Tuning of PID Controllers for Unstable Continuous Stirred Tank Reactors

Transcription

1 nternational Journal of Alied Siene and Engineering , 1: 1-18 Tuning of P Controllers for Unstable Continuous Stirred Tank Reators. rishna a,. Suryanarayana b, G. Aarna b, and R. Padma Sree b, * a eartment of Chemial Engineering, M.V.G.R. College of Engineering, Vizianagaram, ndia b eartment of Chemial Engineering, Andhra University College of Engineering (A) Visakhaatnam, ndia Abstrat: Tuning Proortional ntegral and erivative (P) ontrollers for unstable Seond Order Plus Time elay systems with a Zero (SOPTZ), based on internal model ontrol (MC) and stability analysis (SA) riniles is roosed. The ontrollers designed by the roosed methods are used to ontrol unstable jaketed Continuous Stirred Tank Reators (CSTR), arrying out irreversible first order reation. The erformane of roosed ontrollers is omared with the synthesis method. Simulation results on nonlinear unstable ontinuous stirred tank reators and transfer funtion models are resented to the show the effiieny of the roosed ontrollers. eywords: nternal model ontrol; stability analysis method; synthesis method; CSTR; P ontroller; Unstable systems; Seond Order Plus Time elay system with a Zero (SOPTZ). 1. ntrodution P ontrollers give satisfatory erformane for many of the ontrol roesses. ue to their simliity and usefulness, P ontroller has beome a owerful solution to the ontrol of a large number of industrial roesses. The ontrol systems erformane is omliated by the numerator dynamis (resene of a zero) of the roess. Several roesses exhibit seond order lus time delay system with a zero transfer funtion model. Examles for suh roesses are jaketed CSTR [1], distillation olumn [], autoatalyti CSTR [3] and rystallizer [4]. Many reyle roesses where energy and mass reyle takes lae are reresented by SOPTZ transfer funtion model []. Very limited methods of designing P ontrollers for unstable SOPTZ systems are available in the literature. They are MC method [5] and synthesis method [6]. n the synthesis method [6], losedloo transfer funtion is assumed. From the losedloo transfer funtion, ontroller transfer funtion is derived using roess transfer funtion. Later ontroller transfer funtion is written as P ontroller with a lead lag filter. n the MC method [5], the P ontrollers are designed for unstable FOPT and SOPT systems with and without a zero from MC filter using Malaurin series exansion. * Corresonding author; advan@rediffmail.om Reeived 4 May Chaoyang University of Tehnology, SSN Revised July 011 Aeted 9 Setember 011 nt. J. Al. Si. Eng., , 1 1

2 . rishna,. Suryanarayana, G. Aarna, and R. Padma Sree n the resent work, a simle method for designing P ontrollers based on internal model ontrol riniles and stability analysis is roosed. The P tuning arameters are given as funtion of roess model arameters. Simulation results for various transfer funtion models and nonlinear models are given to show the effiieny of the roosed ontrollers.. Proosed methods.1. nternal model ontrol (MC) method The roess transfer funtion for SOPT with a negative zero is given by Ls (1 + s) e G ( 1s + 1)( s 1) (1) Using Pade s aroximation for the time (1 0.5Ls) delay e Ls, the roess transfer ( Ls) funtion in Eq (1) is written as, (1 + s)(1 0.5Ls) G ( 1s + 1)( s 1)( Ls) () The roess transfer funtion is written as + G G GP (3) Where G + P (s) is invertible art and G - P (s) is noninvertible art. Therefore, the invertible art of the roess transfer funtion in Eq () + (1 + s) isgp (4) ( 1s + 1)( s 1)( Ls) The MC ontroller for this system is given + 1 as, Q [ GP ]. f (5) Where f is MC filter. t onsists of both numerator and denominator dynamis. The order of the numerator is equal to the number of unstable oles of the roess. The order of denominator is seleted in suh a way to make ontroller realizable (the ontroller numerator order should be less than or equal to that of the order of denominator). Therefore MC filter for this transfer funtion model is ηs + 1 given by f 3 ( λs + 1) (6) Using Eq (4) and Eq (6) in Eq (5), MC ontroller is given by ( Ls)( 1s + 1)( s 1)( ηs + 1) Q 3 P (1 + s)( λs + 1) (7) Where λ is MC filter time onstant, is a tuning arameter. The equivalent P ontroller is obtained by using the following equation, Q G (1 GP Q) (8) Substituting Eq () and Eq (7) in the above equation, the following transfer funtion model for the ontroller is obtained. ( Ls)( 1s + 1)( s 1)( ηs + 1) G (9) 3 (1 + s)[( λs + 1) (1 0.5Ls)( ηs + 1)] Eq (9) an be rearranged into the following form, 1 (1 + α0s) G [1 + + s] (10) s ( α1s + αs + 1) This is a P ontroller with a lead lag filter Where, 1 + η ( η 3λ 0.5L) (11) ( 1 + η) (1) 1η ( 1 + η) (13) 3 λ + (3λ + 0.5L) + 3λ η ( 0.5L ) (14) α 0.5L 0 (15) 3 λ α 1 ( η 3λ 0.5L) (16) 3 λ α + (17) ( η 3λ 0.5L) λ is seleted by trial and error roedure. f the value of λ is large, the resonse is sluggish but robust and if it is small the resonse is fast but less robust. f time delay is small, the time delay is aroximated as e Ls 1 Ls, the invertible art of the roess transfer funtion of Eq (1) nt. J. Al. Si. Eng., , 1

