JOURNAL OF COMPUTER SCIENCE AND ENGINEER ENGINEERING, VOLUME 8, ISSUE 1, JULY 2011 32

Application of Fuzzy Logic Controller for a Pressure ressure Process V.Kalaichelvi and Srijan Bhatnagar Abstract—Pressure Pressure is a key process variable in process control industries because pressure provides a critical condition for boiling, chemical reaction, distillation, vacuuming, and air conditioning. Pressure Process rig is a pneumatic control system which allows study of the principles of pressure as the process variable to be controlled. The aim of the present work is to apply different control strategies to a pressure control process. Controllers help in bringing the output of a process to settle at a specified set point. Conventional Controllers like the Proportional, Integral and Derivative (PID) is used to control the pressure process under consideration. The Internal Model odel Control method (IMC) of tuning is used to determine the parameters of the controller.Since ce pressure is a nonlinear process, intelligent control strategies like Fuzzy Logic Controller (FLC) work better for the pressure process. The fuzzy rule ule based system helps in the design aspect of the FLC. The performance of two controllers are compared to understand which controller is better suited for the process under consideration. Simulation results using MATLAB are shown to carry out the design and control aspects of the process. Index Terms—Pressure Process,PID Controller,Fuzzy ontroller,FuzzyLogic Controller,PerformanceCriteria,Robustness

——————————
——————————

1 INTRODUCTION

P

RESSURE control is of prime importance in fields like steam production in power plants, reaction control in chemical industry, heating, ventilating, and air condicond tioning (HVAC) system. In broad view, pressure control is a dynamic and nonlinear process, and hence tuning of the controller on a frequent basis is essential to suit the process operating settings.Erroneous Erroneous pressure control can result in safety hazards, quality, and efficiency problems. For example, exceedingly high pressure inside a closed vessel can be a reason for a blast. These problems cannot be afforded in a process control industry. Therefore, Therefore it is very much necessary to keep pressure in control and maintained inside its safety limits [1]. Controllers help in bringing the output of a process to settle at a specified set point. Conventional Controller like the Proportional, Integral and Derivative (PID) are used to control the pressure process under consideration. The IMC method of tuning is used to determine the parameparam ters of the controller. Since pressure is a nonlinear process, it is difficult to obtain satisfactory results eme ploying conventional controller methods.An .An intelligent control strategies like Fuzzy Logic Controller ontroller (FLC) has been suggested as a promising alternative approach for controlling processes especially those that are too comco plex for analysis by conventional technique techniques. A specially chosen triangular membership function was employed that was strongly motivated by the theory of fuzzy sets developed by Zadeh[2].

Fuzzy logic becomes simple for difficult procedures that are non-linear linear and lack a mathematical model. MoreMor over, fuzzy systems can deal with crucial parameter changes much better than conventional controllers. controllers

2 MODELLING OF PRESSURE PROCESS A pneumatic control system enabling the study of the principles of process control pressure as the process var variable to be controlled ntrolled is called a Pressure Process Rig as shown in figure 1. It facilitates the study of the principles of pressure regulation of a process. The he pressure process rig experiment is used to apply a step disturbance to the process by changing the position of the control trol valve. This step change will result in a new pressure in the system.

Fig.1. Experimental Set up for Pressure Pre Process Rig. ————————————————

• V.kalaichelvi is with the Dept of Electronics & Instrumentation Engg, Engg,BITS PILANI,DUBAI CAMPUS , P.O.BOX.345 055. • SrijanBhatnagar,student , Department of Electrical &Electronics Electronics Engg,BITSPilani,Dubai Campus, Dubai International Academic City, P.O.BOX.345 055.

This section deals with the building of the transfer fun function model of the pressure process using the two-point method.Experimental Experimental data has been implemented through MATLAB software and the resulting graph is presented in figure 2.

