# MODELING AND ANALYSIS OF NON LINEAR CONICAL TANK

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2014 IJIRT Volume 1 Issue 10 ISSN: 2349-6002MODELING AND ANALYSIS OF NON LINEARCONICAL TANK PROCESSJ. Nancy Amala Geetha, G. Subramanian, V. GokulU.G. student, Department of Instrumentation and Control,Saranathan College of Engineering, TrichyAbstract- This paper deals with the differenttuning of PID (Proportional Integral Derivative)controller for a complex nonlinear process suchthat conical tank process. The conical process issuch a difficult problem due to its nonlinearperformance and continuously changing crosssectional area[3]. The difficulty faced in thatprocess is overcome by different type of tuningtechniques. To obtain a optimization process thethese are the techniques used FOPDT, [2]tuningtechniques and IMC controller.Index Terms- FOPDT, PID CONTROLLER,TUNING TECHNIQUEI.INTRODUCTIONIt is important to maintain the level of the tank invarious fields. It mostly in process industries. Thevariation in the level by variable process parameters.It is adjusted and governs by PID controller andvarious tuning techniques [4]. By using thistechniques the conical tank process to achieveoptimization control. The PID controller offers theflexibility to achieve the ultimate limit to loopperformance of industrial processes [1]. A PIDcontroller has historically been considered to be thebest controller.PID controller is a control loop feedback mechanismwidely used in process control systems. A PIDcontroller calculates an error value as the differencebetween a measured process variable and desired setpoint. [1]The controller attempts to minimize theerror by adjusting the process through use of amanipulated variable. A common characteristic ofproportional control is an error between the set pointand control point which is referred todroop(or)offset.[4]IJIRT 101540Fig.1BasicprocessdiagramThe general form of PID controller equationis,The offset is an undesired characteristic ofproportional only and is easily eliminated by addingintegral action. The integral adjusts controllers inaccordance with both the size of the deviation fromset point and the time it lasts [2].Derivative control isa prediction of future errors based on current rate ofchange. The sum of these actions is used to adjust theprocess via a control element such as the position of acontrol valve a damper or the power supplied to aheating element. Among the well-known methods aremodified ZN method(MZN), damped oscillationmethod(DOSC),internal model control(IMC) andISE,ITAE,IAE error performance approach.[5]II.MATHEMATICAL MODELLING OF ACONICAL TANKThe nonlinear process of conical tank used in variousprocess industries. These are concrete mixingindustry, food processing industry, metallurgicalindustry or in various field. The process ofdeveloping the mathematical model by usingconsideration of process parameters is knownmathematical modeling. Based on the input flow oftank and output flow rate through various crossINTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY156

2014 IJIRT Volume 1 Issue 10 ISSN: 2349-6002section area with respect to time. Based on twoconsideration the input flow is a manipulatedvariable.And level of conical tank is a controlvariable[3]. This can be achieved by controlling theinput flow of the conical tank.RFinFig2. Schematic diagram of conical tankProcess operating Parameters are,Fin – Input flow rate of the tankF out – Output flow rate of the tankH - Total height of the conical tank.R - Top radius of the conical tankh - Nominal level of the tankr - Radius at nominal levelFig3. Mathematical modeling of a conical tankThe area of the conical tank is given by(3.1)IJIRT 101540INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY157

2014 IJIRT Volume 1 Issue 10 ISSN: 2349-6002(3.2)(3.3)According to Law of conservation of mass,Inflow rate-Outflow rate Rate of Accumulation(3.4)(3.5)K is the discharge coefficientOn substituting (4.5) in (4.4), we get(3.6)(3.7)Rate of Change of HeightTherefore,(3.8)Substituting the value of A in equation (8), we get(3.9)H(s)/ Fout (s) k e-θs/τ s 1 ------------- (3.10)Where, τ 2A (h)/bK 2 (h)/bBased on specification given by the transfer function is,G(S) 7.14 e-11.10s / (4.69S 1) ---- (3.11) III.TUNING METHODSFor this paper we used 3 different types oftuning techniques they are,Damped oscillation methodModified ZN methodInternal model control (Improve PI)IJIRT 101540DAMPED OSCILLATION METHOD:In many cases, plants are not allowed to undergothrough sustained oscillations, as is the case fortuning using continuous cycling method. Dampedoscillation method is preferred for these cases. Here,initially the closed loop system is operated initiallywith low gain proportional control mode with deadINTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY158