3 Tuning of P Controllers for Unstable Continuous Stirred Tank Reators isg + P (1 + s) ( 1s + 1)( s 1) (18) The MC ontroller for the given transfer funtion is given in Eq (5). Therefore, MC ηs + 1 filter f is given by f (19) ( λs + 1) Using Eq (18) and Eq (19) in Eq (5), MC ontroller is given by ( 1s + 1)( s 1)( ηs + 1) Q (0) P (1 + s)( λs + 1) Substituting Eq (1) and Eq (0) in Eq (8), the following transfer funtion model for the ontroller is obtained. ( 1s + 1)( s 1)( ηs + 1) G (1) (1 + s)[( λs + 1) (1 Ls)( ηs + 1)] Eq (1) is rearranged into P ontroller with a first order lag filter. 1 1 G [1 + + s] () s ( s + 1) f Where, 1 + η ( η λ L) (3) ( 1 + η) (4) 1η + η) (5) ( 1 (6) f λ + (λ + L) η (7) L.. Stability analysis method The roess transfer funtion for unstable SOPT with a negative zero is given by Eq (1). The transfer funtion of the ontroller is given by 1 1 G (1 + )(1 + s)( ) (8) s αs + 1 The ombined transfer funtion model of the roess and the ontroller is given by G G Ls P (1 + s) e 1 1 (1 + )(1 + )( ) s ( 1 s + 1)( s 1) s αs + 1 (9) Let 1 and α, then Eq (9) is written as 1 Ls (1 + ) e s G G s 1 (30) 5 Where ω is rossover frequeny and ω is given by. Phase angle riteria for oenloo transfer funtion [Eq (30)] is given by tan ( ) L ω + tan ( ω ) 0 (31) ω 1 1 tan ( 0.) L ω + tan ( ω ) 0 (3) Eq (3) is solved by using fsolve of MATLAB forω. Using amlitude riteria, is given by k 1+ ω 1 1+ ( ) ω k 1+ ω 1+ (0.) (33) Eq (8) is omared with the onventional P ontroller with a lag filter [Eq ()] and the onventional P settings are given by ( + ) (34) + (35) + (36) α (37) nt. J. Al. Si. Eng., , 1 3

