Design of fuzzy controller for two tank interacting system Mohamed sabith KT Second year M. tech Dept of Electrical Engineering NIT Calicut Calicut, India sabithkt@gmail. com Dr. Abraham T Mathew Professor, Dept of Electrical Engineering NIT Calicut Calicut, India atm@nitc. ac. in Abstract—The control of liquid level in tanks and flow between tanks is a basic problem in the process Industries. Vital industries such as Petro-chemical industries, Paper making industries, Water treatment industries have the coupled tanks processes. The level of fluid in the tanks and interaction between tanks must be controlled.
The aim of the project is to model the the coupled two tank liquid level system and to design a fuzzy controller. For coupled tank systems with non linear and complex characteristics classical PID is difficult to achieve the desired response. Fuzzy logic control is a classic method by which dynamic performance and strong robustness is guaranteed. The project compares the performance of the two tank system with classical PID and fuzzy logic control. Index Terms—PID, fuzzy logic, steady state Introduction through two separate pumps whose output is throttled using a control valve.
Separate disturbance are made to both the tanks using hand valves. The two tanks are connected by means of hand valve, so the level of tank 1 will affect the tank 2 and vice versa. So this is a highly non linear system. Flow transmitters and pressure transmitters are there which give indication of flow and level respectively in a scale of 4-20 mA. The input from this sensors are taken to a computer which is process by a software in which controller is implemented which will give necessary control signal to throttle the control valve to get the necessary level.
A Coupled tanks process is found in the many industries. Generally, The TITO processes have the problems to control their systems because of the existence of interactions between input and output variables. Many control methods such as 2DOF PID [1], Auto tuning PID [2], CDM [3] and Decoupling [4] have been applied to coupled tanks processes for solving their problems. This paper presents control of two tank interacting system with the help of classical PID and Fuzzy control. The paper is organized as follows.
The next section gives details about Coupled-tank process. Section 3 explains about modeling of two tank interacting system. Section 4 explains PID based control. Section 5 explains an implementation of Fuzzy Controller for coupled tank process. Section 6 shows experiment process and results. Finally, conclusions are given in section 7. COUPLED TANK SYSTEM MODELLING OF A TWO TANK INTERACTING SYSTEM Consider the coupled tank, two-input two-output process . The target is to control level of two tanks by the inlet water flow from two pumps P1and P2.
The process inputs are flow rate of two pumps u1(t)and u2(t) which is throttled using control valves. The nonlinear plant equations can be obtained by mass balance equation The overall material balance on the cylindrical tank is: Rate of mass accumulation in the system = rate of mass entering in the system- rate of mass leaving the system There for the dynamics of the tank system can be written as The coupled tank apparatus is shown in the Figure 1. 1. The apparatus is a model consisting of a pump, two cylindrical tanks made of plexiglas, two control valves, and two level transmitters .
The two tanks are installed in a manner as shown in the fig 2. 1The water input to both the tank is provided ??????? 1 ?????? ?????? 1 ?????? = ? ?????? 1 ?????? ? ?????? 1 ? 2 ? ?????? ? ?????? 1 ?????? + ???????????? ???????????? ?????? ?????? ?????? ? ( 2 ? ?????? ? ?????? 2 ?????? ? (2 ? ?????? ? ?????? 1(?????? ) ?????? ??????? 2 ?????? ?????? 2 ?????? = ? ?????? 2 ?????? ? ?????? 2 ? 2 ? ?????? ? ?????? 2 ?????? + ???????????? ???????????? ?????? ?????? ?????? ? ( 2 ? ?????? ? (?????? 1 ?????? ? 2 ? ?????? ? ?????? 2 ?????? ??????
Where A is the cross section area of tank 1 and tank 2, a is the cross section area of outlet hole of tank 1and tank 2 and cross section area of jointed pipe between tank 1 and tank 2 , ? 1 is the valve ratio at the outlet of tank 1, ? 2 is the valve ratio at the outlet of tank 2, ? x is the valve ratio between tank 1 and tank 2. k1,k2 are the gain of the pump. The above equations can be converted to transfer function form and a transfer matrix of the form is obtained. ?1(?????? ) ?????? 11(?????? ) ?????? 12(?????? ) = ? 2(?????? ) ?????? 21(?????? ) ?????? 22(?????? ) ?????? 1(?????? ) ?????? 2(?????? ) nteraction between processes, the control design needs the decoupling controllers to minimize the cross coupling effects Because of the interaction between processes, the control design needs the decoupling controllers to minimize the cross coupling effects The decoupling controllers consist of two decouplers d12 and d21 . The purpose of using decouple is to decouple the multivariable system. This can be done by choosing the following transfer function. D21=-G21/G22 D12=-G12/G11 SIMULINK SIMULATION OF COUPLED TANK SYSTEM WITH PID CONTROL AND DECOUPLERS The modeled coupled tank system was simulated using simulink .
G11 represent the dynamics of the tank 1 ,similarly G22 represent the dynamics of tank2. G12 represent the effect of level of tank 2 on tank1,and G21 represent the effect of level of tank 1 on tank 2. Due to high interaction between the tanks ,its difficult to control with ordinary PID. So as to avoid the interaction Decouplers were introduced. The advantage with the decoupler is that separate PID controllers can be designed for individual loops. Two individual PID controllers were designed for the two loops and tuning of the controllers were also performed.
