Two-PI Controllers Based Quadruple Tank System

Transcription

1 Two-PI Controllers Based Quadruple Tank System Hana El saady 1 and Farag Hossen 2 1 Assistant Lecture, Electrical and Electronics Engineering Department, Tobruk University, Tobruk, Libya. 2 Assistant Lecture, Mechanical Engineering Department, Higher Institute of Comprehensive Occupations, Tobruk, Libya. Abstract This paper aims to design Proportional Integral Derivative (PID) controller to control the desired water level of Quadruple Tank System (QTS). A mathematical model and linear state space model are exploited to analyze the QTS. The performance, in terms of the transient and the steady state response, is verified using MATLAB. Keywords: Quadruple Tank System, PI Controller, Transient response, steady state response. 1. INTRODUCTION The non-linear control systems are engaged extensively in numerous industrial processes, where multiple inputs and multiple outputs are interacted with controlled variables [1]. The Quadruple Tank System (QTS) is widely studied in literature [3][5][7], and it will be explored in the current paper by designing a Proportional Integral Derivative (PID) controller..for long time, PID controllers are the core of industrial control systems, by which the required output parameters such as position, velocity or temperature can be resulted with a minimum error at a short period of time [8]. The PID controllers are originally presented in 191, whereas in 1942, Ziegler Nichols proposed initial tuning rules driving the PID controllers in a popular place [8]. Although this proposed tuning rules have been taken a considerable attention, unfortunately complicated tuning steps of PID parameters are employed to achieve the anticipated process successfully, in turn, leading to a set of suggested approaches in literature. The most well-known process control is the control of water level in tank, where a number of researchers have introduced different valuable approaches [9]. In principle, the key role of the PID's level control is to retain a desired output level at a planned value, and has the ability to run a new intended values consistently with response as high as possible. For QTS, in order to control the level in the two lower tanks, two pumps are employed with two applied inputs voltage named as v1 and v2, whereas and represent the output control levels of the lower tanks. 2. MODELING OF TANK SYSTEM The QTS is considered as a two double-tank process. Considering the water flow with respect to the gravity as shown in Fig 1, the Tank3 and the Tank4 are positioned above the Tank1 and the Tank2. The water is delivered into the four tanks via appropriate position of valves and pumps. The pump1 delivers water into Tank1 and Tank4 while the pump 2 delivers the water into Tank2 and Tank3. The inputs and outputs parameters of the lower tank system are the applied voltages (v1,v2) and water levels of tanks (,) respectively. Figure 1 Schematic diagram of QTS. Volume 7, Issue 7, July 218 Page 1

2 The nonlinear equations for each tank are obtained through mass balance law and Bernoulli s law as follows: (1) (2) (3) (4) Where Ai cross-section of the tank, i =1,2,3 or 4. ai section of the outlet hole. hi water level. v1,v2, input voltages. ) output voltages. ( 1 2 Using eq.1, the tank 1 can be implemented in MATLAB as shown in Fig 2. Figure 2 Simulink Diagram of Tank1. Likewise, Tank2, Tank3, and Tank4 can be implemented to get the whole four tank system as shown in Fig 3 Volume 7, Issue 7, July 218 Page 2

3 3. MODEL LINEARZIATION: Figure 3 Simulink diagram of QTS. The linearization of the model around the two set operating points (minimum phase & non minimum phase) is illustrated in Table 1: Table 1: Parameter values of the process. Units P _ P.4, , 13. ( h, ) ] h 1 2 ( h, ) ] h 3 4 ( v, ) ] v 1 2 ( k 1 2 [cm 12 [cm 1.8, , 4.8 [V 3., , 3.15 k, ) [ 3 / Vs] ( 1 2 cm 3.33, , 3.29, ).7,.6.43,.34 The model can be linearized mathematically as in [1], alternatively, it can be obtained using MATLAB as follows:,, and Volume 7, Issue 7, July 218 Page 3