4 . rishna,. Suryanarayana, G. Aarna, and R. Padma Sree 3. Simulation results n this setion, roosed P ontroller designed by MC method (MC-P ontroller) and roosed P ontroller designed by stability analysis method (SA-P ontroller) are alied to various CSTR transfer funtion models and non-linear models to show the effiieny of the roosed ontrollers. The erformane of the roosed ontrollers is omared with P ontroller designed by synthesis method [3] (SM-P ontroller). Case study-1 Consider a jaketed CSTR arrying first order irreversible exothermi reation. The heat of reation is removed by a oolant in the jaket to maintain temerature of reation. The model equations of jaketed CSTR without jaket dynamis [1] are, dc A F Ea ( C Af C A ) 0 ex( ) C A dt V RT (38) dt dt F ΔH Ea UA ( T f T ) + ( ) 0 ex( ) C A ( T T j ) V ρc RT VρC (39) The above non-linear model equations are linearised around the unstable oerating oint C A lb.mol/ft 3, T R and T j R. The values of the roess arameters are given Table 1 Table 1. Parameter values of Jaketed CSTR for ase study 1 Feed onentration, C Af 0.13 lb.mol/ft 3 Feed temerature, T f R Reator volume(nominal) 668 ft 3 Heat transfer area 309 ft iameter 7.5 ft Oerating volume 500 ft 3 Oerating flow rate Over all heat transfer oeffiient, U Ativation energy, E a 000 ft 3 /hr 75 Btu/hr ft 0 F 3400 Btu/lb.mol Frequeny fator, hr -1 Heat of reation,- Δ H Btu/lb.mol Produt of density and seifi heat, ρ C P 53.5Btu/ft 3 0 F deal gas onstant, R Btu/lb.mol 0 R 4 nt. J. Al. Si. Eng., , 1

5 Tuning of P Controllers for Unstable Continuous Stirred Tank Reators The roess transfer funtion relating the reator temerature to the jaket temerature along with a measurement delay of hr is given by T s s e (40) T s s 1 J The MC-P ontroller, SA-P ontroller and SM-P ontroller arameters are given in Table. The servo and regulatory resonse with these ontrollers are shown in Figure1. Case study Controller C Table. P settings for different methods α 0 α 1 α MC-P SA-P SM-P MC-P SA-P SM-P MC-P SA-P SM-P MC-P SA-P SM-P nt. J. Al. Si. Eng., , 1 5

6 . rishna,. Suryanarayana, G. Aarna, and R. Padma Sree Figure1. Servo and regulatory resonse of jaketed CSTR (linear model) ase study-1 The servo and regulatory erformane of the roosed ontrollers is better than SM-P ontroller. The erformane omarison in terms SE, AE and TAE for linear model for the servo and regulatory resonse is given in Table 3. Table 3. Performane omarison for linear models Case study Controller Servo roblem Regulatory roblem SE AE TAE SE AE TAE MC-P SA-P SM-P MC-P SA-P SM-P MC-P SA-P SM-P MC-P SA-P SM-P nt. J. Al. Si. Eng., , 1

7 Tuning of P Controllers for Unstable Continuous Stirred Tank Reators The simulation of non-linear model equations [Eq (38) and Eq (39)] of the jaketed CSTR with the roosed MC-P ontroller, SA-P ontroller and SM-P ontroller for servo resonse (hange in reator temerature to R) is shown in Figure. Figure. Servo resonse of jaketed CSTR (T to R) The regulatory resonse of jaketed CSTR for the hange in feed temerature from to 53 0 R, hange in feed onentration from 0.13 to lb.mol/ft 3, hange in jaket temerature from to 50 0 R and hange in ratio F/V from 4 to 4. hr -1 are shown in Figure 3, Figure 4, Figure 5, and Figure 6 resetively. Figure 3. Regulatory resonse of jaketed CSTR for hange in feed temerature (T f to 53 0 R) for non-linear model in ase study-1 Figure 4. Regulatory resonse of jaketed CSTR for hange in feed onentration (C Af 0.13 to lb.mol/ft 3 ) or non-linear model in ase study-1 nt. J. Al. Si. Eng., , 1 7

8 . rishna,. Suryanarayana, G. Aarna and R. Padma Sree Figure 5. Regulatory roblem of jaketed CSTR for hange in jaket temerature(t j to 50 0 R) for non-linear model in ase study-1 The erformane of these three ontrollers for nonlinear models in terms of SE, AE and TAE for both servo and regulatory roblems is given in Table 4. The erformane of roosed ontrollers is suerior to the SM-P ontroller. The robustness of the MC-P ontroller, SA-P ontroller and SM-P ontroller is studied for the model unertainties onsidering ± 0% erturbation in arameters suh as Δ H, 0, and U onsidering one arameter at a time. The erformane is reorted in terms of SE, AE and TAE values in Table 5. The ontrollers are designed based on nominal model arameters and alied to the roess with erturbed arameters. For ± 0% Δ H, the ontroller designed by synthesis method ould not stabilize the jaketed CSTR. The robustness of roosed ontrollers is better for model unertainty onsidering one arameter at a time when omared to SM-P ontroller. Figure 6. Regulatory roblem of jaketed CSTR for hange in feed rate to volume of reator (F/V4 to 4. min -1 ) for non-linearmodel in ase study-1 Case study- Consider a jaketed CSTR arrying first order irreversible exothermi reation. The model equations of jaketed CSTR without jaket dynamis [7] are given by dc A F Ea ( C A0 C A ) 0C A ex( ) dt V RT (41) 8 nt. J. Al. Si. Eng., , 1

