Analysis of PI controller by model based tuning method in Real Time Level Control of Conical Tank System using block box modeling

Transcription

1 International Journal of ChemTech Reearch CODEN (USA): IJCRGG, ISSN: , ISSN(Online): Vol.11 No.01, 86-99, 018 Analyi of PI controller by model baed tuning method in Real Time Level Control of Conical Tank Sytem uing block box modeling K.Indhumathi 1*, D.Angeline Vijula, S.Gurunagaan 3 1,3 Cheran College of Engineering, India PSG Intitute of Technology, Coimbatore, India Abtract : Conical tank Sytem find wide alication in roce indutrie becaue it revent the accumulation of olid at the bottom of the tank. Control of liquid level in a conical tank i nonlinear due to the variation in the area of cro ection of the tank ytem with it change in hae. In thi aer the model of the roce i identified uing block box modeling and aroximated to be a firt order lu dead time (FOPTD) model. Alo Non linear conical tank i linearized into four linearized zone baed on the variation in area of CTS uing iecewie linearization method. The Proortional lu Integral (PI) controller i commonly ued to control the level in roce indutrie becaue if it imlicity of imlementation. Tuning of the PI controller i etting the roortional (K ) and integral contant (K I ). In thi aer PI controller i analyzed for Real Time conical tank ytem (CTS) and tuned by Ziegler Nichol method(z-n method), Internal Model Control Tuning(IMC) and Model Reference Adative Control(MRAC) tuning method. The PI controller i imulated uing MATLAB/SIMULINK environment and the tuning method are imlemented in real time for controlling the level in CTS. Keyword : Conical tank ytem, Block box modeling, Piecewie Linearization, Ziegler Nichol tuned PI,Internal Model Control tuned PI, Model Reference Adative Control. 1 Introduction Control of indutrial rocee i a challenging tak for everal reaon due to their nonlinear dynamic behavior, uncertain and time varying arameter, contraint on maniulated variable, interaction between maniulated and controlled variable, unmeaured and frequent diturbance, dead time on inut and meaurement. The control of liquid level in tank i a baic roblem in roce indutrie. In many rocee uch a ditillation column, evaorator, rebolier and mixing tank, the articular level of liquid in the veel i of great imortance in roce oeration. The conical tank ytem i widely ued in many roce indutrie like Petrochemical indutrie, Cement manufacturing indutrie, Food roceing indutrie, Wate water treatment becaue it contribute better drainage of the liquid olid mixture, lurrie. The level control of the conical tank i difficult becaue of it nonlinearity and contantly varying cro ection with reect to height. Here the conical tank which ha nonlinear characteritic i rereented a iecewie linearized model. The PI and PID controller are widely ued in many indutrial control ytem becaue of it imle tructure and robutne. Tuning of the PI controller i etting the roortional, integral contant. The mot common claical controller tuning method are the Ziegler Nichol (Z-N) and Cohen-Coon method. Since it i eaier to ue than other method. Internal model control (IMC) tuning offer an alternative tuning to increae the controller erformance. Model Reference Adative tuning differ from reviou tuning method. MRAC ue Non linear

