COMPARISON OF FUZZY LOGIC CONTROLLERS FOR A MULTIVARIABLE PROCESS

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1 COMPARISON OF FUZZY LOGIC CONTROLLERS FOR A MULTIVARIABLE PROCESS KARTHICK S, LAKSHMI P, DEEPA T 3 PG Student, DEEE, College of Engineering, Guindy, Anna University, Cennai Associate Professor, DEEE, College of Engineering Guindy, Anna University, Cennai 3 Researc Scolar, DEEE, College of Engineering, Guindy, Anna University, Cennai, kartickmay0@gmail.com, p_laksmi@annauniv.edu, deepabalaji30@gmail.com Abstract Te Interval Type- Fuzzy Logic Controller (ITFLC) for a Quadruple Tank Process (QTP) is demonstrated in tis paper. Here te Interval Type- based Fuzzy membersip function is used. Te QTP is made to operate in minimum pase mode. Te vertices of fuzzy membersip functions are tuned wit ITFLC to minimize Integral Absolute Error. Performance of ITFLC and Type- Fuzzy Logic Controller (TFLC) are compared wit decentralized PI controller, by simulation using MATLAB/Simulink. Simulation results sow tat satisfactory performance for bot servo and regulatory responses.it as been observed tat dynamic performance of ITFLC is better tan te oter two controllers. Moreover, compared wit te TFLC controller, ITFLC performs better, particularly in noisy environments. Keywords Quadruple Tank Process, Decentralized PI, Type Fuzzy Logic Controller, Interval Type Fuzzy Logic Controller. I. INTRODUCTION Te multivariable laboratory process, called te Quadruple Tank Process (QTP), consists of four interconnected liquid tanks, two pumps and two valves, [] and is sown scematically in Fig.. Te inputs are te voltages to te two pumps (v, v ) and te outputs are te liquid levels in te lower tanks (, ). Te linearized dynamics of te process exibits a multivariable zero tat can be moved from one side of te complex plane to te oter one by canging te valves positions γ and γ. Tis process is found to be ideally suited to illustrate many concepts in multivariable control. Luyben [] presented a large number of genuine multi-loop control system, wic are made up of Single-Input/Single-Output (SISO) controllers acting in a multiloop fasion. Designing of multivariable decoupling and multi-loop PI/PID controllers in a sequential manner are developed by Siu and Huang [3]. Te metod is based on a singleloop tuning tecniques developed for multivariable systems wit unknown dynamics. Tan et al [4] proposed simple tuning rules for bot stable and integrating processes based on loop-saring H optimal control. Zuang and Aterton [5] designed a diagonal PID controller tuning using an integral performance optimization procedure for a Two Input Two Output (TITO) system. Te caracteristic locus metod usually results in better step response tan te generalized Ziegler-Nicols metod. Jerry M. Mendel [6] presented ITFLC and provided its advantage over Type- Fuzzy Logic. Also, ITFLS models can andle iger levels of uncertainty and tus opens up an efficient way of developing improved control systems and for modeling uman decision making. Oscar Castillo et al [7] designed te fuzzy Lyapunov syntesized system tat is stable and robust. Also te ITFLC membersip functions can perturb or cange te definition domain of te Footprint of Uncertainty (FoU) witout losing te stability of te controller. Wu et al [8] explained te five uncertainty measures for ITFs-centroid, cardinality, fuzziness (entropy), variance and skewness are stated. Formulae for computing tese measures were also obtained. Wu et al [9] designed a GA-based TFLC for te coupledtank liquid-level process and proved te robustness of TFLC wic outperforms TFLC. Hani Hagras [0] applied ITFLC to coupled tank liquid level system sowed tat copes well tan TFLC. Deepa et al [] applied a decentralized PI controller and tuned te PI parameters using bacteria foraging and computed te performance index Integral Square Error (ISE). Suja Mani Malar [] et al compared te performances of soft computing tecniques suc as Neural Networks, Fuzzy Logic and Adaptive Neuro Fuzzy Inference system (ANFIS). Te outline of te paper is as follows. Nonlinear and linearized model of QTP is presented in section. Control tecniques are discussed in section 3, 4 and 5. Simulation results and conclusions are presented in sections 6 and 7 respectively. II. MODEL OF QUADRUPLE TANK PROCESS Te scematic diagram of te Quadruple Tank Process is sown in Fig. and its laboratory setup is sown in Fig.. Process signals from te four tank level transmitters are interfaced wit computer. Control algoritm running on te computer sends outputs to te individual control valves troug interfacing units. Tanks and are mounted below 57

