CONTROLLER TUNING FOR NONLINEAR HOPPER PROCESS TANK A REAL TIME ANALYSIS

Journal of Engineering Science and Technology EURECA 2013 Special Issue August (2014) 59-67 School of Engineering, Taylor s University CONTROLLER TUNING FOR NONLINEAR HOPPER PROCESS TANK A REAL TIME ANALYSIS SURESH MANIC KESAVAN*, TVN PADMESH, CHAN WOEI SHYAN CIARG, School of Engineering, Taylor s University, 47500 Subang Jaya, Selangor DE, Malaysia *Corresponding author: SureshManic.Kesavan@taylors.edu.my Abstract In this work, Proportional + Integral + Derivative (PID) controller design and real time implementation was proposed for a nonlinear hopper tank system in order to solve servo and regulatory problem. Firstly, identification of process transfer function is done through the real time implementation experiment and it is applied to a conventional PID controller. Then tuning methods has been proposed including Cohen-coon (CC), Ziegler & Nichols (ZN), Internal Model Control (IMC) and Tyreus & Luyben (TL). The optimization of tuning parameter is taken up with Integral Square Error (ISE), Integral Absolute Error (IAE) and Integral Time Absolute Error (ITAE). The experimental results show that TL and ZN tuning method are suitable in controlling nonlinear hopper level tank system. Keywords: Nonlinear process, PID controller, Hopper liquid level tank, Tuning method. 1. Introduction In many process industries (petrochemical industries, paper making industries, water treatment industries, etc.) the main issue is to control the level and flow between the tanks. Since many industries involves batch process, it is necessary to control the first process parameter like liquid level or flow, failing to do so may lead to serious shutdown process. So it is necessary to maintain the level of tank at particular set point. Most of the industries deal with nonlinear process tanks such as conical, spherical, hopper type tanks. But the majority of the findings in control theory deal only with the linear system designs. So the control of nonlinear shape of process tank presents a challenging task mainly due to its non-linearity and constantly changing cross section. Hence, the hopper type tank process is taken up for present study. 59

60 Suresh Manic et.al. Nomenclatures A Cross sectional area of hopper tank, cm 2 F in Liquid inflow to hopper tank, cm 3 /s F out Liquid outflow from hopper tank, cm 3 /s h Instantaneous height of conical portion, cm H Total height of conical portion, cm k Process gain r Radius of conical tank, m R Radius of cylindrical tank, cm Greek Symbols θ Delay time, s τ Time constant Abbreviations IAE ISE ITAE PID Integral absolute error Integral square error Integral time absolute error Proportional integral derivative Conventional PID controllers are been proved to best controllers for linear type of processes. But for non-linear control systems, the controller parameters have to monitor continuously for the changes in the process. Many research works has been done for controlling nonlinear systems like conical tank [1] and spherical tank [2]. Anandanatarajan et al. 2006 [3] studied about two different controllers at two different operating points using fuzzy logic controller for a conical tank. PID controller limitations of controlling conical tank have been studied by Lee and Sung [4]. Design of fuzzy controller for conical process tank was studied by Madhubala et al. [5] on tuning the membership functions of the input variables and optimized the peak of the fuzzy sets using genetic algorithm. The result shows that the proposed method is a trial and error method and time consuming. On the other hand, the soft computing based controller like Fuzzy logic Controller (FLC) and Genetic Algorithm (GA) has been proven out performs well than the conventional controller [6]. Anandanatarajan et al. [7] studied on the problem of Zhao s Fuzzy PI which worked properly for servo but failed to regulatory problems. In addition, modified Zhao s Fuzzy PI in regulatory changes is proposed and is compared to conventional control method as well Zhao s Fuzzy PI. Araki [8] presented PID controller including process models, performance evaluation of PID control system, action modes of PID controllers, and design of PID control system on conical tank. Only limited number of research work has been carried out for nonlinear hopper type process tanks. Therefore our research work focused on hopper tank process designing a suitable controller (PID) and comparing results with Internal Model Control (IMC), and Tryeus and Luyben (TL) tuning rules. The error analyses are compared with IAE, ISE and ITAE. The paper is organized as follows. In Section 2, the process and the lab scale experimental hardware set-up are described. In Section 3, simulation studies and real-time conventional control