2 K.Indhumathi et al /International Journal of ChemTech Reearch, 018,11(01): model. Baed on reference model elected the controller adat it arameter to obtain the deired erformance. Literature Review Many reearch work have been carried out in the level control of the conical tank roce. S.Anand et al., [], exlained about the Adative PI Controller which eliminate the ocillation at low level and rovide a more conitent reone. N.S. Bhuvanewari et al., [5] carried out exeriment in conical tank level control uing Neural Network controller. D.Marihiana et al.,[9] deigned the Ziegler Nichol tuning controller and comarion i made between the value of P, PI, PID. Direct Synthei Proortional Integral (DSPI) and Model Predictive Control (MPC) were deigned by H.Kala et al.,[7]. P.Sowmyl et al., [15] ha deigned the fuzzy logic controller and the model of the roce i identified uing tandard te reone baed ytem identification technique and it i aroximated to be a firt order lu dead time (FOPTD) model.d.angelinevijula et al.,[16] ha imulated the MRAC tuned PI in MATLAB. IMC tuned PI i imlemented and roved a better tuning method for Real time conical tank. In thi work CTS i modeled by block box modeling and PI controller i tuned by Z-N tuning, IMC tuning, MRAC tuning. Controller i imulated in MATLAB and imlemented to control Level of Conical tank. Real time Performance of tuning method are analyzed and reented in thi aer. The ection two deal with the hardware decrition of the conical tank ytem. The ection three exlain the modeling of the ytem. The ection four rovide the PI controller deign. Z-N tuning and IMC tuning i exlained. The ection five reent the reult and dicuion for both imulation and real time imlementation. SETPOINT LOAD VARIABLE (DISTURBANCES) PERSONAL COMPUTER CONTROLLER DESIGN (MATLAB) RS-3 DATA ACQUISITION SYSTEM 4-0mA I/P CONVERTER 3-15i PNEUMATIC ACTUATOR AND CONTROL VALVE m CONICAL TANK PROCESS level c 4-0mA DIFFERENTIAL LEVEL TRANSMITTER Figure 1: Block diagram of CTS Hardware Decrition The conical tank i made u of tainle teel and i mounted vertically on the tand. The water enter into the tank from the to and leave to the reervoir, which i laced at the bottom of the tank. The Block diagram of CTS i hown in Fig.1. The level of the water in the conical tank i quantified by mean of the DPT. The quantified level of water in the form of current in the range of (4-0) ma i ent to the DAQ in which ADC convert the analog data to digital data and feed it to the PC. The PC act a the controller and data logger. The controller conider the roce variable a feedback ignal and find the maniulated variable a the outut baed on the redefined et oint. The DAC module of the DAQ convert thi maniulated variable to analog form into 4-0 ma current ignal.the I/P converter convert the current ignal to reure in the range of (3-15) i, which regulate the flow of water into the conical tank baed on the outflow rate of the tank. Block diagram of the CTS i hown in figure 1.

3 K.Indhumathi et al /International Journal of ChemTech Reearch, 018,11(01): The conical tank ytem which exhibit the roerty of non-linearity i conidered here. The hotograh of the conical tank ytem i hown in the Figure with it comonent. Figure : Setu of conical tank ytem 3 Modeling of Conical Tank Proce Modeling i the develoment of mathematical equation, contraint and logical rule of real world roce. In thi aer three tye ofmodeling aroache are carried on. They are a follow, 1. Analytical Modeling where the entire ytem i rereented a mathematical equation.. Black Box Modeling - CTS i modeled by exerimentation. 3. Model uing Piecewie Linearization - Four linearized model are obtained uing iecewie linearization. 3.1 Analytical Model The cro ection ofthe CTS i hown in Figure 3. Figure 3: Conical tank Where,

4 K.Indhumathi et al /International Journal of ChemTech Reearch, 018,11(01): Q in - inflow rate in lh Q o - outflow rate in lh R- Maximum radiu of the tank in cm H- Maximum height of the tank in cm r- Radiu of the tank tank at teady tate in cm h- Height of the tank tank at teady tate in cm According to ma balance equation Accumulation =Inut-Outut dv Qin Q 0 dt (1) The volume of the conical tank can be exreed a equation () dh A Qin Q 0 dt () Where A i the Area of the Tank A r (3) So the height of the tank i, 3 dh Qinh h dt (4) 1 H Where R (5) k v (6) Above equation (4) i Non linear form, Lineariation i done uing Taylor erie method Lineariation of Q in h i, f h, Q f h Q f h h f Q Q h 3 Lineariation of h i, 3 Q h h h h h (8) Now alying teady tate value y= (h-h ) and u= (Q-Q ) The aroximate linear model obtained a, dy y ku dt (9) 5 h 3 (10) k 5 h (11) Above equation imlie that the conical tank ytem i Firt Order Sytem. The tranfer function obtained for 0cm i exreed in equation (1) G ( ) (1) (7) Uing the above Tranfer function et oint will not be reached exactly. Offet error will be reent in the ytem. So, intead of analytical modeling Block box modeling i done.