© 2011 JCSE http://sites.google.com/site/jcseuk/

JOURNAL OF COMPUTER SCIENCE AND ENGINEERING, VOLUME 8, ISSUE 1, JULY 2011 33

Table 1. TABLE 1 CONTROLLER PARAMETERS USING IMC Pressure (psi)

METHOD OF TUNING FOR A PRESSURE PROCESS

kc 0.452 0.05 1.328 Where kc is the Controller gain, τI is the integral time and τD is the derivative time.

3.1 Simulation Results and Performance Characteristics The IMC method resulted in the parameter evaluation of the PID controller parameters. In this section, the PID controller is designed and implemented using MATLAB software and the simulation results are presented

No. of Samples

Fig.2 Openloop response of pressure process.

From fig.2 it is observed that the operating region of the controller is from 42 psi (initial value) to 49 psi (final steady state value). Most pressure processes are nonlinear. Hence, the modelling of these processes is not easy. Therefore, a pressure process is approximated by a first order plus dead-time (FOPDT) model of the form given by

ke − td GPRC ( s) = τs + 1

(1)

Where K is the process gain,td is the dead time and τ is the time constant of the process. Using the values calculated by the two-point method, the transfer function model therefore becomes GPRC ( s) =

0.7e−21.65 1.515s + 1

(2)

Fig. 3 Pressure process model with PID controller

Figure 3 shows the model of the pressure process which is being controlled by the IMC based PID controller. The simulation result for the above model with step input from 42 to 49 psi is shown in figure 4.

3 DESIGN OF IMC BASED CONVENTIONAL PID CONTROLLER Tuning is the process of adjusting feedback controller parameters to obtain a specified closed loop response. The dynamic process data obtained via modelling or testing should initially be checked to ensure that appropriate control action can be found. An IMC method is based on accurate model of the process which leads to the design of a control system that is stable and robust. The IMC method yields the following equations for the evaluation of the PID parameters [3],[4] . τ +0.5td kc = p (3) kp(λ +0.5td )

Fig. 4.Closed Loop Response of a Pressure Process under IMC based PID Controller for a set pont change from 42psi to 49psi

4 FUZZY LOGIC CONTROLLER (4)

τ I = τ p + 0.5t d τ

D

=

τ 2τ

p p

t

d

+ t

d

(5)

A conventional PID controller is designed for a pressure process using IMC method of tuning and is presented in

The block diagram of a fuzzy controller [2] is given in figure 5. In this figure, a fuzzy controller is implanted in a control system which is closed-looped. The plant outputs are represented by y (t), its inputs are represented by u (t), and r (t) is the chosen representation for the reference input .

JOURNAL OF COMPUTER SCIENCE AND ENGINEERING, VOLUME 8, ISSUE 1, JULY 2011 34

for building decisions to control the process and hence have an effect on the design of the controller. Generally, the number of inputs and outputs are kept low (not more than two) to avoid an explosion in the number of rules.The inputs to the fuzzy logic controller used here are ‘error’ and ‘change in error’, while the output is the controlled variable like ‘Pressure’. Figure 6 shows the inputs and outputs for the Fuzzy Logic Controller.

Fig.5.Block Diagram of Fuzzy Logic Controller

The four main parts of the fuzzy logic controller are (i) The information is held in the “rule-base”, which is basically a set of rules. These rules provide the knowledge that helps to control the system in the best possible manner. (ii) The input to the plant should be selected after the inference mechanism assesses the control rules which are applicable at the present time and accordingly takes a decision. (iii) The inputs are altered by the fuzzification block so that they can be inferred and linked to the rules in the rule base (iv) Decisions made by the inference mechanism are translated by the defuzzification boundary into inputs. Essentially, the fuzzy controller is an artificial decision maker that works in real time in a system which is closedloop. It tries to guarantee that performance aims are met by collecting the output data y(t), comparing this data to the reference input r(t), which is finally followed by choosing the plant input u(t). Before getting into the step by step design procedure of the fuzzy logic controller, it is important to understand the concept of membership functions.