9 Tuning of P Controllers for Unstable Continuous Stirred Tank Reators Table 4. Performane omarison for non-linear model (ase study-1) Performane SE AE TAE Controller reator temerature Servo roblem feed temerature feed onentration jaket temerature Regulatory roblem Change in F/V MC-P SA-P SM-P MC-P SA-P SM-P MC-P SA-P SM-P Table 5. Performane omarison under model unertainty for non-linear model in ase study-1 erformane Controller +0% H -0% H +0% 0-0% 0 +0% U -0% U MC-P SE SA-P SM-P unstable unstable MC-P AE SA-P Synthesis unstable unstable MC-P TAE SA-P Synthesis unstable unstable dt dt F ( ΔH ) 0C A Ea UA ( T0 T) + ex( ) + ( T j T) V ρc RT VρC (4) nt. J. Al. Si. Eng., , 1 9

10 . rishna,. Suryanarayana, G. Aarna and R. Padma Sree The above non-linear model equations are linearised around unstable oerating oint C A mol/m 3, T344 0 and T j The values of the arameters are given in Table 6. Table 6. Parameter values of Jaketed CSTR for ase study Feed onentration, C A0 7.5mol/m 3 Feed temerature, T ensity 850g/m 3 Volume 1m 3 nlet flow rate m 3 /se Over all heat transfer oeffiient, UA 1.45J/s 0 Ativation energy, E a 69000J/mol Frequeny fator, s -1 Heat of reation,- Δ H 50000J/mol seifi heat, C P 3.5J/kg 0 deal gas onstant, R 8.345J/mol 0 0 The transfer funtion relating the reator temerature to the jaket temerature along with a measurement time delay of one seond is given by 7 T s s e (43) 7 T j s s The MC-P ontroller, SA-P ontroller, and SM-P ontroller arameters are shown in Table. The servo and regulatory resonse of MC-P ontroller, SA-P ontroller and SM-P ontroller for linear model are shown in Figure 7 and Figure 8 resetively.the erformane of the roosed ontrollers is better than the SM-P ontroller for both servo and regulatory roblem. The erformane omarison in terms SE, AE and TAE for linear model for the servo and regulatory roblem is given Table 3. The simulation of non-linear model equations [Eq (41), Eq (4)] of jaketed CSTR with MC-P ontroller, SA-P ontroller and SM-P ontroller for servo roblem (hange in reator temerature from 344 to ) is shown in Figure 9. The regulatory resonse of jaketed CSTR for hange in feed temerature from 300 to is shown in Figure 10. The regulatory resonse of jaketed CSTR for hange in initial onentration from 7.5 to 7.7 kmol/m 3, hange in jaket temerature from to and hange in F/V from to s -1 is also studied. 10 nt. J. Al. Si. Eng., , 1

11 Tuning of P Controllers for Unstable Continuous Stirred Tank Reators Figure 7. Servo resonse of jaketed CSTR for linear model in ase study- Figure 8. Regulatory resonse of jaketed CSTR for linear model in ase study- Figure 9. Servo resonse of jaketed CSTR (T344 to ) for non-linear model in ase study- Figure 10. Regulatory roblem of jaketed CSTR for hange in feed temerature (T f 300 to ) for non-linear model in ase study- nt. J. Al. Si. Eng., , 1 11

12 . rishna,. Suryanarayana, G. Aarna and R. Padma Sree Table 7. Performane omarison for non-linear model in ase study- Performane SE AE TAE temerature feed temerature feed onentration jaket temerature F/V Controller Servo roblem Regulatory roblem MC-P SA-P SM-P MC-P SA-P SM-P MC-P SA-P SM-P Table 8. Performane under model unertainty for non-linear model in ase study- Performane SE +0% -0% +0% -10% +0% -0% +0% -0% Controller H H E a E a 0 0 U U MC-P SA-P SM-P MC-P AE SA-P SM-P MC-P TAE SA-P SM-P nt. J. Al. Si. Eng., , 1

