Volume 118 No. 20 2018, 2015-2021 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu EMPIRICAL MODEL IDENTIFICATION AND PID CONTROLLER TUNING FOR A FLOW PROCESS 1 S. Meenatchi Sundaram, 2 Tathagata Dey 1 Associate Professor (Senior Scale), 2 Post Graduate Student, Department of Instrumentation and Control Engineering, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal 1 meena.sundar@manipal.edu Abstract: This paper focuses on empirical model identification of a flow control process with delay time and design an optimum PID controller by comparing different tuning techniques. The First order process with delay time (FOPDT) model of the flow control process is identified by Process reaction curve(prc) method and Two-point method. A set of PID tuning techniques namely Zigler-Nichols, Cohen-Coon, Chein-Hrons-Reswick, Wang-Juang-Chan, and AMIGO methods are considered in this work. The PID tuning methods are simulated in SIMULINK environment and the responses are compared in terms of rise time, overshoot, peak value and settling time. The optimum controller values are identified by comparing the responses. Keywords: AMIGO controller, Empirical model, Flow control, Process reaction, Two-point method, Tuning techniques. 1. Introduction The process of identifying a mathematical relationship between input and output variables of a system using experimental data is called empirical modeling. The most common open loop methods to find the empirical model are Process Reaction Curve (PRC), Two-point method and Statistical model identification. In Process Reaction Method, the process is subjected to a step input and the output response after steady state is obtained and plotted. From the plot, the dead time and slope will be calculated. Based on the formula as given in next section, the FOPDT model will be developed [1]. Two-point method is similar to PRC method, but here no need to draw the tangent line at point of inflection. This two are taken in such a way that, 28% of peak amplitude and 63% of peak amplitude. The statistical method uses a regression method to fit the experimental data and it is a closed form solution method which requires an algebraic equation with unknown parameters. Therefore, the transfer function representation must be converted in algebraic representation. Which makes a relationship between the present output and past input and output. Now, the flow control is very useful to petrochemical industry, chemical industry, power plant etc. So, it s very important work to control the flow of a plant. There are many process to control the flow of a process PID controller, Optimization technique, fuzzy controller etc. Here in this paper we designed the PID controller using different method like Zigler-Nichols method, Cohen- Coon method, Chein-Hrons-Reswick method, Wang- Juang-Chan, Approximate M-Constrained Integral Gain Optimization (AMIGO) method and simulated it to check the best response to find out suitable PID parameters to control the flow of the process. 2. Overview of Identification and PID Tuning Empirical Model Identification In process reaction curve (PRC) method as well as twopoint method, the graph provides a first order process with dead time (FOPDT) [1,2] as given in equation 1. θs Y ( s) K pe = (1) X ( s) τ s + 1 Where X(s) and Y(s) are denoting the input and output of the process. K p, and θ (or L) are representing the gain, time constant and dead time respectively. In PRC process, δ denotes the magnitude of set point change. Steady state change in output is represented by. The slope, gain, and time constant can be given as in equation (2) y S = K p = τ = (2) x δ s Where, θ =Intercept of maximum slope with initial value. For two point method, those two points are selected in such a way that 28% and 63% of the value. It can be written as,p1= 0.23* and P2=0.63*. Graph provides the corresponding time t 1 and t 2 for P1 and P2 respectively. Using this method those parameters values are given below; τ = 1.5( t2 t1) θ = t2 τ (3) 2015
