Design of PID Controller for IPDT System Based On Double First Order plus Time Delay Model

Transcription

1 Volume 119 No , ISSN: (on-line version) url: Design of PID Controller for IPDT System Based On Double First Order plus Time Delay Model V.Vijayan 1*, A.Srinivasan 2, K. Palani Thanaraj 3 1, 3 Dept. of EIE, St. Joseph s College of Engineering, Chennai Dept. of ECE, Chennai Institute of Technology, Chennai vinvpn@gmail.com 1*, a.srinivasan2025@gmail.com 2,palanithanaraj.k@gmail.com 3 ABSTRACT In this paper, design of Proportional, Integral and Derivative (PID) controller with filter is explained for Integral plus Dead Time (IPDT) process based on double first order plus time delay model(dfopdt). A double feedback structure is being used. The inner loop (proportional control) is to stabilize the system and outer loop (PID with filter) is used for improving the speed of response. Key words: Double FOPTD, PID with filter, double feedback, Integral plus dead time process. 1. INTRODUCTION Designing of PID controller is for IPDT system is very difficult task. Shamsuzzoha, and Moonyong Lee [1] explained about PID controller tuning for various process. PID controller tuning for integrating process is proposed by Ali and Majhi [2]. Luyben [3] proposed a tuning method with set point filter and PID filter. Chen and Seborg [4] designed a new method of PID controller tuning. Chien and Fruehauf [5] proposed IMC type PID controller tuning. Liu et al [6] proposed a tuning method of unstable system. Vijayan& Panda [7&8] proposed a tuning method of PID controller with set point filter which is used in double feedback structure. Shamsuzzoha [9] explained about PID controller with cascaded filter. Nivetha et al. [10&11] discussed about tunable method of PID controller tuning for integrating process and conical tank system. Yongho Lee [12] explained about PID tuning for integrating process. Atchaya [13] proposed a synthesis method of tuning method for unstable system. Hamamci and Tan [14] proposed a tuning method based frequency domain specifications. Dey et al [15] designed PID controller for integrating process. Devikumari [16],Saranya [17] and Ramadevi [18] explained tuning method for multivariable system. Skogestad [19] gave new method of tuning and model reduction technique. Vijayan et al [20] introduced the stability analysis for PID controller. In this work PID controller for integrating process is designed based on Yongjeh Lee [21] method

2 2. CONTROLLER DESIGN USING DOUBLE FIRST ORDER PLUS TIME DELAY MODEL FIGURE 1 BASIC STRUCTURE The double feedback structure is shown in Figure 1. Gp is the system transfer function. In this work, IPDT processes are considered.the Gc1 is Proportional controller which is tuned by using Zigler-Nichols method. Then, for the inner loop step input is given. It produced response with overshoot as shown in figure 2. Using this response, based on Yongjeh Lee et al(2016) method, double first order with delay time model and outer loop PI controllers (Gc2) are obtained. Gc3 is PID filter. It is in the form of 1. Here, I is the integral time constant which is same as I s 1 outer loop controller. The tuning parameter ( ) is adjusted until the system produces the lowest Integral Time Absolute Error (ITAE). FIGURE 2 STEP RESPONSE OF INNER LOOP

3 3. SIMULATION RESULT 3.1 Example 1 An Integrating plus dead time (IPDT) process (Shamsuzzoha, Moonyong Lee (2008)) is considered e Gp(s) s 6s. Using zigler-nichols method inner loop is tuned. The inner loop Proportional controller is Using Yongjeh Lee method the outer loop PI parameters are obtained as kc = and ki= Then the is adjusted till 1.6 which gives least ITATE value. For comparison Luyben (1996) method is considered. The servo response is shown in Figure 3. Figure 3 Servo Response of the Example 1 Table 1 PID controller setting and performance matrix for Example 1 Method Kc1 Kc I D ITAE PO Double FOPTD Luyben

4 The Table 1 shows that the Double FOPTD method produces better result in terms of less ITAE compared with Luyben method. 3.2 Example 2 A Distillation column model (Shamsuzzoha, Moonyong Lee (2008)) is considered. 0.2e Gp(s) s 7.4s. Using Zigler-Nichols method inner loop is tuned. The inner loop Proportional controller is Using Yongjeh Lee et al the outer loop PI parameters are obtained as kc = and ki= Then the is adjusted till 1.8 which gives least ITATE value. For comparison Lee et al (2000) method is considered. The servo response is shown in Figure 4. Figure 4 Servo Response of the Example 2 Table 2 PID controller setting and performance matrix for Example 2 Method Kc1 Kc I D ITAE PO Double FOPTD Yongho Lee