2 te oter two tanks for receiving water flow by gravity. Eac tank outlet opening is fitted wit a valve. Bot pumps and take suction from te supply tank. Discarge from pump is split between tank and tank 4 and te flows are indicated by rotameter and 4. Similarly, pump splits its discarge between tank and tank 3 and te split flows are indicated by rotameter and 3. Split flows from pump and pump can be varied by manual adjustment of valves. Tank and tank also receive gravity flow from tank 3 and tank 4, respectively. Mass balances and Bernoulli s law yield te following nonlinear equations. [] of te complex plane to te oter one by canging te valves positions. System is in minimum pase wen γ + γ is between and. System is in non minimum pase wen te sum is less tan. Tis process is found to be ideally suited to illustrate many concepts in multivariable control. Fig. Scematic diagram of te Quadruple-Tank Process were, A i Cross-section of Tank i (m ) a i Cross-section of te outlet ole (m ) i Water level (cm) g Acceleration due to gravity (9.8 m/s ) Te voltage applied to pump i is v i and te corresponding flow is k i u i. Te parameters γ, γ [0,] are determined from ow te valves are set prior to an experiment. Te flow to Tank is γ k v and te flow to Tank 4 (-γ )k v is and similarly for Tank and Tank 3. Te measured level signals are k c and k c. Te linearized state space equation is given by Fig. Laboratory setup of Quadruple Tank Process III. DECENTRALIZED PI CONTROLLER Te decentralized control law will be of te form u=diag {C, C } (r-y) as given in te Fig.3. [5] Te corresponding transfer function matrix is Fig. 3 Decentralized PI Structure PI controllers are of te form Te linearized dynamics of te process exibits a multivariable zero tat can be moved from one side

3 IV. TYPE- FUZZY LOGIC CONTROLLER In general, Type- Fuzzy logic uses simple rules to describe te system of interest, rater tan te analytical equations, making it easy to implement. An advantage, suc as robustness and speed, fuzzy logic is one of te best solutions for non-linear system modeling and control. Type- Fuzzy logic controller as four main components. Tey are fuzzifier, knowledge base, inference mecanism and defuzzifier. Fuzzifier converts te crisp input signal into fuzzified signals identified by membersip functions into fuzzy sets. Te knowledge base consists of rule base and data base. Te inference mecanism evaluates wic control rules are relevant at te current time and ten decides wat te input to te plant sould be. Finally te defuzzification process converts te fuzzy output into crisp controlling signal. Te block structure of TFLC is sown in Fig.4 below. Fig. 6 Fuzzy Surface for TFLC V. INTERVAL TYPE- FUZZY LOGIC CONTROLLER Type- Fuzzy Logic Controllers (FLCs) ave been applied to date wit great success to many different applications. However, for dynamic unstructured environments and many real-world applications, tere is a need to cope wit large amount of uncertainties. Te traditional type- FLC using crisp type- fuzzy sets cannot directly andle suc uncertainties. A type- FLC using type- fuzzy sets can andle suc uncertainties to produce a better performance. Hence, type- FLCs will ave te potential to overcome te limitations of type- FLCs and produce a new generation of fuzzy controllers wit improved performance for many applications, wic require andling ig levels of uncertainty. Te block structure of ITFLC is sown in Fig.7 below. Fig. 4 Block Structure of TFLC Te control inputs, error (e) and cange in error (ce) for Type- FLC and its membersip function is sown in Fig. 5 below. Fig. 7 Block Structure of ITFLC Te control inputs, error (e) and cange in error (ce) for Interval Type- FLC and its membersip function is sown in Fig. 8 below. Fig. 5 Membersip Function for TFLC inputs e and ce Te fuzzy surface for error, cange of error and output of te system is generated in MATLAB. And te fuzzy surface seems to ave more rougness tat is sown below in Fig. 6 for TFLC. Fig. 8 Membersip Function for ITFLC inputs e and ce From te defined rules, using te error, cange of error and output te fuzzy surface is generated in MATLAB. Te fuzzy surface for ITFLC wic is

4 comparatively smooter tan TFLC is sown below in Fig. 9 for ITFLC. TABLE III. CONTROLLER PARAMETERS Type of Controller Controller Parameters Decentralized PI K pl = 5.48 K p = K i = 0.53 K i = System response for eigts and of QTP, for te set point of 3.5cm and 7.5cm are sown in Fig.0 and respectively. Fig. 9 Fuzzy Surface for ITFLC Vertices and te bases of te membersip functions are tuned for a given system to get required response. Once te membersip functions are created te next step is te formation of rules between input and output membersip functions. Fuzzy rules are as sown in Table I. Fig. 0 System response for level TABLE I RULE BASE FOR TFLC & ITFLC NB NM NS ZR PS PM PB ce e NB NB NB NB NM NS NS ZR NM NB NB NM NS NS ZR PM NS NB NM NS NS ZR PS PM ZR NM NM NS ZR PS PM PB PS NM NS ZR PS PS PM PB PM NS ZR PS PS PM PB PB PB ZR PS PS PM PB PB PB Fig. System response for level Te servo response for te level for two different step canges i.e. a negative step cange of 35% at 000 second and a positive step cange of 50% at 4000 second are sown in Fig.. Similarly te servo response for te level for two different step canges i.e. a negative step cange of 45% at 000 second and a positive step cange of 60% at 4000 second are sown in Fig. 3. VI. SIMULATION RESULTS Controllers designed in sections III, IV and V are simulated using MATLAB/Simulink. Te parameters of te quadruple tank system are sown in Table II. Parameters of te controllers are given in te Table III. Fig. Servo response for level TABLE II. QUADRUPLE TANK PROCESS PARAMETER VALUES Parameter Values Diameter of Tank 5cm Diameter of outlet.6cm γ 0.6 γ 0.6 Max input flow 600 litres/our Fig. 3 Servo response for level Te regulatory response of te QTP for te process variables (i.e. level and ) are sown in te Fig. 4 and 5 After reacing a steady state, an

