Multiple Model Based Adaptive Control for Shell and Tube Heat Exchanger Process

Multiple Model Based Adaptive Control for Shell and Tube Heat Exchanger Process R. Manikandan Assistant Professor, Department of Electronics and Instrumentation Engineering, Annamalai University, Annamalai Nagar, Chidambaram, Tamil Nadu, India. R. Vinodha Associate Professor, Department of Electronics and Instrumentation Engineering, Annamalai University, Annamalai Nagar, Chidambaram, Tamil Nadu, India. Abstract Shell and Tube heat exchanger system (STHX) is widely used in food processing and chemical industries because it can sustain wide range of temperature and pressure. The main purpose is to exchange heat between hot and cool fluid. The designed controllers will regulate the temperature of outlet fluid to a desired set point in the shortest possible time irrespective of load and process disturbances, equipment saturation and nonlinearity. Due to nonlinear nature, shell and tube heat exchanger system is hard to model and control using conventional methods. Conventional controllers may not give efficient control over process as heat exchange influenced by operating point shifts and disturbances. To accommodate linear controllers with such drawbacks, multiple model strategy has been used. This paper proposes multiple model based PID and multiple model based MRAC control for a nonlinear STHX process. Closed loop control is implemented on the chosen process in simulation using Matlab. The controllers are subjected to both reference tracking and disturbance rejection. Keywords: Shell and Tube heat exchanger, conventional Proptional Integral Derivative controller (PID), Model Reference Adaptive Controller (MRAC), multiple models. Introduction Heat Exchanger works in the principle of three methods conduction, convection, and radiation. Heat exchanger is widely used in areas like chemical, food perseverating, energy production, etc. STHX process has its own nonlinearity and component added non-linearity, hence a challenge is faced in the control aspect. Controlling the outlet hot-water temperature by manipulating cold water inflow is difficult because heating and cooling a material will cause change in its gain and time constant. It is observed in literature that STHX hot water outlet temperature is controlled widely by intelligent and adaptive controllers [6]. In the process industries, model predictive control and Internal Model Control (IMC) have been widely accepted for set-point tracking and overcoming plant model mismatch. Many literatures have reported for system design of STHX. [2] However, only few literature have addressed about mathematical modelling developed from first principle method and control point of view. Simulation studies are presented with conventional fuzzy logic controller for STHX process for a linear range [1]. The detailed study and implementation of hybrid fuzzy logic controller for shell and tube heat exchanger is presented literature [1]. Also the above shell and tube heat exchanger has been addressed in optimization of membership functions and fuzzy rules based on genetic algorithm, Ant colony algorithm and PSO method [2]. All the above literature survey deals, control of STHX process only for a linear range and hence there is a motivation to extend the operating range of the STHX process by multiple model approach [3]. Linear control strategy is simple to design, but it fails as shift in operating point or disturbance effect is severe To utilize the advantages of linear controllers multiple model based techniques have been proposed. The multiple model schemes in the literature pave the way to use local controllers efficiently. In the work of Prakash et. al, [3] multiple model concept has been utilized for single input single output CSTR process. The same concept is utilized for the proposed work via PID control and MRAC. Shell and Tube Heat Exchanger A STHX [4], [13] consists of a bundle of tubes enclosed within a cylindrical shell. One fluid flows through the tubes and second fluid flows within the space between the tubes and the shell. Heat is thus transferred from one fluid to the other through the tube walls, either from tube side to shell