5 The Table 2 shows that the Double FOPTD method produces better result in terms of less ITAE compared with Yongho Lee method. 4. CONCLUSION A design of PID controller fordouble first order system with double feedback structure is explained. Two examples with simulation results were given. The double first order with double feedback method is better compared with Luyben and Yongho Lee methods. The ITAE (Integral Time Absolute Error) is lesser for the present method. 5. REFERENCES [1] M. Shamsuzzoha and M. Lee, Analytical design of enhanced PID filter controller for integrating and first order unstable processes with time delay, Chem. Eng. Sci., vol. 63, no. 10, pp , [2] A. Ali and S. Majhi, PID controller tuning for integrating processes, ISA Trans., vol. 49, no. 1, pp , [3] W.L.Luyben, Tuning Proportional-Integral-DerivativeControllers for Integrator/Deadtime Processes, Ind. Eng. Chem. Res., vol. 35, no. 10, pp , [4] D. Chen and and Dale E. Seborg*, PI/PID Controller Design Based on Direct Synthesis and Disturbance Rejection, Ind. Eng. Chem. Res., vol. 41, no. 19, pp , [5] I.-L. CHIEN, Consider IMC Tuning to Improve Controller Performance, Chem. Eng. Prog., vol. 86, pp , [6] T. Liu, W. Zhang, and D. Gu, Analytical Multiloop PI/PID Controller Design for Two-by- Two Processes with Time Delays, Ind. Eng. Chem. Res., pp , [7] V. Vijayan and R. C. Panda, Design of PID controllers in double feedback loops for SISO systems with set-point filters., ISA Trans., vol. 51, no. 4, pp , Jul [8] V. Vijayan and R. C. Panda, Design of a simple setpoint filter for minimizing overshoot for low order processes., ISA Trans., vol. 51, no. 2, pp , Mar [9] M. Shamsuzzoha, S. Lee, and M. Lee, Analytical design of PID controller cascaded with a lead-lag filter for time-delay processes, Korean J. Chem. Eng., vol. 26, no. 3, pp , [10] J. Nivetha, V. Vijayan, S. Devakumar, C. Selvakumar, and R. C. Panda, Desig of Tunable method of PID Controller for Integrating Process, Int. J. Eng. Comput. Sci., vol. 4, no. 12, pp , [11] J. Nivetha and V. Vijayan, Design of tunable method of PID controller for conical tank system, in 2016 International Conference on Computation of Power, Energy Information and Commuincation (ICCPEIC), 2016, pp [12] Y. Lee, J. Lee, and S. Park, PID controller tuning for integrating and unstable processes with time delay, Chem. Eng. Sci., vol. 55, no. 17, pp ,

6 [13] G. Atchaya, P. Deepa, V. Vijayan, and R. C. Panda, Design of PID Controller with Compensator using Direct Synthesis Method for Unstable System, Int. J. Eng. Comput. Sci., vol. 5, no. 4, pp , [14] S. E. Hamamci and N. Tan, Design of PI controllers for achieving time and frequency domain specifications simultaneously, ISA Trans., vol. 45, no. 4, pp , Oct [15] C. Dey, R. K. Mudi, and D. Simhachalam, A simple nonlinear PD controller for integrating processes., ISA Trans., vol. 53, no. 1, pp , [16] A.H.Devikumari and V.Vijayan, Decentralized PID Controller Design for 3x3 Multivariable System using Heuristic Algorithms, Indian J. Sci. Technol., vol. 8, no. 15, pp. 1 6, [17] Saranya R and Vijayan V, Design of PI Controllers for Unstable MIMO System Using Firefly Algorithm, Int. J. Sci. Res., vol. 4, no. 5, pp , [18] C. Ramadevi and V. Vijayan, Design of Decoupled PI Controller for Quadruple Tank System, Int. J. Sci. Res., vol. 3, no. 5, pp , [19] S. Skogestad, Simple analytic rules for model reduction and PID controller tuning, Model. Identif. Control, vol. 25, no. 2, pp , [20] V. Vijayan, S. Narayanan, P. Kanagasabapathy, and J. Prakash, Stability Analysis of First Order Plus Time Delay System under PI & PID Control for Simultaneous Parameter Variation, in 2005 Annual IEEE India Conference - Indicon, 2005, vol. 2005, pp [21] Y. Lee, D. R. Yang, J. Lee, and T. F. Edgar, Double First-Order Plus Time Delay Models To Tune Proportional Integral Controllers, Ind. Eng. Chem. Res., vol. 55, no. 39, pp , Oct

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