5 Level(cm) K.Indhumathi et al /International Journal of ChemTech Reearch, 018,11(01): Block Box Modelling Block box modelling i ued to obtain the arameter of the tranfer function of the FOPDT model by letting the reone of the actual ytem and that of the model to meet at two oint, which decribe the two arameter τ and t d. The loo i made oen and a te increment (30 lh) i given in inflow rate and the reading are noted till the ytem reache the teady tate value. The exerimental data are aroximated to a Firt Order lu Dead Time (FOPDT) model to obtain the oen loo arameter of the conical tank roce. Theoenloo reone i hown in Figure Time(ec) Figure 4: Oen loo reone of conical tank ytem The tranfer function i aroximated a FOPDT uing oen loo reone and exreed by equation (13) e G( ) (13) 3.3 Model uing Piecewie Lineariation Linearization i a term ued in general for the roce by which a nonlinear ytem i aroximated a a linear roce model. In ractice, all hyical rocee exhibit ome non-linear behavior. The conical tank exhibit nonlinearity by contantly varying it cro ection with reect to height. For fixed inut water flow rate and outut water flow rate of the conical tank, the tank i allowed to fill with water from (0-45) cm. Uing the oen loo method, for a given change in the inut variable the correonding teady tate of the ytem i recorded and the tranfer function i obtained for different zone. Thu the nonlinear model of CTS i linearized into four linear model. The flow rate and the correonding zone are hown in the Table 1. Table 1: Piecewie Linearization Zone Flow rate(lh) Time taken(ec) Steady tate level(cm) The Reone for iecewie linearization hown in the Figure 5.

6 Level(cm) K.Indhumathi et al /International Journal of ChemTech Reearch, 018,11(01): Piecewie Lineariation Time(ec) Figure 5: Oen loo reone of Piecewie linearization A te increment (30lh) i given a an inut to the CTS.It reache the teady tate value at 10cm.So the height (0-10cm) i conidered a zone I. The inflow i incremented to 80lh it reache the teady tate at 19.79cm.The height ( cm) i conidered a zone II. Similarly it i reeated for 30,350lh and zone III, IV i conidered. Once it reache the time after ettling then it goe to the econd region. The tranfer function obtained for the four zone are hown in the Table Table. Linearized model for different level Level(cm) 0-10 Zone I Linearized firt order Model G e S 10-0 Zone II 0-30 Zone III G G e S e S Zone IV G 4 70S 0.109e Controller Deign The PI controller conit of roortional and integral term. The roortional term change the controller outut roortional to the current error value. Large value of roortional term make the ytem untable. The Integral term change the controller outut baed on the at value of error. So, the controller attemt to minimize the error by adjuting the controller outut. The mot common claical controller tuning method are the Z-N and Cohen-Coon method. The Z-N method can be ued for both cloed and oen loo ytem, while Cohen-Coon i tyically ued for oen loo ytem.

7 K.Indhumathi et al /International Journal of ChemTech Reearch, 018,11(01): Ziegler Nichol Tuning Z-N oen loo tuning formula for PI controller i given in the equation 0.09 K (18) ktd K K I (19) I The calculated PI gain arameter can be given a, K = K I = Internal Model Control Tuning Internal model control tuning alo referred a Lambda tuning method offer a robut alternative tuning aiming for eed. Lambda tuning i a form of internal model control (IMC) that endow a PI controller with the ability to generate mooth, non-ocillatory control effort when reonding to change in the et oint.the IMC baed tuning arameter for PI controller can be obtained by determining the controller equation. Otherwie directly the arameter can be calculated by uing the formulae K K t K d I (1) I (0) k Auming =5 ec, The calculated PI gain arameter can be given a K = K I = Model Reference Adative Control Tuning A tuning ytem of an adative control will ene thee arametric variation and tune the controller arameter in order to comenate forit. The arametric variation may be due to the inherent non-linearity of the ytem uch a conical tank. In a conical tank the cro ection area varie a a function of level which in turn lead to arametric variation. The time contant and gain of the choen roce vary a a function of level. In MRAC tuning a reference model decribe the ytem erformance. The adative controller i then deigned to force the ytem (or lant) to behave like the reference model. Model outut i comared to the actual outut and the difference i ued to adjut feedback controller arameter. MRAC ha two loo: an inner loo (or regulator loo) that i an ordinary control loo coniting of the lant and the regulator, and an outer (or adatation) loo that adjut the arameter of the regulator in uch a way a to drive the error between the model outut and lant outut to zero. Block diagram of MRAC i hown in Figure 6.

8 K.Indhumathi et al /International Journal of ChemTech Reearch, 018,11(01): Figure 6. Block diagram of MRAC tuned PI controller Tracking error i, y y m e (16) The cot function i, 1 e J (17) e e J dt d (18) where e denote the model error and θ i the controller arameter vector. γ denote the adatation gain. Intead of θ the PI controller arameter K P,K I are conidered. So the K i, Y U k k a a k c i b b b e (19) Similarly K I Parameter i, Y U k k a a k c i i i b b b e (0) 5 Reult and Dicuion 5.1 Simulation Reult of Block box model (without linearization) The PI Controller i tuned uing ZN, IMC, MRAC tuning and are imulated with block box model of CTS in MATLAB/SIMULINK environment and the reone are obtained & reented in thi ection. Figure 7 reent the reone of ZN tuned PI for nonlinear model of CTS. It i oberved that controller take more time to reach the deired level. Alo diturbance i not rejected by controller which i given at 500 ec.