side or vice versa shown in Figure 1. In this proposed work, water is taken as the medium for both shell and tube. The water is raised to a certain temperature in the process tank using thyristor drivers and this hot water is allowed to flow through the tubes where as shell carries the water in room temperature. The hot and cold water inflow to the shell and tubes are manipulated using pneumatic control valves. RTD is used as temperature sensors at places of hot and cold water inlet and outlet. The hot water outlet temperature of tubes is the variable to be controlled, by manipulating the cold water flow to the shell. Differential Pressure Transmitter (DPT) is used for sensing the flow. 3175

Figure 3: Exchange of heat in co-current and counter current mode. Figure 1: Piping and Instrumentation diagram of Shell and Tube Heat Exchanger (STHX). The direction of flow of hot and cold water decides the operation of STHX process to lie in co-current or counter current mode. If flow in shell and tubes are in same direction the mode is said to be co-current mode and counter current for opposite direction of flow as stated in Figure 2. The exchange of heat between shell and tube [13] are shown in Figure 3 for co-current and counter current mode. Energy Balance Equation The energy balance for shell and tube [4] are given in equation (1) and (2) respectively with specification listed in Table 1. Shell Side: ρ s c s v s dt h s A * co m T s s c s (T ci co ) (T ho T co ) N dt N TUBE SIDE ρ c v dt t t t ho h tat * m c (T T ) (T T ) N dt t t hi ho co (2) ho N (1) Table 1: Parameter specifications of the STHX process at nominal operating point. Inputs Value Units Density of water ( s ρ t ) 1000 Kg/m 3 Specific Heat Capacity of water (cs,ct ) 4230 J/kg C Shell Heat Transfer Area ( As ) 0. 281 m 2 Tube Heat Transfer Area ( At ) 0. 253 m 2 Shell side volume ( vs ) 2. 62 X 10 m 3 Tube side volume ( v t ) 1. 43 X 10 m 3 Heat transfer coefficient of Shell ( hs ) 2162 W/m 2 o C Heat transfer coefficient of Tube ( h t ) 2162 W/m 2 o C Mass flow rate of cold water m ) 0-0. 1222 Kg/s ( s Mass flow rate of hot water m ) 0. 0282 Kg/s ( t Cold water inlet temp ( Tci ) 33 o C Hot water inlet temp ( Thi ) 55 o C Number of control volume (N) 10 NA Figure 2: Co-current and Counter current modes of STHX. White Box Modelling The experiment has been carried out in co-current mode. To observe the model of the process, the hot water of tubes is maintained at a nominal temperature. Then a small step change in cold water inflow rate is given, both in positive and 3176

negative directions to obtain respective reaction curves, as shown in Figure 4. The open loop parameters like process gain Kp, time constant τ and time delay td are obtained from the reaction curves[15], [16]. The closed loop parameters are calculated from the open loop parameters using ZN tuning method. To design multiple model based controller [5], [6], [8], the above procedure is repeated at four different operating points and parameters are listed in Table 2. The Z-N tuning parameters are given in equation (3), (4) and (5). Controller gain 1.2τ K (3) c td *Kp Integral time Ti 2* t d (4) Derivative time Td 0.5 * t d (5) controller PID parameters. Figure 7 shows the closed loop response of STHX process with MM-PID controller. Figure 5: Block diagram of Multiple Model (MM)-PID Controller for STHX within all operating region. Table 3 gives the performance indices of MM-PID for STHX process. It has been observed that setting time is very high and hence there is need for model based approach like Model Reference Adaptive Control (MRAC) [12], [17]. Figure 4: Open loop responses of STHX at different operating regions. Table 2: Open loop and close loop controller parameters at different operating regions. Operating Hot water Zone outlet Temperature o C Process parameters PID Controller Parameters Kp τ td Kc TI TD 1 44. 7 to 47. 06-125. 78 0. 6 0. 9-0. 0064 1. 8 0. 45 44. 7 to 43. 57-61. 053 0. 4 0. 8-0. 01 1. 6 0. 4 2 43. 57 to 44. 7 43. 57 to 42. 91-35. 789 0. 3 0. 7-0. 015 1. 4 0. 3 42. 91 to 43. 57 35 42. 91 to 42. 47-24. 21 0. 2 0. 4-0. 025 0. 8 0. 2 4 42. 47 to 42. 91 42. 47 to 42. 16-16. 842 0. 3 0. 6-0. 035 1. 2 0. 