Sensors & Transducers 2015 by IFSA Publishing, S. L.

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1 Sensors & Transducers 2015 by IFSA Publishing, S. L. Real Time Control of Non-Linear Conical Tank Sitanshu SATPATHY, Prabhu RAMANATHAN School of Electrical Engineering, VIT University, Vellore , Tamil Nadu, India Tel.: Received: 14 January 2015 /Accepted: 27 February 2015 /Published: 31 March 2015 Abstract: In this paper a real time control of non-linear conical tank has been performed. In this article control comparison between fuzzy controller and conventional PI controller is made for the conical tank system. Conical tank is used in most of the industrial processes because it assures optimal stirring and mixing of ingredient. The tank can easily and quickly be emptied and also conical shape ensures efficient cleaning, better mixing and drainage of solid wastes, slurries, thick liquids etc. Moreover these tanks can be used for both boiling as well as extraction process. Controlling the liquid level and flow of liquid in conical tank is a complex process because of the nonlinearity and constantly changing cross section of the tank. A conventional PI (proportional-integral) controller and MISO (multiple input single output) fuzzy controller was used and their performance is compared. Copyright 2015 IFSA Publishing, S. L. Keywords: Non-linear process, Conical tank, PI controller, Fuzzy controller, LabVIEW control design and simulation toolbox, Fuzzification. 1. Introduction Process industries face a major problem in the form of controlling the level of liquid in the conical tanks used in their processes [1, 2]. Controlling of liquid level in a conical tank becomes a challenging problem because of its non-linearity and continuously changing cross section. In industries the liquid has to be pumped in and out of the tank, it has to be transferred to different systems and at the same time a well-defined accurate level of liquid has to be maintained in the tank and its flow should be controlled. Conical tanks are widely used in process industries like food industries, waste water treatment industries, chemical process plants and many other production processes. The liquid level in various chemical processes has to be accurately controlled as it may affect the equilibrium of chemical reactions which would ultimately affect the production process. Because of these reasons process industries are in need of a robust and high performance controller. This paper endeavours to design two controllers, viz., a PI controller and a fuzzy controller and compare their performance. A PI controller is a part of feedback control loop mechanism used in large number of industrial process control systems. It is a solution to almost all control loop problems [3-5]. An error value is calculated by subtracting the process variable from the set point. The main aim of the controller is to reduce the error to zero. This is obtained by tuning the controller by changing the proportional and the integral constants namely K P and K I respectively. PI controller becomes inefficient when the system becomes highly complex or is poorly understood as in [3] and in these conditions fuzzy controller is used [6-11]. A fuzzy controller makes use of human understood crisp variables [12]. These variables are 148

2 then mapped into membership functions and depending upon the number of input and output variables, the desired process rules are formed [13]. The resultant output is then defuzzified and fed into the control device. The selection of membership functions is the major difficulty in this type of controllers. Fuzzy controllers are being extensively used in various industrial processes [14]. Thus fuzzy expert systems make use of fuzzy data, fuzzy logic with rules and membership functions as the basic knowledge base of the system [15-17]. These don t make use of any mathematical model and can be easily controlled [18]. Multivariable fuzzy controllers have also been easily implemented in various processes [19, 20] though simpler approaches are generally preferred. 2. Conical Tank Level System A conical tank system consists of a non-linear conical tank in which the level of the liquid is controlled: F in Inflow (cm 3 /sec); F out Outflow (cm 3 /sec); R Radius of the tank (cm); r Radius of water level (cm); H Height of the tank (cm); h Height of the water in the tank (cm); b Valve coefficient ( cm 2 /sec); Angle between central line joining the two openings and slant height (degree); Here the controlled variable is level (h) and manipulated variable is the inflow of the liquid (F in ). The structure of the tank is given in Fig. 1. Now, tan Using (3) in (1) we get (2) (3) (4) Now, according to law of conservation of mass Accumulation = inflow rate outflow rate F in - F out, (5) where is the rate of change of level with respect to time. Substituting (6) in (5) F out = (6) F in (7) (F in - ) /A (8) Substituting the value of A found in (4) in (8) we get ((F in / / (9) Now on integrating (9) mathematical model of the tank can be obtained. Thus it can be inferred from the above mathematical derivation that the conical tank introduces non-linearity due to changes in its area [21, 22] System Dynamics The setup used for the experiment is shown in Fig. 2. Fig. 1. Conical tank Mathematical Modelling Area of the tank A is (1) Fig. 2. Prototype of the conical tank used. 149