9 K.Indhumathi et al /International Journal of ChemTech Reearch, 018,11(01): Figure 7: Reone of Z-N tuned PI controller without linearization The lambda tuning rule alo called a IMCtuning, offer an alternative tuning aiming for eed. The tuning i very robut meaning that the cloed loo will remain table even if the roce characteritic change dramatically.a hown in Figure 8, et oint i reached with minimum time in other oerating zone. Even if the diturbance given controller reject it and tank level i maintained at etoint. Figure 8: Reone of IMC tuned PI controller without linearization Figure 9 how Reone of MRAC Tuned PI. It i hown that deired level i reached in minimum time. But eak overhoot reented in MRAC tuning method.

10 K.Indhumathi et al /International Journal of ChemTech Reearch, 018,11(01): Figure 9.Reone of MRAC tuned PI 5. Simulation Reult of Piecewie model (Linearied Model) The PI arameter obtained for the four linearied model uing Z-N tuning and IMC tuning. The imulated reone are hown below. Figure 10:Reone of Z-N tuned PI controller with iecewie linearied model

11 K.Indhumathi et al /International Journal of ChemTech Reearch, 018,11(01): Figure 11: Reone of IMC tuned PI controller with iecewie linearied model Comaring both the imulation reult it i clear that IMC tuned PI roduce le overhoot and minimum ettling time for linearied model.mrac tuned roduce le overhoot and minimum ettling time for Non linear model. Table 3:Comarion of erformance of Z-N tuned PI, IMC tuned PI and MRAC tuned PI controller through imulation Performanc e Indice Settling Time (ec) Peal Time (ec) Peak overhoot (%) ZN PI Block Box model(nonlinear Model) Piecewie Model(Linear model) Zone I Zone III Zone I Zone II Zone III Zone IV IMC MRAC ZN IMC MRAC ZN IMC ZN IMC ZN IMC ZN IMC PI PI PI PI PI PI PI PI PI PI PI PI PI IAE ISE Real Time level control uing PI Controller The imulated PI Parameter for the four linearized model are imlemented in real time CTS. The reone are hown in figure 1.

12 Level(cm) Level(cm) K.Indhumathi et al /International Journal of ChemTech Reearch, 018,11(01): Tank level Setoint Time(ec) Figure 1: cloed loo reone of conical tank ytem uing Z-N tuned PI Controller with linearization A hown in above figure controller take long time to reach the et oint. In order to eed u the reone IMC tuning arameter are imlemented in real time for linearized model. The reone i hown in Figure Tank level Setoint Time(ec) Figure 13: cloed loo reone of conical tank ytem uing IMC baed PI Controller with linearization MRAC Tuned PI i imlemented and hown in figure 14. It how that conical tank Sytem ocillateand deired level i not reached for given et oint.

13 Level(cm) K.Indhumathi et al /International Journal of ChemTech Reearch, 018,11(01): Level Setoint Time(ec) Figure 14: cloed loo reone of conical tank ytem uing MRAC tuned PI Controller with Non linear Model Comarion of Z-N, IMC tuned PI controller uing real time reult i hown in table 4.To comare the erformance of the rooed controller variou arameter uch a rie time, eak overhoot and ettling time, IAE are conidered. Table 4:Comarion of Z-N tuned PI, IMC tuned PI Controller through real time imlementation Piecewie Model(Linear model) Performance Indice Zone I Zone II Zone III ZN PI IMC PI ZN PI IMC PI ZN PI IMC PI Settling Time Rie Time Peak Time Peak overhoot(%) IAE From the table it i clear that four linearized model roduce the better erformance comared to ingle model.mrac Tuned PI give better erformance in imulation. For linearized model IMC tuned PI roduce better erformance comared to Z-N tuned PI in real time. 6 Analyi and Concluion Conical tank ytem i a highly nonlinear ytem becaue of it variable cro ection. In thi aer three different modeling aroache are done. The Z-N tuned PI, IMC tuned PI, MRAC tuned PI controller are imlemented in real time CTS. From the reult it ha been oberved that ocillation are more in the reone of Non linear model with ZN tuned PI the controller. Moreover the ytem i not reaching the et oint in all oerating zone. MRAC tuned PI controller give better erformance uing Non linear model. While imlementing thee tuning method in Real time level control of CTS it i oberved that MRAC tuned PI for Non linear model roduce ocillation and deired level i not reached. So it i neceary to linearize the nonlinear ytem and Controller ha to be deigned for linearized model. Piecewie linearization baed control ytem give better erformance with both the controller and from the real time exerimentation it i roved that IMC baed PI give even better erformance than Z-N tuned PI.