3 Multiple Model PID Controller (MM-PID) In this work, multiple model based control scheme MM-PID has been proposed for the STHX process. The multiple model based control system consists of a family local linear PID controllers and a scheduler [9], [14], [15], is shown in Figure 6. At each sampling instant the scheduler will assign weights to each local controller and the weighted sum of the outputs will be applied as input to the plant. Table 2 provides the local Figure 6: Servo response of MM-PID controller. Table 3: Performance indices of MM-PID controller Sampling Instants 0 10000 to 20000 30000 40000 to 10000 to 40000 to 50000 Ts 14000 22300 35000 46000 ISE 207 232 11385 1702 IAE 796 359 5169 1944 Multiple Model Adaptive Controller The Model Reference Adaptive Control strategy [12], [17] is used to design the adaptive controller that works on the principle of adjusting the controller parameters θ 1 and θ 2. This adjustment is done by adaptation of gain-γ and γ, so that the output of the plant tracks the output of a reference model having to minimize the error. E=T ho (t) T ho m (t). Hence the cost function J, can be minimized [9], [10], [17]. In the proposed work, Multiple Model MRAC (MM-MRAC) for STHX process, the reference model is tend to be selected 3177

based on operating point changes. The block diagram of Multi Model MRAC is shown in Figure 7, where Lyapunov type bypasses the filter that MIT rule has. The equations related with MRAC are given from equations (6) to (10). The servo response of MM-MRAC (with Lyapunov and MIT rule) is shown in Figure 8 with respective manipulated cold water flow. Table 4, gives the performance measure of STHX process for set point change in hot water outlet of tubes. MM- MRAC (with MIT rule) performs better than MM-MRAC (Lyapunov) since it has better setting time with minimum ISE and IAE values. Plant equation: T ho (t) = STHX equ (m S(t)) (6) W n 2 Model equation: T m ho (t) S 2 +2δW n +W 2 (m n S(t)) (7) Controller: (m S(t)) = θ 1 sp(t) θ 2 T ho (t) (8) E= T ho (t) T ho m (t) (9) The control law to minimize error between plant and model is, d ( γ dt m S(t) = { sp(t) [T ho (t) T ho m (t)]sp(t) ) d ( γ T dt ho (t) [T ho (t) T ho m (t)]t ho (t) ) } (10) Where θ 1, θ 2 are updating parameters and γ is the adaptation gain Figure 7: Block diagram representation of MM-MRAC [Lyapunov & MIT] Controller for STHX process. A clear enlarged vision for large range of hot water outlet temperature servo response of 3. 5 O C tracking is shown in figure 9. Figure 9: Servo response of MM-MRAC [Lyapunov & MIT] Controller showing clear vision between 230 to 300 samples. Table 4: Performance indices for servo response of STHX process (MM-MRAC Lyapunov & MIT). Sampling Instants 75 to 149 150to 249250 to 299300to 349 MM-MRAC %Mp 0 0 0. 064 0 LYAPUNOV Ts 100 190 267 308 ISE 66 895 4968 52 IAE 193 1165 1919 141 MM-MRAC %Mp 0 0 0. 107 0 MIT Ts 95 188 266 306 ISE 65 635 3563 42 IAE 183 762 1346 116 Regulatory Responses The hot water outlet temperature can be disturbed by changing the flow rate and temperature of tubes hot water [refer Figure 10 and 11]. The servo regulatory response [refer Figure 12] has been obtained for STHX process by increasing the flow rate to 0. 0362 Kg/sec from its nominal of 0. 0282 Kg/sec (at 300 th sec) and decreasing the temperature to 54 O C from its nominal of 55 O C (at 400 th sec). The clear vision of above said servo regulatory response is made in Figure 13. Similarly Figure 14 gives the vision of decrease in flow rate (at 600 th sec) by 0. 008 Kg/sec to its nominal value of 0. 0282 Kg/sec and increase in temperature by 3. 5 O C from its nominal of 54 O C (at 700 th sec). Figure 8: Servo responses of sampling instants MM-MRAC [Lyapunov & MIT] Controller. Figure 10: Block diagram representation for disturbed by changing the flow rate and temperature of tubes hot water inlet. 3178

