EVALUATION AND SELF-TUNING OF ROBUST ADAPTIVE PID CONTROLLER & FUZZY LOGIC CONTROLLER FOR NON-LINEAR SYSTEM-SIMULATION STUDY

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1 EVALUATION AND SELF-TUNING OF ROBUST ADAPTIVE PID CONTROLLER & FUZZY LOGIC CONTROLLER FOR NON-LINEAR SYSTEM-SIMULATION STUDY By Dr. POLAIAH BOJJA Sree Vidyanikethan Engineering College Tiruapti, India and Dr. S.Rominus Valsalam Mr.Abir Raj Methkar Head & Addl. Director Senior Scientist Control & Instrumentation Group Centre for Development of Advanced Computing (CDAC) (A Scientific Society of the Ministry of Communications and Information Technology, Department of Electronics & Information Technology, Govt. of India) Thiruvananthapuram

2 1. Development of dynamic mathematical model Case 1: Conical Tank (Non-Linear system) Case 2: Tool wear mechanism (Non-linear system) 2. To Determine Non-linearity of the system under different conditions 3. Model based Design of Open-loop Control system 4. Model based tuning of Closed-loop PID control system 5. Fuzzy Logic model and Controller design 6.Comparison of Performances of the Controllers

3 CASE1: Conical tank system Many process industries use conical tanks because of its shape contributes to better drainage of solid mixtures, slurries and viscous liquids. Control of conical tank process presents a challenging problem due to its non-linearity and constantly changing cross section area of the tank. 12 April 2013 Department of E.I.E. 4

4 THE NON-LINEAR CONICAL TANK MODEL EQUATIONS: F i n F o u t = A ( h ) d h 1 1 d t tanq= R Cross sectional area of the H tank at any level(h 1 ) A(h 1 )= r2 h1= F b h 1 H2 x x x 1 in 1 π h2 R2

5 Open Loop Response for Conical Tank model X Y Plot P ro c e s s o u tp u t (P V ) Sampling Instants 12 April 2013 Department of E.I.E. 6

6 SIMULATION RESULTS USING PID CONTROLLER FOR CONICAL TANK MODEL CONVENTIONAL CONTROL SYSTEM Set point + - Controller Process Black Box Controlled Variable Set point Steady State Error Time ADVANCED CONTROL SYSTEM Understand and Adapt PROCESS MODEL ESTIMATOR Manipulated Variable Steady State Error Set point + - Controller Process Sensor Set point Estimate Measurement Time

7 Output of the controller Response of the PID Controller for Conical Tank model Sampling Instants 12 April 2013 Department of E.I.E. 8

8 Fuzzy Logic Controller Fuzzy Logic is successfully used in today's process control systems Fuzzy logic fills an important gap in engineering design methods left by mathematical and logic-based approach Fuzzy design can accommodate the ambiguities of human languages and logics Fuzzy logic provides both an intuitive method for describing systems in human terms and automates the conversion of those system specifications into effective models 12 April 2013 Department of E.I.E. 9

9 Block Diagram of FUZZY LOGIC CONTROLLER (FLC) Crisp Values Fuzzifier Inference Engine Defuzzifier Crisp Values Membership Functions Fuzzy (IF THEN) Rules Fuzzy Variables Linguistic Variables 12 April 2013 Department of E.I.E. 10

10 Fuzzification of Input variables INPUT VARIABLES ERROR CHANGE IN ERROR FUZZY SUBSETS N,Z,P N,Z,P MEMBERSHIP FUNCTION Triangular MF Triangular MF 12 April 2013 Department of E.I.E. 11

11 The triangular curve is a function of a vector, x, and depends on three scalar parameters a, b, and c, as given by b a c The parameters a and c locate the "feet" of the triangle and the parameter b locates the peak. 12 April 2013 Department of E.I.E. 12

12 Fuzzification of Output variables FOR OUTPUT VARIABLE Output Variable : Fuzzy logic Controller output, m(t) Fuzzy Subsets : VL,L,M,H,VH Membership function : Singleton Membership Function A singleton is a Fuzzy set whose membership function is equal to one at one point and equal to zero at all other points. Singletons are special membership functions used for outputs in order to simplify the defuzzification 12 April 2013 Department of E.I.E. 13