Real Time Study on Controller Tuning for Nonlinear Hopper Process Tank 61 are discussed. In Section 4, optimization using error analysis tools are discussed. In Section 5, Real time results are compared with simulation results and discussed. Finally, results and conclusions are discussed. 2. Process Description The design for the research work is constructed as a prototype of the non-linear hopper process tank with the conical and cylindrical portion situated at School of Engineering; Taylor s University, Malaysia. The experimental model is to be used to maintain the level of liquid at a desired constant value. This is achieved by controlling the inflow of liquid into tank. A disturbance in the form of set point change is introduced into the system during normal operating conditions. The geometrical cross section of process tank is shown in Fig. 1. The inflow and outflow rates are measured using suitable level sensors. Fig. 1. Geometrical Cross-Section of the Process Tank. 2.1. Lab scale experimental setup Figure 2 shows the fabricated set up of process tank. The experimental set-up, Fig. 3, consists of conical section at the bottom and cylindrical section at the top open to the atmosphere. The setup also consists of centrifugal pump, level sensor arrangement, inlet and outlet valve, air pump, air regulator, IP converter, Pressure gauge, interfacing card, level indicator and PID controller. The height of the conical and cylindrical portion of the tank is 50 cm each. The centrifugal pump is capable of discharging liquid at the rate of 3500 L/h is used and a PVC pipe is used to connect the pump and the control valve. The minimum voltage applied to the pump for discharge is 104 V. 2.2. Process modeling The process transfer function is obtained in terms of the process characteristics namely the process gain and the process time constant.

62 Suresh Manic et.al. Fig. 2. Fabricated Set-up of the Process Tank. Fig. 3. Experimental Set-up. The mass balance equation governing the system dynamics is given by Eqs. (1) and (2) [9] (1) (2) where A = R 2, F in is inflow rate of the tank, 125 cm 3 /s, F out is the outflow rate of the tank cm 3 /s, R is the top radius of the conical tank, 20 cm, H is the total height of the tank, 100 cm, and r is the radius at any height h i = 20 cm. The transfer function relating the height h and the inflow rate F in with parameters (k, τ) can be obtained as Eq. (3) ( ) ( ) ( ) ( ) (3) where The nominal transfer function is shown in Eq. (4) ( ) ( ) where k 0 and τ 0 are evaluated at a nominal height h 0. From the system identification, process parameters of different operating regions are obtained (Table 1). The process tank is divided into four (I-IV). It is evident from Table 1, when the level of the tank raises the process gain and delay time decreases because of accumulation of integral error. Table 1. Process Parameters at Different Valve Opening. Inflow Range Level range % (cm 3 /s) (cm) k 0 τ 0 (s) θ 40 (I Region) 0-15 2.70 0.75 0.15 60 (II Region) 15-30 0.68 1.50 0.70 80 (III Region) 30-40 0.18 0.78 0.22 100 (IV Region) 40-50 0.09 0.30 0.30 (4)

Real Time Study on Controller Tuning for Nonlinear Hopper Process Tank 63 2.3. Controller identification Identified four PID controller tunings methods are as follows: Cohen-Coon (C-C) Ziegler and Nichols (Z-N) Internal Model Control (IMC) Tryeus and Luyben (1997) (TL) Tuning technique, C-C can be fit to a first order process with dead time model with the advantages that the procedure does not involve trial and error with only a single experiment is necessary [9]. As for ZN method is one of the popular methods among others in tuning PID controllers. The controller settings are easily calculated and a process model is not necessary [10]. For IMC tuning method, it involves lamda tuning (λ) which is obtained by trial and error. At last TL method is an alternative method for ZN, with modified formulas for the controller parameter that provide better performance. 3. Simulation Block diagram shown in Fig. 4 for the hopper tank process system was created by using MATLAB Simulink software. The system simulation response is analysed for 40% to 100% valve opening. Fig. 4. Simulink Block Diagram for Nonlinear Hopper Process Tank. 4. Criteria of Error Integral Analysis The best performance of the controller was selected by using three different tuning criteria IAE, ISE and ITAE. Each of this error integral is a form of penalty function representing the size and duration of error [11]. Table 2 gives the details of the tuning methods that aim to minimize the penalty Table 2. Integral Criteria for Load Changes of PID Tunings. 5. Results and Discussion Error Integral ISE IAE ITAE a 1 1.495 1.435 1.357 b 1-0.945-0.921 0.947 a 2 1.101 0.878 0.842 b 2 0.771 0.749 0.738 a 3 0.560 0.482 0.381 b 3 1.006 1.137 0.995 The hopper tank process includes controller tuning settings using C-C, Z-N, IMC and LT methods. These tuning method results were compared by means of MATLAB Simulink software. The performance of the controller is compared on the time domain specification like rise time, settling time and overshoot.