5 input disturbance of 33% i.e. 00 litres/our, is given at 600 second. TABLE VI. COMPARISON OF REGULATORY RESPONSE OF DECENTRALIZED PI, TFLC & ITFLC Controller Settling Time (s) Oversoot (%) IAE Fig. 4 Regulatory response for level PI TFLC ITFLC VII. CONCLUSION Fig. 5 Regulatory response for level Comparison of performances of decentralized PI, TFLC and ITFLC are given in Table IV, V and VI respectively. It can be observed tat ITFLC as less settling time and over/undersoot in all te tree responses. But in servo response te IAE is very less in TFLC. TABLE IV. COMPARISON OF STEP RESPONSE OF DECENTRALIZED PI, TFLC & ITFLC Type of Control Decentralize d PI Settling Time (s) TFLC ITFLC Peak Oversoot (%) IAE TABLE V. COMPARISON OF SERVO RESPONSE OF DECENTRALIZED PI, TFLC & ITFLC Interval Type- Fuzzy Logic and Type- Fuzzy Logic Controllers are designed to control te level of te quadruple tank process. Te ITFLC results are compared wit TFLC and decentralized PI controllers. Te settling time of tank for TFLC is 00. sec and ITFLC is 80.3 sec and tank for TFLC is 78 sec and ITFLC is 60 sec. Te Integral Absolute Error for tank for TFLC is 6.6 and for ITFLC is 8.9. From servo response it can be observed te system settles faster wit ITFLC tan conventional TFLC for a given set of controller parameters, but te IAE is iger tan ITFLC. From te regulatory responses it can be found tat disturbance rejection is faster wit ITFLC tan conventional TFLC and decentralized PI controller. REFERENCES [] K.H.Joansson, Te Quadruple Tank Process A Multivariable Laboratory Process wit an adjustable zero, IEEE Transactions on Control Systems Tecnology, Vol. 8, No.3, May 000, pp [] W.L.Luyben (986), Simple metod for tuning SISO controllers in multivariable systems, Ind. Eng. Cem. Process Des. Dev. pp [3] S.J.Siu and S.H.Huang, Sequential design metod for multivariable decoupling and multiloop PID controllers, 998, Industrial & Engineering Cemistry Researc, Vol. 37, pp [4] W.Tan, J.Z. Liu and P. K. S. Tam, PID tuning based on loop-saping control. IEEE proceedings on Control Teory and Applications, 998, 45(4), pp [5] M.Zuang and D.P Aterton, PID controller design for a TITO system, IEEE Proceedings on Control Teory and Applications, 994, 4, pp -0. [6] Jerry M.Mendel, New results about te centroid of an interval type- fuzzy set, including te centroid of a fuzzy granule,information Sciences,7: , 007. [7] Oscar Castillo, Systematic design of a stable Type- Fuzzy logic controller, Journal of Applied Soft Computing, Elsevier, Volume 8 Issue 3, 008, Pages [8] H. Wu and J. Mendel, Uncertainty bounds and teir use in te design of interval type- fuzzy logic systems, IEEE Transactions on Fuzzy Systems, vol. 0, pp , Oct. 00.

6 [9] D. Wu and W. Tan, Type- FLS modeling capability analysis, Proceeding of te 005 IEEE International Conference on Fuzzy Systems, pp. 4 47, Reno, USA, May 005. [0] Hani Hagras, Type - FLCs: a new generation of Fuzzy Controllers, IEEE Computational Intelligence Magazine 007. [] DeepaTangavelusamy and Laksmi Ponnusamy, Study and comparison of PI controller tuning tecniques using Bacteria Foraging and Bacteria Foraging based Particle Swarm Optimization International Journal of Electrical Engineering. ISSN Volume 5, Number 5 (0), pp [] R.Suja Mani Malar and T.Tyagarajan, Modeling of Quadruple Tank System Using Soft Computing Tecniques, European Journal of Scientific Researc, Vol. 9 No., pp ,