4.1 Membership Functions The membership function is defined as a graphical depiction of the level of involvement of each of the inputs. It links a weight factor with each of the inputs that are managed. Fuzzy set model allows an element to have a grade with which it belongs to a set. This grade is called a membership in a set, and a fuzzy set is a class in which every element has a membership value. [5] 4.2 Design of Fuzzy Logic Controller

Fig. 6 .Inputs and Output for the Fuzzy Logic Controller

Step 2: Partition the Universe of Discourse (UOD) of each fuzzy variable into number of fuzzy sets, assigning each a linguistic label. A Universe of Discourse (UOD)is defined as the range of values the inputs and outputs of a system can have.The linguistic variables and values offer a language that gives ideas regarding the control decision-making process for the structure recognised by the selection of fuzzy controller inputs and outputs.The input and output fuzzy variables are assigned the following linguistic variables: Error – Negative Big (NB), Negative Medium (NM), Negative Small (NS), Zero (Z), Positive Small (PS), Positive Medium (PM), Positive Big (PB) Change in error - Negative Big (NB), Negative Medium (NM), Negative Small (NS), Zero (Z), Positive Small (PS), Positive Medium (PM), Positive Big (PB) Pressure - Negative Big (NB), Negative Medium (NM), Negative Small (NS), Zero (Z), Positive Small (PS), Positive Medium (PM), Positive Big (PB) Step 3: Assign Membership values to Fuzzy Variables and choose appropriate scaling for the variables. In this step, the input and output fuzzy variables are assigned membership values. Change in the scaling gains of the input and output fuzzy variables can substantially impact the performance of the subsequent control system and therefore are often considered as tuning factors of a fuzzy controller.The variables are normalized to -1 to +1.Figures 7 to 9 illustrate the assigning of membership values of fuzzy variables for error,change in error and output pressure.

This step is important to guarantee that the controller is provided with the proper information to make good conclusions and has the correct control inputs to guide the system in the directions required to attain highperformance operation.The choices of inputs and outputs have an effect on the kind of information that is accessible

Membership Function

Step 1: Define Inputs and Outputs for the FLC.

Fig.7 Membership finction for Error

JOURNAL OF COMPUTER SCIENCE AND ENGINEERING, ENGINEER VOLUME 8, ISSUE 1, JULY 2011

Membership Function

35

Membership Function

Fig.8 Membership Function for Change in error

Fig. 10.Rule Rule fired when ‘error’=0 and ‘changeinerror’=0

Fig.9 Membership Function for output pressure

Step 4 Create rule base A rule base is a set of rules that specifies how the plant will be controlled. The rule-base base of the fuzzy controller contains the linguistic variables, the membership memb functions associated with them, and all linguistic rules. The overall form of the linguistic rules is of the form If premise Then consequent (6)

Figure 10 shows the rule fired when the ‘error’ and ‘change in error’ values are equal zero. This figure shows how the inference mechanism combines the rules in the rule base and forms a single decision at a particular iinstant of time. Step 6: Infer the output contributed by each rule and defuzzify the aggregated fuzzy set to form the Crisp Output as shown in Figure 12.

Table 2 gives the 7x7 fuzzy rule base for a pressure process for inputs like Error and change in Error(CE) and output.

TABLE 2 FUZZY RULE TABLE ABLE FOR A PRESSURE PROCESS

Fig. 11 Simulation Block Diagram of FLC for a Pressure Process The defuzzification action is the final constituent of the fuzzy controller. Defuzzification functions on the implied fuzzy sets and combines their effects to deliver the most definite controller output which is also the plant input.

Linguistic rules are not exact. They are just abstract ideas about how decent control can be accomplished that could be inferred differently by different people. Step 5: Determine which rules fire The inference mechanism determines which rules are relevant to the current situation. In this step, the inference mechanism looks to combine the recommendations of all the rules and end with a single decision.

4.3 Simulation Results of Pressure Process under Fuzzy Logic Controller Using these steps and the rule base formation, the Fuzzy Logic Controller is modelled and simulated for the pre pressure process [6].Figure 12 shows the Closed loop response l of the pressure process which is being controlled by the Fuzzy Logic Controller for a set point changes from 42 to 49 Psi.