Tank 1 is subjected to a setpoint input of 15cm at time of 30 seconds and it is having an setpoint of 5cm. Similarly Tank 2 is subjected to a setpoint input of 25cm at time of 50 seconds and it is having an initial setpoint of 10. The response of the simulated system is shown in fig below,both the level of tank 1 and tank 2 follows the setpoint with small peak overshoot. Where h1, h2 are the liquid level in two tanks and u1,u2 are the input into the two tank . Where transfer matrix Gij(s)has the value as following G11(s)= ?????? 1 ???????????? +?????? 2 ?????? + ?????? ?????? 2???????????? ?????? 1???????????? +?????? ?????????????????? +2?????? 1?????? 2 1 1 1 ?????? 2 + ?????? +( + + ) ?????? 1?????? 2???????????? ?????? 1?????? 2 ?????? 1???????????? ?????? 2???????????? G22(s)= ?????? 2 ???????????? +?????? 1 ?????? + ?????? ?????? 1???????????? ?????? 1???????????? +?????? 2?????????????????? +2?????? 1?????? 2 1 1 1 ?????? 2 + ?????? +( + + ) ?????? 1?????? 2???????????? ?????? 1?????? 2 ?????? 1???????????? ?????? 2???????????? ?????? 2 1 ?????? ???????????? ?????? 1???????????? +?????? 2?????????????????? +2?????? 1?????? 2 1 1 1 ?????? 2 + ?????? +( + + ) ?????? 1?????? 2???????????? ?????? 1?????? 2 ?????? 1???????????? ?????? ???????????? G12(S)= G21(S)= ?????? 1 1 ?????? ???????????? ?????? 1???????????? +?????? 2?????????????????? +2?????? 1?????? 2 1 1 1 ?????? 2 + ?????? +( + + ) ?????? 1?????? 2???????????? ?????? 1?????? 2 ?????? 1???????????? ?????? 2???????????? Design of Decouplers The theoretically modeled system was simulated using simulink as shown in fig. below . G11(s) represents the tank 1 and G22(s) represents the tank 2. The effect of tank 1 on tank 2 is given by G21(s) and the effect of tank 2 on tank 1 is given by G12(s). This coupled tank system is having high interaction and it also exhibits non linear characterstics.
Because of the The input variable error(e) is shown below,for all these inputs five membership functions are used. The five membership functions are NB,N,Z,P,PB. Fuzzy controller The traditional control, which includes the classical feedback control , has encountered many difficulties in its applications. The design and analysis of traditional control systems are based on their precise mathematical models, which are usually very difficult to achieve owing to the complexity, nonlinearity, time varying and incomplete characteristics of the existing practical systems.
One of the most effective ways to solve the problem is to use the technique of intelligent control system, or hybrid methodology of the traditional and ntelligent control techniques. The output variable is shown below As i have 2 inputs with 5 membership functions,I used 25 rules(IF THEN ). The surface of the rulebase is as shown below The above fig shows how a fuzzy controller is implemented . The Fuzzy controller takes two input and have one output, error and rate of change of error are given as input to the fuzzy controller . depending on the input the fuzzy controller produces required control action.
For all input and output triangular membership functions are used. The input rate of change of error(de) is shown below The two tank system with fuzzy controller is subjected to an input,the first tank is set to a initial level of 5cm then it is subjected to a step change of 15 cm at 25 seconds,for the second tank it is set to a initial level of 10 cm and final level of 20 cm. With fuzzy controller the outputs obtained is as shown below [1] Suparoek Kangwanrat1, Vittaya Tipsuwannaporn ? Design of PI Controller Using MRAC Techniques for Coupled-Tanks Process? International Conference on Control, Automation and Systems 2010 Oct. 7-30, 2010 in KINTEX, Gyeonggido, Korea [2] V. R. Ravi , T. Thyagarajan ? Application of Adaptive Control Technique to Interacting Non Linear Systems” IEEE Transactions On Systems, Man, And Cybernetics—Part B: Cybernetics, 33( ), 2003, 514–521 [3] [3] Dr. S. AbrahamLincon, P. Selvakumar ? Design of PI Controller using Characteristic Ratio Assignment Method for Coupled Tank SISO Process? International Journal of Computer Applications (0975 – 8887) Volume 25– No. 9, July 2011 [4] Li LIANG ? The application of fuzzy PID controller in coupled-tank liquid-level control system?
IEEE Transactions on Industrial Informatics, vol. 6, no. 1, pp. 25-35, 2010 [5] Jutarut Chaorai-ngern, Arjin Numsomran, Taweepol Suesut, Thanit Trisuwannawat and Vittaya Tipsuwanporn ?PID Controller Design using Characteristic Ratio Assignment Method for Coupled-Tank Process.? Proceedings of the 2005 International Conference on Computational Intelligence for Modelling, Control and Automation CONCLUSION The output obtained for fuzzy controller doesnot show peak overshoot as in th case of a PID controller ,the problem observed with fuzzy controller is that small oscillations will be prescent at steady state REFERENCES