13 Tuning of P Controllers for Unstable Continuous Stirred Tank Reators The erformane of the roosed ontrollers for nonlinear models in terms of SE, AE, and TAE for both servo and regulatory roblems is given in Table 7. For both servo and regulatory roblem, MC-P ontroller and SA-P ontroller gives better resonse omared to SM-P ontroller. The robustness of the MC-P ontroller, SA-P ontroller and SM-P ontroller is studied for the model unertainties onsidering ± 0% erturbation in arameters suh as Δ H, E a, 0, and U onsidering one arameter at a time. The erformane is reorted in terms of SE, AE and TAE values in Table 8. The ontrollers are designed based on nominal model arameters and alied to the roess with erturbed arameters. The roosed MC-P, SA-P and SM-P ontrollers are robust under model unertainty onsidering one arameter at a time. Case study-3 Consider a onstant volume jaketed CSTR arrying first order irreversible exothermi reation. The model equations of jaketed CSTR without jaket dynamis [8] are given dca q Ea by ( CA0 CA) 0CA ex( ) (44) dt V RT dt dt q ( ΔH ) 0C A Ea UA ( T0 T) + ex( ) + ( T j T) V ρc RT VρC (45) The above non-linear model equations are linearised around unstable oerating oint C A mol/l, T and T j The values of the arameters are given in Table 9. Table 9. Parameter values of jaketed CSTR for ase study -3 Volume (V) 100 l nlet flow rate (q) 100 l/min Feed temerature (T 0 ) Feed onentration (C A0 ) 0.5 mol/l Overall heat transfer oeffiient (UA) Seifi heat (C ) 0.39 J/(g 0 ) Heat of reation (- Δ H) J/mol Ativation energy (E/R) Frequeny fator ( 0 ) ensity ( ρ ) 1000 g/l nt. J. Al. Si. Eng., , 1 13

14 . rishna,. Suryanarayana, G. Aarna and R. Padma Sree The transfer funtion relating the reator temerature to the jaket temerature along with a measurement time delay of 0.06 min is given by T.09s s e (46) T j s s 1.6 The MC-P ontroller, SA-P ontroller, and SM-P ontroller arameters are shown in Table. The servo and regulatory resonse of MC-P ontroller, SA-P ontroller and SM-P ontroller for linear model are shown in Figure 11. The servo erformane of SM-P ontroller shows a large overshoot omared to the roosed ontrollers. For regulatory roblem, roosed ontrollers erform better than SM-P ontroller. The erformane omarison in terms SE, AE and TAE for linear model for the servo and regulatory roblem is given Table 3. The simulation of non-linear model equations [Eq (44), Eq (45)] of jaketed CSTR with MC-P ontroller, SA-P ontroller and SM-P ontroller for servo roblem (hange in reator temerature from to ) is shown in Figure 1. Figure 11. Servo and regulatory resonse of jaketed CSTR for linear model in ase study-3 Figure 1. Servo resonse of jaketed CSTR (T31.73 to ) for non-linear model in ase study-3 The regulatory resonse of jaketed CSTR for hange in feed onentration from to 0.6 mol/l is shown in Figure 13. The regulatory resonse of jaketed CSTR for hange in jaket temerature from 300 to 90 0, hange in oolant flow rate from 100 to 110 l/min, and hange in feed temerature from 350 to is also studied. 14 nt. J. Al. Si. Eng., , 1

15 Tuning of P Controllers for Unstable Continuous Stirred Tank Reators Figure 13. Regulatory resonse of jaketed CSTR for hange in feed onentration (C Af to 0.6 mol/l) for non-linear model in ase study-3 The erformane of the roosed ontrollers for nonlinear models in terms of SE, AE, and TAE for both servo and regulatory roblems is given in Table 10. For servo roblem, P ontroller designed by synthesis method gives best erformane in terms of SE, AE and TAE. However, the resonse shows large overshoot (refer to Figure 11 and Figure 1). The ontrollers designed by roosed methods give less overshoot for servo resonse. Table 10. Performane omarison for non-linear model in ase study-3 Performane SE AE TAE temerature feed temerature feed onentration jaket temerature Change in q Controller Servo roblem Regulatory roblem MC-P SA-P SM-P MC-P SA-P SM-P MC-P SA-P SM-P nt. J. Al. Si. Eng., , 1 15

