Dynamic Simulation and Composition Control in A 10 L Mixing Tank

Transcription

1 roeeding of International Conferene on Chemial and Material Engineering ISBN : SE.4 - Dynami Simulation and Composition Control in A L Mixing Tank Yulius Deddy Hermawan Chemial Engineering Department, Faulty of Industrial Tehnology, UN Veteran Yogyakarta Jl. SWK 4 (Lingkar Utara), Condongatur, Yogyakarta INDONESIA ydhermawan@upnyk.a.id Abstrat : The open loop experiment of omposition dynami in a L mixing tank has been suessfully done in laboratory. A L tank was designed for mixing of water (as a stream-) and salt solution (as a stream- with salt onentration, onstant). An eletri stirrer was employed to obtain uniform omposition in tank. In order to keep the liquid volume onstant, the system was designed overflow. In this work, omposition ontrol onfigurations have been proposed; they are Alternative- and Alternative-. For Alternative-, the volumetri-rate of stream- is hosen as a manipulated variable, while the volumetri-rate of stream- is hosen as a manipulated variable for Alternative-. The omposition ontrol parameters for both alternatives have been tuned experimentally. The volumetri-rate of manipulated variable was hanged based on step funtion. The outlet stream s omposition response ( ) to a hange in the input volumetri-rate has been investigated. This researh gave roportional Integral Derivative (D) ontrol parameters. The gain ontrollers K [m 6 /(gr.se)] for Alternative- and Alternative- are 4 and 4459 respetively. Integral time onstant ( I ) and Derivative time onstant ( D ) for both alternatives are the same, i.e. I = 6 seond, and D = 4 seond. Furthermore, losed loop dynami simulation using omputer programming was also done to evaluate the resulted tuning parameters. The developed mathematial model of omposition ontrol system in a mixing tank was solved numerially. Suh mathematial model was rigorously examined in Silab software environment. As an be seen from our losed loop simulation, losed loop responses in D ontrol were faster than those in and ontrols. Keywords: losed loop, open loop, D ontrol, mixing tank, step funtion.. Introdution A mixing tank is frequently used in hemial proess industries, for examples as a blending tank and/or a ontinuous stirred tank reator. Liquid omposition in a mixing tank is one of important parameters for mixing proesses or hemial reation proesses in reator. The propagation of mass disturbane is possibly ourred in mixing proesses. Therefore omposition ontrol should be implemented to overome the propagation of mass disturbanes. Composition ontrol parameters suh as proportional gain ontroller (K ), integral time onstant ( I ), and derivative time onstant ( D ) should be tuned properly, sine they really affet the stability of mixing proess. However designed omposition ontrol system must be able to give a stable response in faing the mass disturbanes. Therefore the study on dynami simulation and omposition ontrol is very important. Some studies of proess dynami and ontrol have been done. Reently, Hermawan et al [] have presented the open loop omposition dynami in a L Mixing Tank experimentally. Hermawan et al [] have also presented the design of ontrol onfiguration of non-interating-tank system using quantitative analysis of relative gain array. Hermawan [] has implemented roess Reation Curve (RC) for tuning of temperature ontrol parameters in a L Stirred Tank Heater. Widayati and Hermawan [4] have studied the mixing harateristi in a horizontal stirred tank. The goals of this researh are to propose the omposition ontrol onfiguration and to tune the omposition ontrol parameters (D Control parameters) in a L Mixing Tank. The resulted omposition ontrol parameters of proposed onfigurations are examined through dynami simulation. In order to ahieve the aims of this researh, this work was done in two parts, i.e. open loop experiment in laboratory for tuning of omposition ontrol parameters and losed loop simulation using omputer programming to explore dynami behavior of ontrolled system. The open loop experiment in laboratory was arried out to tune omposition ontrol parameters. The volumetri rate of input stream was hosen as a manipulated variable to maintain the onentration of output stream at the onstant value. In order to examine the ontrol onfiguration, the mass disturbanes were made based on step funtion. The Silab software was utilized to arry out dynami simulation. September,, Semarang Indonesia