14 K.Indhumathi et al /International Journal of ChemTech Reearch, 018,11(01): Reference 1. Abhihek Sharma, Nithya Venkatean (013); Comaring PI controller Performance for Non Linear Proce Model, International Journal of Engineering Trend and Technology, Vol.4, No.3, Anand, S,; Awin, V,;Kumar, S.R. (011); Simle Tuned Adative PI Controller for Conical Tank Proce, Recent Advancement in Electrical, Electronic and Control Engineering,Vol 6,No.11, Angeline Vijula, D,; Vivetha, K,;Gandhimathi, K,;Praveena (014);Model baed Controller Deign for Conical Tank Sytem,International Journal of Comuter Alication,Vol.85,No.1, Anna Joeh,Samon Iaac, J. (013); Real Time Imlementation of Model Reference Adative Controller for a Conical Tank, International Journal of Theoretical and Alied Reearch in Mechanical Engineering, Vol., No.1, Bhuvanewari, N.S,; Uma, G.;Rangawamy, T.R. (009); Adative and Otimal Control of a Non- Linear Proce uing Intelligent Controller,Alied oft comuting, Vol.9, No.1, George Stehanooulo (1984);Chemical Proce Control, Prentice-Hall ublication, New Jerey, Eatern Economy Edition. 7. Kala, H,; Aravind, P; Valluvan, M, (013); Comarative Analyi of different Controller for a Nonlinear Level Control Proce,Proceeding of IEEE Conference on Information and Communication Technologie, Keavan, E; Rakehkumar, S, (013); PLC baed Adative PID Control of Non Linear Liquid Tank Sytem uing Online Etimation of Linear Parameter by Difference Equation, International Journal of Engineering a nd Technology, Vol.5, No., Marhiana, D;Thiruakthimurugan, P,(01); Deign of Ziegler Nichol Tuning Controller for a Nonlinear Sytem, Proceeding of International Conference on Comuting and Control Engineering, Michael L;Luyben,William L;Luyben, (1997);Eential of Proce Control, McGraw-Hill ublication, Singaore, International Edition. 11. Nithya, S,; Sivakumaran, N,; Balaubramanian, T,; Anantharaman, N,(008); Model baed Controller Deign for a Sherical Tank Proce in Real Time, International Journal of Simulation, Sytem, Science and Technology, Vol. 9, No.3, NithyaVenkatean,Anantharaman, N,(01); Controller Deign baed on Model Predictive Control for a Non-Linear Proce, Mechatronic and it alication (ISMA), IEEE,Vol.5, No.1, Prakah, R,; Anita, R, (011);Neuro- PI Controller baed Model Reference Adative Control for Nonlinear Sytem, International Journal of Engineering, Science and Technology,Vol.3, No.6, SatheeKumar, J,; SatheehKumar,; Poongodi, P,; Rajaekaran, K., (010);Modelling and Imlementation of LabVIEW Baed Non-linear PI Controller for Conical Tank, Journal of Control & Intrumentation Vol.1, No.1, Sowmyal, P,; Srivigneh, N,;Sivakumaran, N,; Balaubramanian, G,(01); A Fuzzy Control Scheme for Nonlinear Proce, Proceeding of International Conference on Advanced Engineering Science and Management, Angeline Vijula, D, Indhumathi,K,(014); Deign Of Model Reference Adative controller For Conical Tank Sytem, International Journal of Innovative Reearch in Technology, Vol 1,No. 7, Angeline Vijula, D, Indhumathi, K,(016);Deign and Imlementation of IMC Tuned PI Controller for Nonlinear Conical Tank Sytem Uing Piecewie Linearization,International Journal of Printing, Packaging & Allied Science, Vol. 4, No. 4, *****