Figure 11: Response for representation of disturbance by changing the temperature and the flow rate of tubes hot water inlet. Figure 14: Regulatory responses of Inflow (@ 600) and temperature (@ 700) for MM-MRAC [Lyapunov & MIT] Controller for STHX. Table 5 gives the performance measure of servo-regulatory response of STHX process. The values from Table 5 infer that MM-MRAC (MIT) performs better in both possibilities of disturbance namely increasing the flow rate and decreasing the temperature of inlet hot water tubes and vice-versa. Table 5: Performance indices for regulatory response of STHX process (MM-MRAC Lyapunov & MIT). Figure 12: Servo & Regulatory responses for all operating region of MM-MRAC [Lyapunov & MIT] Controller for STHX. Time in sec and 299 to 399 599 to 699 399 To 499 699 To 799 Regulatory In Flow disturbance temperature dist 0. 008 0. 008 1 O C 3. 5 O C Lit/Sec Lit/Sec MM-MRAC %Mp 0 0 0 2. 77 LYAPUNOV ts 330 610 422 724 ISE 24 15 5 73 IAE 27 21 18 50 MM-MRAC %Mp 0 0 0 2. 49 MIT ts 337. 4 607 428 730 ISE 22 14 4 68 IAE 34 20 16 45 Conclusion In this paper, an attempt has been made to control the STHX process over a wide operating temperature with multiple model approach the simulation utilizing differential equation model of STHX process reveals that MM-MRAC [Lyapunov & MIT] gives better performance with good setpoint tracking and disturbance rejection. Reference Figure 13: Regulatory responses of Inflow (@ 300) and temperature (@ 400) for MM-MRAC [Lyapunov & MIT] Controller for STHX. [1] Venkatesan, N. Sivakumaran, N and Sivashanmuguham, P, Experimental Study of Temperature Control using Soft Computing, International Journal of Computer Applications (0975-8887) Volume 52-No. 9, August 2012, pp. 1-6, 2012. 3179

[2] Sivakumar, P, Prabhakaran, D and Kannadasan, T, Temperature Control of Shell and Tube Heat Exchanger by Using Intelligent Controllers-Case Study, International Journal Of Computational Engineering Research, vol. 2, pp. 285-291, 2012. [3] Vinodha, R, Lincoln, S, A and Prakash, J, Multiple Model and Neural based Adaptive Multi-loop PID Controller for a CSTR Process, International Journal of Electrical and Electronics Engineering, 2009. [4] Manikandan, R, Sivaraman, E, Arulselvi, S, Md. Shabuilla, Neuro modeling of shell and tube heat exchanger, International conference on challenges in Biotechnology and food technology, pp. 16-19, Annamalai University., Chidambaram, Jan 9-10, 2012. [5] Tan, W., Marquez, H. J., Chen, T., & Liu, J. Multimodel analysis and controller design for nonlinear processes, Computers and Chemical Engineering, Vol 28, pp. 2667-2675, 2004. [6] Manikandan. R;Vinodha. R; Lincoln. S, A; Prakash. J; Design and Simulation of Model based Controller for 2X2 CSTR Process,, IEEE Xplore Digital Library, doi. 10. 1109/ICGCEE. 2014. 69922475, pp. 1-7, 2014 [7] Dougherty, D and Cooper, D, A practical multiple model adaptive strategy for single-loop MPC, Control Eng. Pract., vol. 11, no. 2, pp. 141-159, 2003. [8] Dhanalakshmi, R and Vinodha, R, Design of control schemes to adapt PI controller for conical tank process, International Journal Advance Soft Computing its Application., vol. 5, no. 3, pp. 1-20, 2013. [9] Wang, R and Safonov, M. G, Stability of unfalsified adaptive control using multiple controllers, Proc. 2005, American Control Conference., pp. 3162-3167, 8-10 june 2005. [10] Sukumar Kamalasan, Adel. a. Ghandakly, Khail. Al. olimat, A fuzzy logic based multiple reference model adaptive control, Journal Control and Intelligent Systems, Volume 36, Issue 2, 2008. [11] Ahmad, M. A., Ishak, A. A, Ismail, N. K., New hybrid model reference adaptive supervisory fuzzy logic controller for shell and tube heat exchanger temperature system, in Control and System Graduate Research colloquium (ICSGRC), IEEE, doi. 10. 1109/ICSGRC. 2012. 6287134, pp. 49-54, 16-17 July 2012. [12] Roffel, B and Betlem, B. H, Process dynamics and control: modeling for control and prediction Wiley. 2006. [13] John. H. Lienhard. IV/ John. H. Lienhard V, A heat transfer text book, third edition, Phlogiston Press., vol., 10. no., 1., 1986. [14] Astolfi. A, Karagiannis. D, and Ortega. R, Nonlinear and adaptive control with applications. London: Springer-Verlag, 2008. [15] Padmasree, R. and Chidambaram. M, Control of unstable System Narosa Publications, ISBN, 978-81- 7319-700, 2005. [16] Wayne Bequette. B. Process Control, Modeling Design and Simulation. Prentice Hall of India, First Edition 2004. [17] Karl J. Astrom, Adaptive Control, Pearson education, Second Edition, 2006. 3180