2 roeeding of International Conferene on Chemial and Material Engineering ISBN : SE.4 - Notes: : Main Tank (as a mixingtank) : Feedingtank of stream- : Feedingtank of stream- 4 : Tank for making a disturbane 5 : Storage tank 6 : Transfer pump 7 : Three way valve 8 : Valve 9 : Stirrer 9b 9 (t) 7 4 f 8b 9a f 8a 8 Feed Sumber water f (t) 5a 6a Main Tank (as a mixing tank) 5b 6b 5 6 pembuangan Fluid outlet Figure. Experimental apparatus setup. Material and Methods Experimental apparatus setup is shown in Figure. As an be seen from Figure, No. is a main tank that represents a mixing tank. This mixing tank has input streams, i.e. stream- and stream-, and output stream, i.e. stream-. In normal ondition, stream- and stream- ome from the feeding tank No. and No. in Figure, respetively. In this work, water was used as a stream- with its volumetri rate f [m/se], and salt solution as a stream- with its volumetri rate f [m /se] and onentration [gr/m ]. The input onentration is onstant. The output stream (stream-) has volumetri rate f [m /se] and onentration [gr/m ]. The onentration is measured by means of Condutivity-meter. Sine the liquid volume is kept onstant, the system is designed overflow. A stirrer is employed to obtain uniform omposition in the mixing tank. The material balane of the mixing tank an be written as follows: d dt t f t f t f t f t t / V [] In this researh, omposition ontrol onfigurations are proposed, i.e. Alternative- and Alternative- as shown in Figure. Open loop tuning experiment is done for either alternatives by hanging the opening valve of stream- (No. 8a in Figure ) or stream- (No. 8b in Figure ) to inrease/derease its volumetri rate immediately. The output onentration ( ) response to a hange in input volumetri rate is then investigated. The resulted response will similar with that response given by first order plus dead time (FODT) model. D Control parameters are then tuned by fitting the resulted FODT as proposed by Ziegler-Nihols [5]. These open loop experiments should be started from its initial (normal) onditions. In order to evaluate the resulted D Control parameters, dynami simulation is arried out by means of omputer. A simple feedbak ontrol system is implemented to maintain liquid onentration in tank ( ) onstant by manipulating the volumetri rate of stream- or stream-. Thus, the equation of manipulated variables for both of ontrol onfiguration alternatives an be written as follow: K Alternative-: f t f K et et Alternative-: f t f K et et Where e(t) is defined as: e t S t I K I dt K D dt K D det dt det dt = error [5] September,, Semarang Indonesia [] [4]

3 roeeding of International Conferene on Chemial and Material Engineering ISBN : SE.4 - f (t), f (t), f (t), f (t), Notes: CC S C S C CC Alt. CV MV D f (t), (t) f (t), (t) f f f f (t) CT CT (t) CV: Controlled Variable MV: Manipulated Variable D: Disturbane (a) Alternative- (b) Alternative- Figure. Composition Control Configuration: (a) Alternative-, (b) Alternative-. The developed mathematial model of omposition ontrol system in the mixing tank is solved numerially with the easiest way of expliit Euler. The free software Silab is hosen to arry out the losed loop dynami simulation. The losed loop responses of omposition ontrol will then be explored in this work.. Result and Disussion. Steady state parameters of mixing tank are listed in Table. Based on steady state material balane, the proess time onstant is found 7 seonds (.6 minutes). Therefore the system is onsidered quite sensitive to the hanges of input disturbanes... Tuning of Composition Control arameters for Alternative- For Alternative-, volumetri rate of water (f ) is onsidered as a manipulated variable to maintain liquid omposition in tank ( ). Figure.a shows the influene of f on. Volumetri rate of water is dereased by an amount of 76 m /se immediately; the onentration rises about. gr/m. The tuning results of omposition ontrol parameters (,, and D) for Alternative- are listed in Table... Tuning of Composition Control arameters for Alternative- For Alternative-, volumetri rate of salt solution (f ) is onsidered as a manipulated variable to maintain liquid omposition in tank ( ). Figure.b shows the open loop omposition response to a hange in the volumetri rate f. The onentration inreases (about. gr/m ) as the volumetri rate f inreases (about 7 m /se). The tuning results of omposition ontrol parameters (,, and D) for Alternative- are also listed in Table. Table. Steady state parameters No Variable Steady state Volumetri rate of stream-, f (m /seond) 6 Volumetri rate of stream-, f (m /seond) 7 Volumetri rate of stream-, f (m /seond) 77 4 Conentration of stream-, (gr/m ) 5 Conentration of stream-, (gr/m ).5 6 Conentration of stream-, (gr/m ).4 7 Liquid volume in tank, V (m ) 6 Table. Tuning results of omposition ontrol parameters. Type of Feedbak Control roportional Gain K [m 6 /(gr.se)] Integral time τ I [se] Derivative time D [se] K Alt- Alt- τ I Alt- Alt- D Alt- Alt- /( K. td) /( K. td) tD D. /( K. t ) td 6 6.5tD 4 4 D September,, Semarang Indonesia

