NONLINEAR CONTROLLER DESIGN FOR A SHELL AND TUBE HEAT EXCHANGER AN EXPERIMENTATION APPROACH

Transcription

1 International Journal of Electrical, Electronic and Data Communication, ISSN: Volume-3, Iue-8, Aug.-25 NONLINEAR CONTROLLER DESIGN FOR A SHELL AND TUBE HEAT EXCHANGER AN EXPERIMENTATION APPROACH MITHUN.P, 2 SATHEESHBABU.R, 3 I.THIRUNAVUKKARASU, 4 V.I.GEORGE, 5 SHREESHA.C PG Student, M.Tech (Control Sytem), 2 Reearch Scholar, 3 Aociate Profeor, 4,5 Profeor, Department of Intrumentation and Control Engineering, MIT, Manipal Univerity, India. 3 it.arau@manipal.edu Abtract- In thi paper the outlet water temperature control of the hell and tube heat exchanger wa implemented in real time ytem with the Generic Model Control (GMC) and adaptive control technique in imulation. The teady tate model of the heat exchanger i ued for the GMC and the dynamic model of the hell and tube heat exchanger i ued for the adaptive control technique. MATLAB-2-Simulink wa ued a a tool to implement the control algorithm in hardware loop. I. INTRODUCTION Heat exchanger are device that facilitate the exchange of heat between two fluid that are different temperature while keeping them from mixing with each other. Heat exchanger are mainly ued in chemical proceing and power production plant. Since they are relatively eay to ue experimentally and they how nonlinear and non-tationary propertie, the heat exchanger are frequently ued a a demontration of control. Thi paper deal with two type of controller. Generic model controller (GMC) baed on the teady tate model of the STHE [6] and Adaptive controller [,2] baed on the dynamic model of STHE. The generic model control ue the invere of the teady tate model of the STHE to control the nonlinear proce. The model may contain empirical feature or may be purely empirical. GMC integrate the proce model with proportional and integral error term imilar to PI controller to adjut the control input to achieve a deired cloed loop trajectory. In adaptive control, the controller i divided into two part. Non-linear tatic part (NSP) and linear dynamic part(ldp). The non-linear part of the controller i developed uing imulated or meaured teady tate characteritic of the STHE, it inverion, exponential approximationand ubequently it differentiation. Then NSP and non-linear model of STHE i approximated by a continuou time external model (CT-ELM).The parameter of the CT-ELM i obtained by the application of an external delta model with ame tructure a the CT-ELM model. Then in dynamic linear part of the controller, an adaptive controller i developed uing polynomial approach and pole placement method. II. PHYSICAL SYSTEM: SHELL AND TUBE HEAT EXCHANGER Fig.. Heat Exchanger Phyical Experimentation Experimental Setup Table..Technical Specification of the Heat Exchanger Setup The hell and tube heat exchanger ha hot water in the tube ide and cold water in the hell ide. The outlet temperature of the hot water i controlled by varying the cold water flow rate. So that outlet hot water temperature i the controlled variable and inlet cold water temperature i the manipulated variable. III. CONTROL METHODOLOGY Nonlinear Controller Deign For A Shell And Tube Heat Exchanger An Experimentation Approach 38

