# Matlab simulation of temperature control of heat exchanger using different controllers

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2 2 eeraj Srivastava et al.: Matlab Simulation of Temperature Control of Heat Exchanger using Different Controllers Fig 1. Shell and tube heat exchanger system control scheme Assumptions Different assumptions have been considered in this research paper. (i) Inflow and the outflow rate of fluid are same, so that the fluid level is maintained constant in the heat exchanger. (ii) The heat storage capacity of the insulating wall is negligible. A thermocouple is used as the sensing element which is implemented in the feedback path of the control architecture. The temperature of the outgoing fluid is measured by the thermocouple and the output of the thermocouple is sent to the transmitter unit, which eventually converts the thermocouple output to a standardized signal in the range of 4-20 ma. This output of the transmitter unit is given to the controller unit. The controller implements the control algorithm, compares the output with the set point and then gives necessary command to the final control element via the actuator unit. The actuator unit is a current to pressure converter and the final control unit is an air to open valve. The actuator unit takes the controller output in the range of 4-20 ma and converts it in to a standardized pressure signal in the range of 3-15 psig. The valve actuates according to the controller decisions. Fig 1 shows the control scheme adopted in heat exchanger system Sources of Disturbances There can be two types of disturbances in this process. (i) the flow variation of input fluid (ii) the temperature variation of input fluid Mathematical Modeling of Heat Exchanger System In this section the heat exchanger system, actuator, valve, sensor are mathematically modeled using the available experimental data. The experimental process data s are summarized below[2]. Exchanger response to the steam flow gain 50// Time constants 30 Exchanger response to variation of process fluid flow gain 1// Exchanger response to variation of process temperature gain 3/ Control valve capacity for steam 1.6 / Time constant of control valve 3 The range of temperature sensor Time constant of temperature sensor 10 From the experimental data, transfer functions and the gains are obtained as below. Transfer function of process Gain of valve 0.13 Transfer function of valve. Gain of current to pressure converter 0.75 Transfer function of disturbance variables (i) Flow (dominant). (ii) Temperature Transfer function of thermocouple. 3. roportional-integral-derivative (ID) Controller The mnemonic ID refers to the first letters of the names of the individual terms that make up the standard threeterm controller. These are for the proportional term, I for the integral term and D for the derivative term in the controller. ID controllers are probably the most widely used industrial controller. Even complex industrial control systems may comprise a control network whose main control building block is a ID control module. In ID controller roportional () control is not able to remove steady state error or offset error in step response. This offset can be eliminated by Integral (I) control action. Output of I controller at any instant is the area under actuating error signal curve up to that instant. I control removes offset, but may lead to oscillatory response of slowly decreasing amplitude or even increasing amplitude, both of which are undesirable. Derivative (D) control action has high sensitivity. It anticipates actuating error, initiates an early correction action and tends to increase stability of system[2]. Ideal ID controller in continuous time is given as! " # ) \$ % &* '(' #+ ( (' (', (1) Laplace domain representation of ideal ID controller is 3.1. Tuning of ID Controller -. /!1# \$ % #+ ( (2) Ziegler and ichols proposed rules for determining values of!, ( based on the transient response characteristics of a given plant. Closed loop oscillation based ID tuning method is a popular method of tuning ID controller. In this kind of tuning method, a critical gain 5 is induced in the forward path of the control system. The high value of the gain takes the system to the verge of instability. It creates oscillation and from the oscillations,

3 Automation, Control and Intelligent Systems 2014, 2(1): the value of frequency and time are calculated. Table 1 gives experimental tuning rules based on closed loop oscillation method[3,4]. Table 1. Closed loop oscillation based tuning methods. Type of Controller 6 7 B C B D 0.5K 9 0 I 0.45K T 0 ID 0.6K 9 0.5T 0.125T The characteristic equation 1#-F0 in this case is obtained as below 900 #420 = #43# #10 (3) Applying Routh stability criterion in above eq gives Auxiliary equation is 420 = # #10 (4) and For the ID controller the values of parameters obtained using Ziegler ichols closed loop oscillation based tuning methods are! ( 3.60 Usually, initial design values of ID controller obtained by all means needs to be adjusted repeatedly through computer simulations until the closed loop system performs or compromises as desired. These adjustments are done in MATLAB simulation. 4. Fuzzy Logic Controller (FLC) The design of fuzzy logic controller is attempted in heat exchanger. The fuzzy controllers are designed with two input variables, error and rate of error and one output variable (i.e.) the hot water flow rate to the shell side. The mamdani based fuzzy inference system uses linear membership function for both inputs and outputs. For the fuzzy logic controller the input variables are error and rate of error, and the output variable is controller output. Triangular membership functions are used for input variables and the output variable. The universe of discourse of error, rate of error and output are [-13, 13], [-4, 4] and [-5, 5] respectively. The rule base framed for shell and tube heat exchangers are tabulated in Table 3[5,7]. The structure of the rule base provides negative feedback control in order to maintain stability under any condition. For the evaluation of the rules, the fuzzy reasoning unit of the FLC has been developed using the Max-Min fuzzy inference method[8]. In the particular FLC, the centroid defuzzification method is used. Linguistic variables for error, rate of error and controller output are tabulated in table 2.[6] Fig 2, 3 and 4 shows membership functions of different variables implemented in FIS editor in MATLAB toolbox and fig 5 shows surface view of all variables in 3 dimension[9]. B M S Z GH G I B M S Z Table 2. Linguistic variables. Very big negative Big negative Medium negative Small negative Zero Table 3. Rule base for fuzzy logic controller. B M S B B M B M S S B M S Z M M S Z S B S Z S M Z S M B S M B Fig 2. Membership function for error. Fig 3. Membership function for rate of error. Fig 4. Membership function for control output. Small positive Medium positive Big positive Very big positive Z S M B B M S Z B M S Z S M S Z S M S Z S M B Z S M B S M B M B B