4 Conentration [gr/m ] Conentration [gr/m ] Vol. rate f [m /se] Vol. rate f [m /se] roeeding of International Conferene on Chemial and Material Engineering ISBN : SE Waktu Ziegler Nihols Fitting:.8(ΔCV) t = 8 se Manipulated Variable t = 48 se.6(δcv) t = 48 se t t se t D t 8se CV gr.se K.E 4 6 MV m ΔMV = Δf = -76 m /se Controlled Variable ΔCV = Δ =. gr/m t = 8 se (a) Alternative Manipulated Variable ΔMV = Δf = 7 m /se Controlled Variable ΔCV = Δ =.9 gr/m t = se t = se Ziegler Nihols Fitting:.8(ΔCV) t = se.6(δcv) t = se t t 4se t D t 8se CV gr.se K.56E 4 6 MV m (b) Alternative- Figure. Tuning of Composition Control arameters: (a) Alternative-, (b) Alternative-... Dynami Simulation of Composition Control for Alternative- Closed loop responses to a hange in volumetri rate f are illustrated in Figure 4. The disturbanes were made by following both funtions of step inrease and step derease. For step inrease s disturbane, volumetri rate f is inreased by an amount of 7 m /se at time equals seonds. As an be seen, the omposition ontroller (,, and D) attempts to return onentration to its normal value of.4 gr/m. Conentration an be returned to its set point by both of and D Controls. Control produes an offset of.9 gr/m. Closed loop response of D Control is fastest ompared to and Controls; Conentration an be returned to its set point at time equals 5 seonds. For step derease s disturbane, volumetri rate f is dereased by an amount of 56 m /se at time equals seonds. The onentration dereases first, and then rises to its normal value. However Control still produes an of about.8 gr/m. Closed loop response of D Control is the fastest; the set point of an be ahieved at time equals se..4. Dynami Simulation of Composition Control for Alternative- Figure 5 shows losed loop responses to a hange in volumetri rate f. For this alternative, the disturbanes were also made by following both funtions of step inrease and step derease. For step inrease s disturbane, volumetri rate f is inreased by an amount of 6 m /se at time equals seonds. As shown in Figure 5, onentration dereases as volumetri rate f inreases, and then onentration an be returned to its set point by both of and D Controls. Control produes an offset of.9 gr/m. Closed loop response of D Control is the fastest one; onentration an be returned to its set point at time equals 5 seonds. For step derease s disturbane, volumetri rate f is dereased by an amount of 76 m /se at time equals seonds. The onentration inreases as the volumetri rate of water dereases, and then drops to its normal value for and D Controls. Again, Control still produes an of about.4 gr/m, and D Control gives the fastest response. September,, Semarang Indonesia

5 Vol. rate f [m /se] Vol. rate f [m /se] Conentration [gr/m ] Conentration [gr/m ] Vol. rate f [m /se] Vol. rate f [m /se] Vol. rate f [m /se] Vol. rate f [m /se] Conentration [gr/m ] Conentration [gr/m ] Vol. rate f [m /se] Vol. rate f [m /se] roeeding of International Conferene on Chemial and Material Engineering ISBN : SE.4-5 Step Inrease f Step Derease f (a) (b) D D () D 8 4 D Figure 4. Closed Loop Responses of Composition Control Alternative- to a hange in volumetri rate f : (a) Volumetri rate f, (b) Conentration, () Volumetri rate f Step Inrease f Step Derease f (a) (b). D D () D D Figure 5. Closed Loop Responses of Composition Control Alternative- to a hange in volumetri rate f : (a) Volumetri rate f, (b) Conentration, () Volumetri rate f September,, Semarang Indonesia

6 roeeding of International Conferene on Chemial and Material Engineering ISBN : SE Conlusion This paper has disussed tuning of omposition ontrol parameters and dynami simulation in a L mixing tank. Two alternatives of omposition ontrol onfigurations have been proposed. Closed loop dynami behaviours of the two ontrol onfigurations have been explored. Aording to my dynami simulation, the tuning results of omposition ontrol parameters produe stable responses. This researh reveals that D Composition Control produes the fastest responses ompared to both of and Composition Controls. Aknowledgements I appreiate the tehnial support on the use of free software SCILAB. I gratefully aknowledge Ir. Gogot Haryono MT of UN Veteran Yogyakarta for valuable disussion. I also thank Agustin M and Abiad H for helping me during my researh in laboratory. Nomenlature,, onentration of stream,, [gr/m] S set point of liquid onentration in tank [gr/m] e error [gr/m] f,, volumetri rate of stream,, [m/seond] K steady state gain of the proess [(gr.seond)/m6] K proportional gain ontroller [m6/(gr.seond)] t time at w t t D effetive proess dead time [seond] V liquid volume in tank [m] Greek letters CV steady state hange in ontrolled variable [gr/m] MV step hange in manipulated variable [m/seond] effetive proess time onstant [seond] D derivative time onstant [seond] integral time onstant [seond] I Referenes [] Hermawan YD, Haryono G, Agustin M, Abiad H.. Composition Dynami in A L Mixing Tank, Seminar Nasional Teknik Kimia Kejuangan, Department of Chemial Engineering, Faulty of Industrial, UN Veteran Yogyakarta : C5- C5-6. (in Indonesian) [] Hermawan YD, Suksmono Y, Narno utra RM, uspitasari M.. Design of roess Control Configuration for Non- Interating-Tank System using Quantitative Analysis of Relative Gain Array, Seminar Nasional Teknologi Simulasi (TEKNOSIM), Department of Industry and Mehanial Engineering, Faulty of Engineering, Gadjah Mada University : (in Indonesian). [] Hermawan YD.. Implementation of roess Reation Curve for Tuning of Temperature Control arameters in A L Stirred tank Heater, Journal of Materials Siene and Engineering, Vol., No. 4 September : [4] Widayati TW, Hermawan YD. 7. Mixing Charateristi in A Horizontal Stirred Tank, Seminar Nasional Teknik Kimia Kejuangan 7, Department of Chemial Engineering, Faulty of Industrial, UN Veteran Yogyakarta : B- B-6. (in Indonesian) [5] Smith CA, Corripio AB riniples and ratie of Automati roess Control, John Wiley & Sons, nd Ed., New York : September,, Semarang Indonesia