3 Height (h) is measured using differential pressure transducer whose output is in the form of 4-20 ma current signals. Control valves fitted with positioners act as the actuating element which takes 4-20 ma as input signal. This current signal is converted into 0-5 V using I/V converter and further interfaced with PC using NI USB DAQ hardware. NI LabVIEW software is used for programming and as a man machine interface [23]. The specification of the conical tank is summarized in Table 1. Table 1. System specifications of the conical tank. Material Upper diameter Bottom diameter Height Thickness 3. Real Time Control SS316 (stainless steel grade) 400 mm 150 mm 600 mm 2 mm 3.1. Implementation of PI Controller Controllers designed in this article are implemented in LabVIEW using Control Design and Simulation toolbox. The K P and K I parameters used are specified in Table 2. The block diagram of the PI controller implemented is shown in Fig. 3. Table 2. KP and KI parameters of the PI Controller. Set point KP KI Implementation of Fuzzy Controller Fuzzy controller used has two input variables and one output variable. Error and change in error as the input variables and output to the valve as the output variable. For fuzzification, triangular membership functions were used for both the input and output variables with seven fuzzy sets. Membership functions used in one of the variables is shown in Fig. 4. Fuzzy sets used are defined by variables negative large (NL), negative medium (NM), negative small (NS), zero (Z), positive small (PS), positive medium (PM) and positive large (PL). The rule base used in the system is shown in Table 3, and input and output scaling factors in Table 4. The rule base is referred from [24, 25]. To improve its performance, controller is tuned with input and output scaling factors. These are one of the most important factors affecting the system performance [26-28]. Input-output relationship is shown in Fig. 5. Centre of gravity method is used for defuzzification, as there is no loss of information in it [29]. The block diagram of the controller is shown in Fig. 6. Fig. 3. PI controller implemented in LabVIEW. 150

4 Table 4. Input and output scaling factors. Variable Scaling factor Error 5 Change in error 5 Output 5 Fig. 4. The input membership function of the fuzzy controller. Table 3. The rule base used in the MISO fuzzy controller used. E e PL PM PS Z NS NM NL NL Z NS NM NL NL NL NL NM PS Z NS NM NL NL NL NS PM PS Z NS NM NL NL Z PL PM PS Z NS NM NL PS PL PL PM PS Z NS NM PM PL PL PL PM PS Z NS PL PL PL PL PL PM PS Z Fig. 5. Input output relationship of the fuzzy system. Fig. 6. Fuzzy controller implemented in LabVIEW. 4. Results and Comparison Real time implementation of PI and Fuzzy controllers was done in LabVIEW environment. Performances of these controllers were compared on the basis of rise time, settling time, steady state error and overshoot. From the graph shown in Fig. 7 and Table 5 it can be observed that the implemented fuzzy controller has a better transient time response than the conventional PI controller used. Fuzzy controller s rise time and settling time is better than PI whereas PI controller s response is very slow and takes comparatively large time to settle. Zero steady state error in case of fuzzy controller is attained much faster as compared to the PI controller. There is no overshoot in case of both the controllers. 151

5 Fig. 7. Transient response of the PI and The fuzzy controller. Table 5. Some of the points in the performance graph of PI and Fuzzy controller. Instance PI Fuzzy Set Point Conclusion The non-linear conical tank is controlled using fuzzy and PI controller. It is found that the performance of the Fuzzy controller is better than the PI controller. Fuzzy controller gave zero steady state error and also had better settling time whereas the PI has very slow response. Conical tanks are required in most of the industrial processes and use of fuzzy controller provides an efficient control of the process. Fuzzy controller doesn t require a system transfer function, rules are easy to frame and also has a better performance in case of complex industrial processes. Thus fuzzy controller can be used as an alternative to PI controllers for controlling non-linear tanks [30]. The controlled and stable operation of non-linear processes such as conical tank attracts lots of researches, increasing its scope more and more. LabVIEW provides the most comprehensive approach for virtual instrumentation. This approach finds use in applications such as biomedical, communication, energy, automation, and many others. It can be easily used for designing, testing and prototyping new technology. LabVIEW ignores the hardware issues and low-level programming and mainly focuses on designing algorithms, data flow charts, modelling, and so on. Some key benefits of LabVIEW include ease of implementation, faster results and designing, using various embedded technology, data acquisition etc. Data acquisition is most important aspect of gathering and generating information. LabVIEW provides a large set of data acquisition devices. Thus virtual instrumentation platform provided by LabVIEW is a powerful and flexible tool for various scientific researches. Acknowledgements The authors would like to thank Vellore Institute of Technology, Vellore for providing facilities required to conduct this research. References [1]. N. S. Bhubaneswari, G. Uma, T. R Rangaswamy, Adaptive and optimal control of a non-linear process using intelligent controllers, Applied Soft Computing, 9, 2009, pp [2]. Rajni Jain, N. Sivakumaran, T. K. Radhakrishnan, Design of self-tuning fuzzy controllers for nonlinear systems, Expert Systems with Applications, 38, 2011, pp [3]. Astrom, K. J., Wittenmark, B., Adaptive control (2 nd ed.). Boston, MA, USA, Addison-Wesley Longman Publishing Co., Inc, [4]. Haddad, W., Chellaboina, V., Nonlinear dynamical systems and control: A lyapunov-based approach. Princeton University Press, [5]. Sastry, S., Bodson, M., Adaptive control: Stability, convergence and robustness. Dover books on electrical engineering series, Dover Publications, [6]. Mamdani, E. H., Twenty years of fuzzy control: Experiences gained and lessons learnt, in Proceedings of the 2 nd IEEE International Conference on Fuzzy Systems, pp , San Francisco, CA,

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