64 Suresh Manic et.al. 5.1. Performance analysis based on simulation results Results are simulated for CC, IMC, ZN and TL methods and discussed in this section. Four regions of step input have been analysed and observed from 40% valve opening to 100% valve opening from 20% of initial liquid level. Figure 5 shows the simulated results of C-C tuning method. From the simulated results step response for 40% step input is better than 60%, 80% and 100% in terms of time domain specifications. In the simulation the process system behaved with a faster response with 2.25 seconds rise time and minimum offset of 0.005 cm as compared to others step changes. In addition, it had a minimum time delay, 2.13 seconds. Figure 6 shows the simulated results of IMC tuning method. From the simulated results step response for 60% step input is better than 40%, 80% and 100% in terms of time domain specifications. However, process responded with longest time delay among the others step changes, 2.7 seconds. For 40% step input, it gives an unsteady response with continually aggressive oscillation while the remaining step inputs have given a large offset value about 0.75 cm. Fig. 5. Simulated Response for C-C Tuning Method. Fig. 6. Simulated Response for IMC Tuning Method. Figure 7 shows the simulated results of ZN tuning method. From the simulated results step response for 40% step input is better than 60%, 80% and 100% in terms of time domain specifications. 60% step response also shows better results closer to 40% step change, but 40% step change has a fast response than 60% with a longer time in achieving steady state or the set point value. Figure 8 shows the simulated results of LT tuning method. From the simulated results step response for 40% step input is better than 60%, 80% and 100% in terms of time domain specifications with fast response and less delay time. 80% and 100% have shown an offset value more than 0.25 cm as well as slow response. As for 60% step input, it has an aggressive oscillation that persist for a long time. Fig. 7. Simulated Response for Z-N Tuning Method. Fig. 8. Simulated Response for L-T Tuning method.

Real Time Study on Controller Tuning for Nonlinear Hopper Process Tank 65 5.2. Performance analysis based on real time implementation The tuning rules of CC, IMC, ZN and TL from the simulation performance are implemented and analysed in real time hopper tank control system, Figs. 9 (a)-(d). Different set point had been set on each controller tuning settings which clearly showed that both CC and IMC tuning method had given an aggressive response in the real time implementation. The response gives an oscillation that persists over a long time and it does not reach steady state. (a) Cohen-Coon Method. (b) Ziegler-Nichols Method. (c) IMC Method (d) Tyreus-Luyben Method. Fig. 9. Real Time Responses with Different Methods. The performance of the ZN and TL are much better as compared to others tuning methods. By comparing ZN and TL tuning, it is observed that TL has lesser overshoot and faster time that track the set point changes than ZN tuning method. As over all, TL performs much significantly stable than ZN and others controller (CC, IMC). Indeed, it has shown oscillatory behaviour and exhibits lesser peak time as compared to Cohen Coon and IMC controller tuning, but it is completely different than simulated results as mentioned in previous section. This has been proven that Cohen Coon and IMC method does not fit well in controlling a closedloop control system of a real time hopper tank. Therefore both ZN and LY tuning method for 80% and 100% has been selected and tested for the further studies on comparison between simulated and real time experimental results. Comparison of performance response between ZN and TL tuning method based on ISE, IAE and ITAE is shown in Table 3. Table 3. Comparison of Performance Response between ZN and TL Methods. Tuning rules Zeigler Nichols Tyreus & Luyben Rise time (min) 10.4 10.1 Settling time (min) 10.2 9.5 Overshoot (cm) 18.8 17

