 2. 5 2.1 5 2.2 8 2.3 10 3. 11
ix 3.1 11 3.1.1 11 3.1.2 14 3.1.3 16 3.2 17 3.3 PID 18 3.3.1 P ( ) 18 3.3.2 PD( - ) 18 3.3.3 PID ( - - ) 19 3.3.4 PID 20 3.4 22 3.4.1 PID 23 3.4.2 26 3.4.3 27 4. 29 30 41
1 1. 1. 1.. 1970..,. 1980.... 1990 [1]. (PEM : Pe rs o na l Enviro nme nt Mod ule)
2., (Tas k a re a) (Ambie nt a re a).,,,, [1].
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).,,.,.
4...,.,. PID. PID..
5 2. 2. 1. (UFAC : Unde r Floo r Air Co nd itio ning) [4 ]. Fig. 1. 5.00 3.45 2.25 m, 0.2 0.4 m 4, 0.3 0.3 m 4 (UFAC : Unde r Floo r Air Cond itio ning) [5]. 0.25 0.2 m PEM. Fig. 2 PEM 4 4 [5].,, 2 0. k -. x, y, z 75 46 27, Vo lume Method) [6] [7].. (Finite
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)
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 ) - 2 3 k ij (8) - u i = t t T x i (9) t = c k 2 (10) Ta ble. 1, Ta ble 2 [4 ] [8 ].
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
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 26 24. Cas e B A 24 26., (z) 1.1 m,. Cas e B. C, D xy.
10 2.3. PEM...
11 3. 3. 1 3.1.1.,. 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)
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)
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 1 1 - G 2 G 3 G s = G 4 1 - G 5 G 6 (26)
14 3.1.2,, [10]..,.,., Dittus - Boe lte r. (the rma l c ond uctivity ta ble) [8 ]... V h 0.0056 m 3 V s 0.0 123 m 3 m 0.0 168 kg/ s m ah C a 6.6 14 J / K U w 2.468 W/ m 2 K A w 0.189 m 2
15 m s C a 14.35 J / K U s 1.86 1 W/ m 2 K A s 0.393 m 2 m h C h 1385.44 J / K U h 225.76 W/ m 2 K A h 0.03 14 m 2 m w C w 726.84 J / K h o. w 644.27 W/ m 2 K m d C d 259.58 J / K h o. d 0.648 W/ m 2 K G 1 = G 2 = 0.000774 ( s + 0.0036 3)( s + 3.7017) 0.00549 ( s + 0.0036 3)( s + 3.7017) G 3 = 0.000642 s + 0. 1682 G 4 = G 5 = G 6 = G h = G s = 1. 1790 s + 1.230 0.0509 s + 1.230 0.0028 s + 0.0038 0.000774 (s + 0. 1682) ( s + 3.7017 )( s + 0.003624)( s + 0. 1681) 1. 1790 ( s + 0.0038) ( s + 0.0036 8)( s + 1.230)
16 3.1.3 Fig. 7 s imulation. [10 ]. Fig. 7. PEM,.,.
17 3.2 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 140.3 [W/ V]. q ss = V ss K h = 17.24 ( T i + 273) - 17.22 ( T + 273) (27) 23 43, (ove rs hoot), (s aturatio n).
18 3.3 P ID ( - - ) 3.3.1 P( ). (P ) Fig. 10 G c G c ( s) = K P (28),,., (Sa turatio n) K P 0.108. Fig. 9, 7. 3.3.2 PD( - ). - (PD ) G c ( s) = K P + K D s (29) -
19,. Fig. 10 -. 15%. -, - (ze ro) s. 3.3.3 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 0.013 PID. PID s, P PD.
20 Fig. 11 (ove rs hoot),. PID, Fig. 11,,.,.,. 3.3.4 PID.., -. -. (type numbe r).,
21., -.
22 3.4. 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.
23 [1]. 3.4.1 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 - 1 1 + 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)
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 - 1 + z - 2 1 - 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.
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. 3 8. (u). [18 ].
26 3.4.2 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 2 1 + z - 1 1 - z - 1 E ( z ), u D ( z ) = 2 T 1 - z - 1 1 + 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.
27 3.4.3 25 43. Fig. 11 PID -. L Simulink Fuzzy log ic too lbox. L 1.0. L L L. Fig. 15. PID PID. L. L. L., L
28. Fig. 16 Fuzzy PID L. PID PID.
29 4. PID. (1). (2) PID,. (3) PID PID. (4). (5) PID. (6) PEM.
30 C C1 C2 C3 k 0.09 1.44 1.92 0.8 1.0 1.3 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 26.0 28.0 30.0 V elocity T em perature Case A Case A bott om 0.125 m/ s 26.0 diffu ser inlet V elocity Case B,C,D 0.0625 m/ s Case B Case C Case D T em perature 24.1 24.1 24.1 Outlet Pressure p =p a t m Out door T em perature 0 T able 2 Boun dary con dition s.
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.
32 F ig. 1 T he calculation dom ain. F ig. 2 Dim en sion s of the in door area.
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 )
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 )
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.
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.
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.
38 F ig. 11 Sy stem respon se w hen K P =0.7, K D =2.19, K I =0.013.
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.
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
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