2 International Journal of Electrical, Electronic and Data Communication, ISSN: A dicued in the abtract in thi paper two control algorithm were deigned, imulated and implemented for a hell and tube heat exchanger proce namely i) Generic Model Control ii) Adaptive Control. 3.. Generic Model Control (GMC) The teady tate model for GMC i developed baed on the energy balance equation of the hell and tube heat exchanger decribed a follow. The heat tranfer rate i The heat rate gained by the cold water i WhereU: overallheattranfer coefficient, A: urfacearea T: water outlet temperature, Tin: waterinlettemperature, F: cold waterinlet flow rate, : denityofwater, Cp: waterheatcapacity,ubcript denoted h for hot water and c denoted for cold water. The teady-tate equation for hot water outlet temperature can be derived by combining Eq ()&(2). Volume-3, Iue-8, Aug.-25 The model i not exactly true to the proce. There for the manipulated variable calculated for invere model will not make the proce be exactly at the et point. So, the output will contain an offet error. In GMC, thi offet i eliminated by integrating the actuating error. The output target can be et by a PI output added to the meaurement: Where K i the proportional gain, varie between K.and.2. AndK2i integral gain. i The target value can be written a Thi equation how the PI action in the GMC. Hence the target i The target value given by Eq. (9) i ubtituted into the teady-tate model invere of Eq. (5) to generate the control action. The cold water inlet valve ha equal percentage characteritic. There for the flow rate and control ignal can be related a Where u i the control ignal. m and are contant and empirically determined from the intalled valve characteritic. In GMC-SS, the teady-tate model i inverted to get the control action By ubtituting equation(4) in (3) and rearranging, the control action, i.e., valve percentage i given by Block Diagram Of The Gmci Shown In Fig Adaptive control Adaptive control ue the dynamic model of the proce for developing the controller. The dynamic model of a counter flow cooling hell and tube heat exchanger can be decribed by three partial differential equation. The parameter in equation ()-(2) are Fig.2 GMC Controller block diagram The concept of GMC control action i to aimfora y- value (CV)targetabout%or2%beyondtheetpoint.The logic i that a target value lightly beyond make the controller puh the proce a bit fat erininitial tage. Then, inlater tage a the proce approache thee tpoint,the target relaxe to the et point. The out puttargeti Where ttand for the time, z for the axialpace variable, T for temperature, q for flow of fluid, v for fluid flow velocitie, d for inner diameter of the tube, d2for outer diameter of the tube, d3 for diameter of thehell, for denitie, cp for pecific heat capacitie, αfor heat tranfer coefficient, n i the number of tubeand Li the length of tube. Subcript denoted rdecribe the hot water, w the metal wall oftube, c cold water and the upercript teady-tate value. A from ref. [3] the parameter and teady ate input ued are given in Table 2. Nonlinear Controller Deign For A Shell And Tube Heat Exchanger An Experimentation Approach 39

3 International Journal of Electrical, Electronic and Data Communication, ISSN: Table 2.Parameter and Steady-State Input IV. CONTROLLER DESIGN Volume-3, Iue-8, Aug.-25 A previouly introduced, the controller conit of a nonlinear tatic part and a linear dynamic part a hown in Fig.4. Finite difference method i employed for the computation of teady tate and dynamic characteritic. For thi the pace interval z, L i divided into a et of dicrete node point { z i } for i= to n. Uing finite difference method PDE are approximated by a et of ODE in the form Fori=..., n, j=n-i+, and, with initial condition T ( i,) T ( i), T ( i,) T ( i), r r w Tc ( i,) Tc ( i).h=l/n i the dicretization tep. The Steady State Characteritic Of The Heat Exchanger Are Shown In Fig.3. w Fig.4 Controller Scheme. The LDP create a linear dynamic relation which repreent a difference of the hot water outlet temperature adequate to it deired value. Then, the NSP generate atatic nonlinear relation between and a correpondingincrement (decrement) of the coolant flow rate. 4. Non Linear Static Part of the Controller The normalized value of flow rate and temperature are obtained by In practice, the error will be preent in meaured data. So that the imulated teady tate characteritic in reality i hown in Fig.5. u Fig 5. Steady-tate characteritic in preence of diturbance Fig. 3 teady tate characteritic of the heat exchanger From thi the operating point around which the change take place during the controli choen a =.9 and T rout q c = The upper and lower limit of the operating point i q U c =.8 3 L m /, q c =.5 m 3 / 3.2. The control input and controlled output are conidered in the form The invere characteritic i approximated by econd order exponential function a hown in Fig.6 Fig 6 Approximation of the invere characteritic Nonlinear Controller Deign For A Shell And Tube Heat Exchanger An Experimentation Approach 4