JOURNAL OF COMPUTER SCIENCE AND ENGINEERING, VOLUME 8, ISSUE 1, JULY 2011 36

Fig.12.Closed Loop Resonse of pressure process under FLC for a set point change of 42 psi to 49 psi

4.4 Performance Analysis of Pressure Process The performance characteristics help to judge the performance of any system. The Integral Square Error (ISE) and Integral Absolute Error (IAE) are therefore measured for the pressure process under PID controller and FLC. The Integral Square Error (ISE) is a measure of the system error through the entire time, i.e. from t = 0 to t = ∞. It is defined as [7]

Fig.14 Performance Measures of Pressure Process Under FLC

5 COMPARISON BETWEEN PID AND FLC This section compares the performances of the two controllers, namely, the IMC based PID and the FLC. The simulation results of the two controllers have been overlapped in figure 15 which helps decide the better controller.

∞

ISE = ∫ e 2 (t ) dt

(7) where e(t) = error signal The Integral Absolute Error (IAE), on the other hand, is a measure of average error over a certain time period, T, and is defined as: 0

IAE =

∫

T

0

e (t ) dt

(8) The ISE and IAE values are calculated for the set point change of 42-49 psi under both controllers and are shown in Figures 13 and 14.

Fig.15.Simulation results of IMC based PID and FLC for a Pressure Process

Table 3 summarizes the ISE, IAE,Settling time(ts),Peak time( tp) values for the two controllers. TABLE 3 PERFORMANCE ANALYSIS OF IMC BASED PID AND FLC FOR A SET POINT CHANGE OF 42-49 PSI

ISE IAE ts tp Fig.13 Performance Measures of Pressure Process Under IMC based PID Controller

IMC based PID controller 106.4 65.4 98 55

Fuzzy Logic Controller 64.75 51.9 27 26

The ISE and IAE values for the pressure process under Fuzzy Logic Controller for set point change of 42-49Psi are found to be smaller than for the IMC based PID controller. The settling time is also less for the Fuzzy Logic Controller.

JOURNAL OF COMPUTER SCIENCE AND ENGINEERING, VOLUME 8, ISSUE 1, JULY 2011 37

6 ROBUSTNESS ANALYSIS Robustness, in terms of controller design, refers to a range of parametric changes within which the controller functions in its usual behaviour. It is a key issue in the analysis and design of a control system [8],[9] and [10]. In this section, the values of the three transfer function parameters, namely, K (Process Gain), τ (Process Time Constant) and td (Dead-time) are changed for both the controllers to determine the robustness of both. Figure 16 shows the Fuzzy Logic Controller designed with a change in the K (Process Gain) value of the transfer function model. The numerator of the process is hence changed from 0.7 to 1.8 (60% change). Fig.18 Pressure Process Model withr IMC based PID Controller for 60% change in the value of Process Gain

Fig. 16.Pressure process model with FLC for 60% change in the value of Process Gain

The simulation result of the above model is shown in figure 17.

Fig. 19 Simulation results of Pressure Process for 60% Change in the value of Process Gain.

Similarly, the value of τ, process time constant, is changed from 1.515 to 2.424 which is a 60% increase for both the controllers. The FLC model with this change is shown in figure 20. Fig. 17.Simulation Results of Pressure process under FLC for 60% Change in the value ofProcess Gain

From the figure, it is clear that despite a 60% change in the Process Gain value of the process model, the controller is still able to bring the process to the desired set point. Figure 18 shows the PID Controller designed with the same change in the K (Process Gain) value of the transfer function model from 0.7 to 1.8 (60% change).Figure 19 gives the simulation results of pressure process for 60% change in process gain. It is observerd from figure 19 that the process becomes unstable for variations in process gain.

Fig. 20.Pressure process model using FLC for 60% change in the value of Process time constant

The simulation result of the above model is shown in figure 21.

JOURNAL OF COMPUTER SCIENCE AND ENGINEERING, VOLUME 8, ISSUE 1, JULY 2011 38

Fig. 24.Simulation Results of Pressure process under FLC with a 60% change in the value of dead-time Fig. 21. Simulation Results of Pressure process under FLC for 60% Change in the value of Process time constant

The same change in dead-time is simulated using the PID controller. The output for the same is shown in figure 25.