66 Suresh Manic et.al. 5.3. Comparison of experimental and simulated results The tuning methods of ZN and TL have been chosen as a comparison between real time and experimental results of the hopper tank system for 80% step input by minimum error criterion of ISE, IAE and ITAE. The performances of ZN and TL tuning method based on error analysis are shown in Table 4 and it is evident that TL is better than ZN for 80% step input response. Table 4. Error Analysis for Different Tuning Methods at 80% Step Input. Method ISE IAE ITAE ZN (Ziegler & Nichols) 27.86 26.01 25.44 TL (Tyreus & Luyben) 21.38 20.55 19.67 For 80% step input, TL tuning has shown a similarity response with ZN tuning. From Figs. 10(a) and (b), it shows that both simulated and real time experimental responses eventually achieved the steady state or set-point of 10 cm. On the other hand, ZN does not reach the steady state although real time result has achieved it, at set-point of 7.5 cm. From this observation, both controllers have proven that at 80% step input for TL will be the suitable tuning method than ZN tuning method with set-point change and disturbance responses. (a) Tyreus-Luyben Method. (b) Ziegler-Nichols controller Method. Fig. 10. Comparison of 80% Step Input between Simulated and Real Time Response for Different Methods.

Real Time Study on Controller Tuning for Nonlinear Hopper Process Tank 67 6. Conclusions The control systems of a nonlinear hopper tank response vary with different types of tuning rules. In general from the simulated results as the step input increases, settling time increase with a larger offset value. However, in decreasing of step input there is more aggressive response behaviour that exhibits a high overshoot. The result between simulated and real time experimental will never be exactly similar due to human factor may occurs when running the process. Tuning method of TL in PID controller has given good and acceptable performance with less aggressive oscillation as well as fast settling response at 80% step input. Besides, it also shows good result for disturbance rejection with fast settling response. In addition, it has the minimum error integral value and followed by ZN method. This concludes TL method is most suitable for the chosen nonlinear hopper process tank based on error analysis. References 1. Bhuvaneswari, N.S.; Uma, G.; and Rangaswamy, T.R. (2009). Adaprive and optimal control of a non-linear process using intelligent controllers. Applied Soft Computing, 9(1), 182-190. 2. Kumar, D.D.; and Meenakshipriya, B. (2012). Design and implementation of nonlinear system using gain scheduled PI controller. Procedia Engineering, 38, 3105-3112. 3. Anandanatarajan, R.; Chidambaram, M.; and Jayasingh, T. (2006). Limitations of a PI controller for a first order non-linear process with dead time. Instrumentation Systems and Automation, 45(1), 185-200. 4. Sung, S.W.; and Lee, I.-B. (1996). Limitations and countermeasures of PID controllers. Industrial & Engineering Chemistry Research, 35(8), 2596-2610. 5. Madhubala, T.K.; Boopathy, M.; Sarat Chandra, J.; and Radhakrishnan, T.K. (2004). Development and tuning of fuzzy controller for a conical level system. Proceedings of the International Conference Intelligent Sensing and Information Processing, 450-455. 6. Nithya, S.; Sivakumaran, N.; Radhakrishnan, T.K.; and Anantharaman, N. (2010). Soft computing based controllers implementation for nonlinear process in real time. Proceedings of the World Congress on Engineering and Computer Science, Volume II, 264-268. 7. Anandanatarajan, R.; Chidambaram, M.; Jayasingh, T. (2004). Imporved design of FLC for a first order nonlinear process with dead time. Proceedings of International Conference on Intelligent Sensing and Information Processing, 466-471. 8. Araki, M. (2008). PID control. Encyclopedia of Life Support Systems (EOLSS), 2(1), 26. 9. Suresh, K.; and Balu, K. (2007), Design of fuzzy estimator to assist fault recovery in a non-linear system. International Journal of Computer Science and Network Security Publications, 7(5), 1-7. 10. Romagnoli, J.A.; Palazoglu, A. (2012). Introduction to process control. CRC press. 11. King, M. (2001). Process control A practical approach. Wiley press.