4 International Journal of Electrical, Electronic and Data Communication, ISSN: The approximation ha done uing leat quare method and ha the form T Now for each rout the difference of the coolant flow rate in the output of NSP can be computed a Volume-3, Iue-8, Aug.-25 In thi w i the reference ignal and v i the diturbance, y i the controlled output and u i the control input.the tranfer function G i given by (22). Both the reference w and the diturbance v are conidered to be tep function. The controller ha the tranfer function in the form 4.2CT and Delta External Linear Model Fig7. Non-Linear component of the cloed loop The non-linear component of the cloed loop coniting of NSP and the STHE model. The tep repone of the non-linearcomponent imulated around above defined operating point i hown in Fig.8. Where q and p are polynomial in that fulfil the condition degq degp. The controller i deigned uing polynomial approach.a controller which atifie tability, internalproperne, aymptotic tracking of tep referenceand tep diturbance attenuation i given by a olution of the polynomial equation With a table polynomial d( ) on the right ide. For tep input ignal w and v, the polynomial p i in the form y Then, the controller tranfer function take form In thi paper, the polynomial d with root determining the cloed-loop pole i choen a Where n i a table polynomial obtained by pectral factorization Fig 8. Step Repone Of The Nonlinear Component From the above tep repone the econd order CT- ELM habeen choen in the form of the econd order lineardifferential equation Or, in the tranfer function repreentation a 4.3 Parameter etimation The parameter a, a, b i obtained by delta model parameter identification method [5]. The delta model correponding to the CT-ELM model ha the form ' Where i the forward hift operator. t i the dicrete time. A the ampling period i too mall, the delta operator become the derivative operator and ' ' ' delta model parameter a, a, b reache the a, a, b of the CT model 4.4 Linear Dynamic Part of the Controller The feedback control loop i hown in Fig.9. Fig 9. Control Sytem Structure i a tuneable parameter that can be elected by imulation experiment. The polynomial n ha the form With coefficient Then, the controller parameter can be obtained fromolution of the matrix equation Where RESULTS AND CONCLUSION GMC controller i implemented in real time ytem and the reult are hown in Fig. with variou etpoint and the adaptive controller i imulated uing MATLAB-2 SIMULINK and it cloed loop repone i hown in Fig.and Fig.2 with variou etpoint. In both cae cold water flow rate i ued a the manipulated variable. Satifactory reult were obtained in imulation and real time experimentation and the controller effort taken by the nonlinear controller i comparatively le compared to the conventional controller deigned for thi particular experimentation etup [4] Nonlinear Controller Deign For A Shell And Tube Heat Exchanger An Experimentation Approach 4

5 International Journal of Electrical, Electronic and Data Communication, ISSN: Volume-3, Iue-8, Aug.-25 Fig 2.Cold Water Flow Rate For Variou Α Value. REFERENCES Fig. Cloed Loop Repone Of The GMC Controller With The Real Time Experimental Setup For The Setpoint 5 C And 48 C. Fig. Controlled Output Reponeof The Adaptive Controller With The Variou Α Value. [] Dotál, P. J. Vojtěšek, and V. Bobál. 2a. "Simulation of the 2DOF nonlinear adaptive control of a chemical reactor". In: Proceeding of 25th European Conference on Modelling and Simulation, Krakow, Poland, [2] Dotál, P. J. Vojtěšek, and V. Bobál. 24a. "Non linear control of hell and tube heat exchanger". In: Proceeding of 28th European Conference on Modelling and Simulation, [3] Bobál, V., J. Böhm, J. Fel, and J. Macháček. 25. Digital elf-tuning controller, Springer Verlag, Berlin, 25. [4] Satheehbabu.R, Dr.I.Thirunavukkarau et al., Temperature control of a hell and tube heat exchanger uing PID algorithm, International Journal of Advancement in Electronic and Electrical Engineering IJAEE, Vol.3, Iue.3, Sep.24. [5] N. K. Sinha. Identification of continuou-time ytem from ample of input-output data uing the δ-operator. Control Theory and Advanced Technology, vol. 9, pp. 3 25, 993, [6] R. Ruell Rhinehartet al Comparion of model-baed and conventional controller on a pilot-cale heat exchanger ISA Tranaction 52 (23) Nonlinear Controller Deign For A Shell And Tube Heat Exchanger An Experimentation Approach 42