A. Controller and PID Tuning PID controller algorithm is widely used in industry to control the process variable like flow, level, temperature, pressure etc. The general equation of a PID controller is given below; K p t d y( t) = K pe( t) + e( t) dt K ( ) 0 ptd e t T + (4) i dt K p =Proportional Gain T i =Integral time constant= 1/K i T d =Derivative time constant= K d Here, e(t) represents the error signal, which is difference between the reference signal u(t) and output signal y(t). Different tuning techniques used in this work are briefed below. i. Ziegler-Nichols Method: iii. Chien-Hrones-Reswick Method: This method of tuning was developed from the Ziegler- Nichols open loop method for better performance of response speed and overshoot. The quickest aperiodic response is labeled with 0% overshoot and the quickest oscillatory process is labeled with 20% overshoot [3]. iv. Wang Juang Chan Method: Based on the optimum ITAE criterion, the tuning algorithm proposed by Wang, Juang, and Chan is a simple and efficient method for selecting the PID parameters. If the K p, θ, parameters of the plant model are known, the controller gives a suitable response [4]. v. AMIGO Method: In this open loop method, the controller parameters are calculated based on the parameters of K p, θ and τ of the process reaction curve. In closed loop method, the controller parameters are calculated based on the ultimate gain Ku and ultimate period Tu [3]. ii. Cohen-Coon Method: Cohen and Coon design method is the second popular method after Ziegler Nichols method. This method is similar to the Ziegler Nichols reaction curve method in that it makes of the FOPDT model to develop the tuning parameters. The controller settings are and based on the three parameters K p, θ, and τ of the open loop step response [3]. Table 1. Formulas of Different Tuning Techniques The issue of modifying PID controllers keeping in mind the end goal to limit the effect of unsettling influences in SISO frameworks has been tended to in various different considers. Astromand Hagglund (2004) are proposed an inexact technique that fulfills this objective essentially. The method, which is named as AMIGO (Approximate M-constrained Integral Gain Optimization), consists in applying a set of equations to calculate the parameters of the controller as like as Zigler-Nichols method [5]. The formulas used for the above said methods are listed in table 1. 2016
3. Plant Study and Observation The schematic diagram and the flow control process are shown in in figure 1. Figure 1. Schematic Diagram of Flow Control Process and Hardware Setup The process setup consists of supply water tank fitted with pump for water circulation. A Differential Pressure transmitter is used for flow sensing which measures differential pressure across orifice meter. The process parameter (flow) is controlled by microprocessor based digital indicating controller which manipulates pneumatic control valve through I/P converter. The control valve is fitted in water flow line. These units along with necessary piping are fitted on support housing designed for tabletop mounting. The controller can be connected to computer through USB port for monitoring the process in SCADA mode [6]. A. Plant Model Identification The hardware setup is put into manual mode and allowed to stabilized for initial controller output. A step change in terms of controller output of 25% is given and the response is plotted as shown in figure 2. Table 2. Model parameters using PRC Method Figure 2. Step Response of the Flow Control Process Using PRC method the model is identified and the open loop response parameters are listed in table 2. Slope (S) 15 Rise Time 9.9538 sec. Magnitude of set point change (δ ) 25 Settling Time 17.8226 sec. Steady state change in output( ) 68 Overshoot 0 K p 2.78 Peak 2.7182 Time constant (τ ) 4.53 Peak time 33.1697 Sec. Time delay (θ or L) 0.1 Amplitude Obtained from MATLAB Amplitude of the FOPDT model 90 80 70 60 50 40 30 20 10 0 0 20 40 60 80 2.72 25*2.72=68 2017