4 4. SIMULATION AND RESULTS 4.1 Simulation results without controller The change in the level of liquid in the tanks is as a function of change in the applied voltage of the pumps. In that, Fig4 and Fig5 show that the water level is increased as the voltage increasing The measured vules of level, Time(sec) Figure 4 Open loop response of the QTS at (v1 = v2 = 3). 15 The measured values of and Time [sec] Figure 5 Open loop response of the QTS at (v1 = v2 = 3.15). 4.2 Simulation results with Proportional Integral (PI) controller For controlling the level of tanks at desired values, two PI controllers are introduced as shown in Fig 6 and their parameters are tuned as given in Table 2. MATLAB environment are used to obtain the system's performance, showing the transient and the steady state response. The simulated results show that two PI controllers provide a fast response without overshoot and no steady state errors as shown in Fig.7 and Fig.8. Volume 7, Issue 7, July 218 Page 4

5 Figure 6 Simulink diagram of controlled QTS System. Parameters of PI controller Table2 Tuned values of the two PI Controllers. PI controller 1 PI controller 2 Tuned vales Kp 7 7 Ki 6 6 Tuned vales 18 Response of QTS with PI Controllers Level of Tank Set Point of Tank1 Set Point of Tank Time in Second Figure 7 Closed loop response of controlled QTS at desired values. Volume 7, Issue 7, July 218 Page 5

6 Step Response of Tank1 and Tank2 Set Ponint Level of Tank CONCLUSION Time in Second Figure 8 Unit step response of QTS. In this paper, the Quadruple Tank System was investigated with a minimum phase system. Mathematical model and linearization of nonlinear system were determined. The two PI controller's parameters were tuned to control the liquid level at desired values in the two lower tanks, leading to a great enhancement in the system response. References: [1] Sazuan Nazrah Mohd. Azam, and John Bagterp Jørgensen, Modeling and Simulation of a Modified Quadruple Tank System. IEEE International Conference on Control System, Computing and Engineering, November 215, Penang, Malaysia. [2] Yousof Gholipour,and Ahmad Zare. Comparing the effect of PI and I controllers on a four tank process. International Journal of Recent Research in Electrical and Electronics Engineering (IJRREEE). Vol. 1, Issue 1, pp: (1-6), Month: April - June 214. [3] Serkan Özkan, Tolgay Kara and Mehmet Arıcı, Modelling, Simulation and Control of Quadruple Tank Process. Electrical and electronics Engineering Department, Gaziantep University, Gaziantep, Turkey [4] W. Belhaj and O. Boubaker. On MIMO PID Control of the quadruple-tank process via ILMIs Approaches : Minimum and Non-Minimum Case studies. The International Federation of Automatic Control December 18-2, 213. Mumbai, India. [5] Mostafa.A. Fellani, and Aboubaker M. Gabaj, PID Controller design for two Tanks liquid level Control System using Matlab. International Journal of Application or Innovation in Engineering & Management. Volume 4, May 215. [6] Parvat. B.J., Deo.S.A, and KaduC.B. Mathematical Modeling of Interacting and Non Interacting Tank System.International Journal of Application or Innovation in Engineering & Management (IJAIEM ). Volume 4, Issue 1, January 215. [7] Parvathy Prasad, The Performance Analysis Of Four Tank System For Conventional Controller And Hybrid Controller. International Research Journal of Engineering and Technology (IRJET). Volume 3, Issue 6, June 216. [8] Mostafa.A. Fellani, Aboubaker M. Gabaj. PID Controller design for two Tanks liquid level Control System using Matlab.International Journal of Application or Innovation in Engineering & Management (IJAIEM). Volume 4, Issue 5, May 215. [9] Surbhi Sharma, Manisha Arora, and Kuldeepak Kaushik. Analysis of Liquid Level Control of Coupled Tank System By Pi, Pd, Pid Controller. INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH. VOLUME 4, ISSUE 11, NOVEMBER 215. [1] Jayaprakash.J. SenthilRajan T, and Harish Babu T'' State Variable analysis of four tank system''. International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering. An ISO 3297: 27 Certified Organizatio. Vol. 3 Issue 8, August 214. AUTHORS Hana El saady received the B.Sc. in Electrical and Electronic Engineering from Omar Almuktar University in 2 and M.Sc. degree in Communication, Control, and Digital Signal Processing from Strathclyde University UK in 21. She currently works at Department of Electrical and Electronics Engineering of Tobruk University. Farag Hossen received the B.Sc. in Mechanical Engineering from Omar Almuktar University in 2 and M.Sc. degree in Advanced Manufacturing Systems from Teesside University UK in 211.He currently works at Department of Mechanical Engineering of Higher Institute of Comprehensive Occupations Volume 7, Issue 7, July 218 Page 6