A 60% change in process time constant is introduced in the transfer function model of the pressure process and the effect of IMC based PID controller is analyzed as shown in figure 22.

Fig. 25 Simulation Results of Pressure process under PID controller for 60% Change in the value of dead-time Fig. 22.Pressure process model using PID controller for 60% change in the value of Process time constant

The simulation result of the above model is shown in figure 23.

Fig. 23.Simulation Results of Pressure process under PID controller for 60% change in the value of Process time constant

Now the value of td, Dead-time, is changed from 21.65 to 34.64 which is a 60% increase. The simulation result for the same using FLC is shown in figure 24.

7 CONCLUSION This paper describes the design and implementation of a fuzzy logic controller and IMC based PID Controller to control the pressure process. The proposed controller is simple in structure and it is proved to be effective in improving stability of the process. By using triangular membership functions, the fuzzy logic controller achieved better control results. The ISE and IAE values are smaller for the FLC as compared to the IMC based PID controller. The settling time is also less for the Fuzzy Logic Controller. By checking the robustness of the two controllers, fuzzy logic controller is seen to be better than the PID controller for a 60% change in the process parameters. Also the Fuzzy Logic Controller response settles down while the PID controller response does not.On the basis of these promising results, it is possible that a Fuzzy controller could also be used to stabilize the pressure process aand it gives better performance than the conventional controller.

JOURNAL OF COMPUTER SCIENCE AND ENGINEERING, VOLUME 8, ISSUE 1, JULY 2011 39

REFERENCES [1]

[2]

[3] [4]

N.Kanagaraj, P.Sivashanmugam and S.Paramasivam, “Fuzzy Coordinated PI Controller: Application to the Real-Time Pressure Control Process”, Advances in Fuzzy Systems,Hindawi Publishing Corporation,Volume 2008, doi:10.1155/2008/691808. I.A.Zadeh, “Outline of a new approach to the analysis of Complex systems and decision Processes”,IEEE Transactions on system,Man and Cybernetics,SMC3(1),p.no.28-44. Seborg, Edgar, and Mellichamp. Process Dynamics and Control. Singapore: John Wiley & Sons, 2004. A.Zheng,M.V.Kothari & M.Morari, ”Antiwindup Design for Internal Model Control”, International Journal of Control,60,10151024.

[5] Kevin M. Passino, Stephen Yurkovich. Fuzzy Control. Addison Wesley Longman, Menlo Park, CA, 1998. [6]

S.R.Vaishav, Z.J.Khan, “Design and performance of PID and Fuzzy Logic Controller with Smaller Rule Set for Higher Order System”, Proceedings of the World Congress on Engg and Computer Science , 2007. [7] Bequette, Wayne B. Process Control: Modelling, Design and Simulation. New Jersey: Prentice Hall PTR, 2003. [8] M.Suresh, G.J.Srinivasan& R.R.Hemamalini,”Integrated Fuzzy Logic Based Intelligent Control of three Tank system”Serbian Journal of Electrical Engineering, Vol.6, No.1, 2009,pp 1-14. [9] Han-Xiong Li, H.B.Gatland, “Conventional Fuzzy Control and its Enhancement”, IEEE Transactions, Vol.26,1996. [10] K.RamCharan, B.Amarendra Reddy and P.AnanthBabu,”SelfTuning of a Robust Fuzzy PI-PD Controller”, International Journal of Computer Applications,Volume 1-No.13,2010.

Dr.V.Kalaichelvi has completed her Ph.D in Instrumentation Engg, in the year 2007 at Annamalai University. She is presently working as Asst.Professor in the Department of Electronics and Instrumentation Engg, BITS PILANI, DUBAI CAMPUS. Her research interest includes Control systems, Process Control, Neural Networks and Fuzzy Logics. She has published several research papers in National and International conferences and Journals. Srijan Bhatnagar is a student of Electical& Electronics Engg department. He graduted in 2011 and received merit scholarships throughout his graduation.