2014 IJIRT Volume 1 Issue 10 ISSN: 2349-6002thtime is zero. The gain is increased slowly till a decayK be the proportional gain setting for obtaining 1/4thdratio (p /p ) of 1/4 is obtained in the step response in2decay ratio. [1]1the output, as shown in Fig. 5. Under this condition,the period of damped oscillation, T is also noted. LetdThe optimum settings for a P-I-D controller are:(Table 1)CONTROLLERPIDKC1.1GdKIPd/3.6KDPd/9MODIFIED ZN METHOD:In some of control loops the measure ofoscillation, provide by ¼ decay ratio and corresponding to large overshootsfor setpoint changes are undesirable thereforemore conservative methods are oftenpreferable such as modified Z-N.These modified settings that are shown inTable 2 are some overshoot and no overshoot.[4]The optimum controller settings are:(Table 2)CONTROLLERKCSome overshoot0.33KcuNo overshoot0.2KcKIPu/2Pu/2KDPu/3Pu/3INTERNAL MODEL CONTROL:The Internal Model Control (IMC) method was developed with robustness in mind. The Ziegler-Nichols open loopand Cohen-Coon methods give large controller gain and short integral time, which isn't conducive to chemicalengineering applications. The IMC method relates to closed-loop control and doesn't have overshooting oroscillatory behavior. The IMC methods however are very complicated for systems with first order dead time. In thiswe chose the 87 for the optimum control.[4]The optimum controller settings are:(Table 3)CONTROLLERKCKIImprove PI(2 d)/ 2 IV.KDd/2-Recommended / d( 0.2 always) 1.7PERFORMANCE CRITERIA FOR CONICAL TANK: (Table 4)TechniquesDampedoscillationmethodModified ZNmethodInternal modelcontrolRise time0.441Settling time26Overshoot195Peak time8.7731.733.61.713.695.8745.323.51.24IJIRT 101540INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY159

2014 IJIRT Volume 1 Issue 10 ISSN: 2349-6002TechniquesDamped oscillationmethodModified ZN methodInternal model controlV.ERROR PERFORMANCE CRITERIA:(Table .629VI.VII.SIMULATION GRAPH:CONCLUSIONIn this paper the PID controller by using threedifferent type of tuning techniques arediscussed. For better optimum control we chose theIMC (Improve PI) but it has over high over shootthan the modified ZN tuning method and it hassettling time also high. So in my point of view for thenonlinear conical tank the best tuning method ismodified ZN method it has low settling time and lowovershoot as compare to IMC tuning method anddamped oscillation method and then it also has lowerror criteria performance. So the Modified ZNmethod gives the better and optimum control.IJIRT 101540REFERANCES[1] Process Control (Principles and Applications) BySurekhaBhanot[2] K. Ogata: ―Modern Control Engineering,Prentice-Hall India,Fourth Edition[3] P. W .Mur rill, P. D. Schnelle, B. G. Liptak, J.Gerry, M. Ruel, F. G. Shin sky, Tuning PIDController.[4] Lee J., W. Cho; ”An Improved Technique for PIDController Tuning from Closed LoopTests”, AI Chef J, 36, 1891(1990)[5] Luyben W.L, M.L. Luyben; “Essentials ofProcess Control”, McGraw-Hill, 1997INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY160

2014 IJIRT Volume 1 Issue 10 ISSN: 2349-6002[6] Erickson K.T., J.L. Hedrick; “Plant wide ProcessControl” John Wiley & Sons, 1999[7] G. K. I. Mann, B. G. Hu, and R. G. Gosine,―Time-domain baseddesign and analysis of newPID tuning rules, Proc. Inst. Elect. Eng.—ControlTheory and Applications, vol. 148, no. 3, pp. 251–261, 2001.[8] J. Nagrath, M. Gopal, ―Control SystemEngineering, New Age International Publications, 3rdEdition, 2002IJIRT 101540INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY161

Fin – Input flow rate of the tank F out – Output flow rate of the tank H - Total height of the conical tank. R - Top radius of the conical tank h - Nominal level of the tank r - Radius at nominal level Fig3. Mathematical modeling of a conical tank The area of the conical tank is given by (3.1) R

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