16 . rishna,. Suryanarayana, G. Aarna and R. Padma Sree The regulatory resonse of the MC-P ontroller is the best when omared with the ontroller designed by synthesis method. The robustness of the MC-P ontroller, SA-P ontroller and SM-P ontroller is studied for the model unertainties onsidering ± 0% erturbation in arameters suh as Δ H, 0, E a and U onsidering one arameter at a time. The erformane is reorted in terms of SE, AE and TAE values in Table 11. The ontrollers are designed based on nominal model arameters and alied to the roess with erturbed arameters. The roosed ontrollers are robust for model unertainty onsidering one arameter at a time omared to SM-P ontroller. Table 11. Performane under model unertainty for non-linear model in ase study-3 Performane SE AE TAE +0% -0% Controller H H +0% -10% +0% -0% +0% -0% E a E a 0 0 U U MC-P SA-P SM-P MC-P SA-P SM-P MC-P SA-P SM-P Case study-4 The following transfer funtion model is onsidered[6]. G 0.3s (0.3119s +.07) e s).85s.31s + 1 P ( (47) The P arameters of the MC-P ontroller, SA-P ontroller, and SM-P ontroller are given in Table. The servo and regulatory resonse of the roess transfer funtion model with MC-P ontroller, SA-P ontroller and SM-P ontroller are shown in Figure 14. The erformane of MC-P ontroller and SA-P ontroller for the servo and regulatory roblem are better than the SM-P ontroller. The erformane omarison of MC-P ontroller, SA-P ontroller, and SM-P ontroller in terms of SE, AE, and TAE is shown in Table nt. J. Al. Si. Eng., 01.10, 1

17 Tuning of P Controllers for Unstable Continuous Stirred Tank Reators Figure 14. Servo and regulatory resonse for ase study Conlusions Two P ontroller design methods based on internal ontrol riniles and stability analysis method for unstable SOPTZ system is roosed. The ontrollers designed by MC method and stability analysis method are used to ontrol the various unstable jaketed stirred tank reators arrying out first order irreversible reation. Simle equations for the P arameters are given in terms of roess model arameters. The erformane of the ontrollers designed by MC method and stability analysis method is omared with the ontroller designed by synthesis method. The roosed ontroller erforms better for both servo and regulatory roblems than the ontroller designed by synthesis method. The erformane of ontrollers designed by MC method and stability analysis method for model unertainty onsidering one arameter at a time is studied. When there is ±0% unertainty in ΔH, the ontroller designed by synthesis method ould not stabilize the reator (Case study 1). The ontrollers designed by roosed methods give robust erformane. The erformane omarison for model unertainty is given in terms of SE, AE and TAE for both servo and regulatory roblems. Simulation results on non-linear model equations of jaketed CSTR arrying out irreversible first order hemial reation show that the ontrollers designed by roosed methods erform better than the ontrollers designed by synthesis method. Referenes [ 1] Bequette, B. W Proess ontrol, Modeling, design and simulation. Prentie Hall ndia. New elhi. [ ] Jaobsen, E. W On the dynamis of integrated lants Non-minimum hase behavior. J Proess Control, 9: [ 3] Padmasree, R. and Chidambaram, M Control of unstable systems. Narosa ublishers. New elhi. [ 4] austhubh, S. M. and Chidambaram, M Control of sothermal Crystallizers, Pro. CHEMCON, Calutta., eember 18 th to 1 st.000. [ 5] Lee, Y., Lee, J., and Park, S P ontroller tuning for integrating and unstable roesses with time delay. Chemial Engineering Siene, 55: [ 6] Wang, L.W. and Hwang, S. H dentifiation and ontrol for unstable roesses of three dynamis, Chemial Engineering Siene, 19: [ 7] Wright, R. A. and ravaris, C Two degree of freedom outut feedbak nt. J. Al. Si. Eng., , 1 17

18 . rishna,. Suryanarayana, G. Aarna and R. Padma Sree ontrollers for disrete time nonlinear systems. Chemial Engineering Siene, 61: [ 8] Feng, L., Wang, J. L., and Poh, E mroved robust model reditive ontrol with strutured unertainty. J Proess Control, 17: nt. J. Al. Si. Eng., 01.10, 1