4 4 eeraj Srivastava et al.: Matlab Simulation of Temperature Control of Heat Exchanger using Different Controllers 5. Simulation Fig 5. 3D Surface view. The simulation for different control mechanism discussed above were carried out in Simulink in MATLAB and simulation results have been obtained. Fig 6 and 7 shows the ID controller and FLC system block diagram which is simulated in matlab. Fig 6. ID Controller. Fig 7. Fuzzy logic controller. Fig 8 and 9 shows step response of ID and FLC system where x axis denote time and y axis denote set point value. Fig 8. ID Step response. Fig 9. FLC Step response. 6. Simulation Result and Discussion To evaluate the performance of the different controllers this paper has considered two vital parameters of the step response of the system. The first parameter is the maximum overshoot and the second parameter is the settling time. eak Overshoot: It indicates maximum positive deviation of output with respect to its desired value. It is defined as[8] %K! 5L' MO5 Q100 % 5 Settling Time: It is the time required for the response to reach and stay within a specified tolerance band of its final value. The tolerance band is taken randomly as 2%. In this paper control of temperature of heat exchanger is done by 2 different controllers. In ID controller we set the parameters by using Ziegler ichols closed loop method. After this we simulated the model in MATLAB and tuned the parameters until the response is satisfactory. In step response, we found overshoot and large settling time both of which are undesirable. Moreover there are three tuning parameters which simultaneously be adjusted to get desired result. Then a Fuzzy logic controller is developed with 9 membership functions for each variable. There were total 81 rules generated. The response is smooth as well as fastest as compared to ID controllers. So FLC is recommended because it is easy to implement, low cost and no need to know exact plant parameters. Different parameters are tabulated ated in table Conclusion In this paper, a comparative study of performance of conventional (ID) and intelligent (FLC) controllers is studied. The aim of the proposed controller is to regulate the temperature of the outgoing fluid of a shell and tube heat exchanger system to a desired temperature in the shortest possible time and minimum or no overshoot After comparing results for different controllers, we obtain that fuzzy logic controller is the one which gives quick response without any oscillations. It is easy to implement fuzzy logic as it is computer oriented. ID controller, though good for industrial process but due to oscillatory response and large settling time is now going to be replaced by new technology like Fuzzy logic and eural network.

5 Automation, Control and Intelligent Systems 2014, 2(1): Control System Feedback ID Controller Table 4. Comparison of different parameters. Maximum Overshoot (%) Settling Time (sec) FLC 0 65 omenclature R S T U T V R W T X YWZ G roportional gain Integral time Derivative time Critical gain Time period of oscillation Angular frequency of oscillation Controller transfer function Error between desired output and actual output References [1] Anton Sodja et.al, "Some Aspects of Modeling of Tube-and- Shell Heat-Exchangers," in roc of 7th Modelica Corif-, Italy, pp , Sep [2] Subhransu adhee, Yuvraj Bhushan Khare, Yaduvir Singh Internal Model Based ID Control of Shell and Tube Heat Exchanger System, IEEE, JA [3] Katsuhiko Ogata, Modern Control Engineering. 5 th edition [4] Kiam Heong Ang, Gregory Chong and Yun Li, "ID Control System Analysis, Design, and Technology," IEEE Trans., Control Syst. Technol., vol. 13, no. 4, pp , Ju [5] Mridul andey, K. Ramkumar & V. Alagesan Design of Fuzzy Logic Controller for a Cross Flow Shell and Tube Heat-Exchanger, IEEE, Mar 2012 [6] Zadeh L.A., Fuzzy relation Equations and Applications to Knowledge Engineering, Kluwer Academic ublishers, Holland, 1989 G Rate of error [7] Larsen.M., Industrial application of Fuzzy Logic Control, academic press, inc., may, [8] BS Manke, Linear Control System. 9 th edition 2010 [9] Fuzzy Logic Toolbox Help file in MATLAB version 7.11

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