FOPDT model using PRC method of Using two-point method the model is identified identification is given in equation (5). and the open loop response parameters are listed in 0.1s 2.72e table 3. (5) 4.53s + 1 Table 3. Model parameters using Two-point Method 28 % point (P 1 ) 19.04 Rise Time 5.6034 sec. 63% point (P2) 42.84 Settling Time 10.5263 sec. Time t 1 46.5 Overshoot 0 Time t 2 48.5 Peak 2.72 τ 2.55 Peak time 21.0203 Sec. θ or L 0.55 Amplitude Obtained from 2.72 MATLAB K p 2.72 Amplitude of the FOPDT model 25 * 2.72 =68 FOPDT model using Two Point method of identification is given in equation (6) 0.55s 2.72e (6) 2.55s + 1 Step information of the modelsare shown in figure 3. Figure 3. Step response of models using (i) PRC Method (ii) Two-point method 4. PID Controller Design The PID controller design is carried out for the tuning techniques discussed above and the values of both the models are given in table 4. Table 4. PID Tuning Parameters Using PRC and Two-Point Method Methods PRC Method Two-point method Kp T i T d Kp T i T d Ziegler-Nichols 20 0.2 0.05 2.045 1.1 0.275 Choen-Coon 22.298 0.2438 0.0362 2.365 1.24 0.3842 Chein-Hrones-Reswick 10 4.53 0.05 1.023 2.55 0.275 Wang-Juang-Chan 9 4.58 0.049 0.911 2.825 0.248 AMIGO 20.585 6.625 0.05 2.286 2.807 0.258 2018
The response of the above PID values are analyzed in Simulink and the results are discussed in next section. 5. Results and Conclusion A detailed study has been done on the response analysis of the above said methods are the responses are given in figure 4 and 5 for PRC method and two-point method respectively. The parametric values in terms of rise time, over shoot, peak value and settling time are listed in table 5 for both the models. To summarize the work, the empirical model identification of the flow process was carried out using PRC method and Twopoint method and the FOPDT model were obtained. Different tuning techniques like Ziegler-Nichols, Cohen-coon, Chien-Hrons-Reswick, Wang-Juang-Chan and AMIGO method are used to design the PID values. It is observed that using PRC method FOPDT model, Cohen-Coon method of tuning provides the best response among others but in this method the overshoot is also higher than other methods. WJC method and CHR method provides less overshoot. ZN method and AMIGO are also providing a moderate response. In case of two-point method, Chein-Hrones- Reswick tuning method gives a better response compared to other tuning methods. Ziegler-Nichols, Cohen-Coon & Wang-Juang-Chan Methods shows a moderate settling time and rise time. In AMIGO method, since the rise time is less but the settling time is very high compare to others. Figure 4. PID response for PRC Model Table 5. PID Tuning Parameters Using Two-Point Method PRC Method Two-point method PID Tuning Method Rise Overshoot Peak Settling Rise Overshoot Time(sec) Peak Settling Time(sec) (%) Time(sec) Time(sec) ZN Method 0.0666 67.58 1.6759 1.8349 0.2905 46.7702 1.4677 4.4105 Cohen- Coon CHR Method WJC Method AMIGO Tuning 0.0599 80.3154 1.8032 3.0269 0.2081 69.95 1.6996 5.7299 0.152 5.9782 1.0598 NaN 1.3844 0.8550 1.0086 2.7451 0.1812 1.3725 1.0137 NaN 1.5775 0.9928 1.0099 3.1020 0.0653 67.01 1.6701 2.6849 0.2768 48.166 1.4817 10.3688 2019
Figure 5. PID response for Two Point Method Model References [1] Ljung,L.(1998), System identification. Englewood Chiffs,NJ:Prentice Hall,pp.69-115 [2] Marlin. E.T process control-designing processes and control system for dynamic performance. Ontario: McGraw-Hill, pp.175-206 [3] Derek P., Dingyu X. &YangQuan C.(2007). Linear feedback control.philadelphia: Society For Industrial & Applied Mathematics,pp.183-235 [4] N.Gireesh, Dr. G. Sreenivasulu, Comparison of PI controller performances for a conical tank process using different tuning methods, International Conference on Advances in Electrical Engineering (ICAEE),2014 [5] L.Eriksson, T.Oksanen,K.Mikkola, PID controller tuning rules for integrating processes with varying time-delays, Journal of Franklin Institute,Elsevier,vol.346,No.5,pp.470-487,2009. [6] Apex Process Trainers - Product Code 302, User Manual. [7] S.V.Manikanthan and V.Rama Optimal Performance of Key Predistribution Protocol In Wireless Sensor Networks International Innovative Research Journal of Engineering and Technology,ISSN NO: 2456-1983,Vol-2,Issue Special March 2017. [8] T. Padmapriya and V. Saminadan, Inter-cell Load Balancing Technique for Multi- class Traffic in MIMO - LTE - A Networks, International Conference on Advanced Computer Science and Information Technology, Singapore, vol.3, no.8, July 2015. 2020
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