13 RULE BASE Change in Error Error N Z P N VL L L Z M M M P H H HH 12 April 2013 Department of E.I.E. 14

14 DEFUZZIFICATION If the membership functions of the output values are singletons, the calculation is given by COG. Center of gravity method where a i are the singleton values of the individual rules. 12 April 2013 Department of E.I.E. 15

15 Out put of Fuzzy Logic Controller for Conical tank model TIME (Sec) 12 April 2013 Department of E.I.E. 16

16 TABLE: PERFORMANCE CRITERIA OF THE APPROACH CONTROLLERS FOR CONICAL TANK MODEL Type of Controller Set point for Conical tank Settling Time (sec.) ISE IAE Conventional Controller (PI Control) Fuzzy Logic Controller April 2013 Department of E.I.E. 17

17 By comparing the responses of open-loop controller and PID controller with Fuzzy Logic Controller It is observed that there is an improvement in settling time and values of ISE & IAE. It is concluded that the Fuzzy Logic controller is the best suitable for Conical tank model than PID controller 12 April 2013 Department of E.I.E. 18

18 CASE 2: FLOW DIAGRAM FOR THE PROPOSED TOOL WEAR MECHANISM Empirical model Developments of Dynamic mathematical model for Tool Wear Design of PI Controller Simulation Studies And controller of Flank wear Design the Tuning of PID controller using NN & Fuzzy logic controller Simulation Studies And controller of Flank wear Comparison of Controllers of dynamic models for Non-Linear Tool Wear Model

19 NON-LINEAR TOOL WEAR MODEL What is Tool wear: during any machine process the tool is subjected to 3-distinct factors( force, temp, cutting speed.,) Types of tool wear 1.Face wear The face of the tool is the surface over which the chip passes during its formation. The wear takes the form of a cavity or crater wich has its origin not along the cutting edge.

20 2.Flank wear the flank wear is the clearance Face of the cutting tool, along Which the major cutting edge is Located. 3. Nose wear Its part of the flank wear, some times proceeds at a faster rate than flank wear.

21 Cutting conditions Experiment conditions for metal cutting process Cutting Speed(v) and 250,740 and 1150 rpm and Work piece Feed rate(f) and Depth of Cut(d) 1.07 m/rev 0.5,0.8 and 1.0 mm Al+10% of Sicb Particulate reinforced Composite material Cutting Tool K10 Cement Carbide

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23 THE NON-LINEAR FLANK WEAR MODEL EQUATIONS: * W f 1 = V l o c W f 1 + V l o c K F F c fa cos( α r ) * W f 2 c = K D o V F = F + F c ( K r) exp ac 273 w W A e + θ f ( n1 = K4 f 1 5α K6 KVc )a o 7 f Tool wear W f is the sum of two components of the flank wear W f1 and W f2 θ f = n2 n3 K 9Vc f + where K T,K 9,K 10,n 2,n 3 and n 4 are the model parameters, depending on the cutting conditions and tool work piece combination K 10 W f n4

24 Lo αr Kf Kd Ac -K e K5 K6 K7 Cw Kg K n 1 n2 n 3 n

25 Fig: Open Loop Response for Tool Wear model The transfer function of the model is given by: G(s)=0.0041/4.85S+1 Table:P1 controller parameters for Tool wear model: K c T i(sec)

26 SIMULATION RESULTS USING CONTROLLER FOR TOOL WEAR MODEL

27 SIMULATION AND EXPERIMENTAL RESULTS TUNING OF PID CONTROLLER BY NN FOR NON-LINEAR SYSTEM (TOOL WEAR MODEL) THE METHOD USING A BACK PROPAGATION Neural Net IS PROPOSED TO REALISE THE REAL TIME SELF TUNING OF PID CONTOLLOR. THE COMPUTER SIMULATIONS&EXPERIMENT TO THE NON-LINEAR PLANT (TOOL WEAR MODEL). THE ZIEGLER-NICHOLS OF SYNTHSIS TUNING FORMULA IS BASED ON THE EMPIRICAL KNOWLEDGE OF ULTIMATE GAIN (Ku)&ULTIMATE PERIOD(Tu) AS SHOWN IN TABLE. PROPORTIONAL GAIN PID PI Synthsis method(pi Kp=0.6 Ku INTEGRAL TIME Ti=0.5 Tu DERIVATIVE TIME Td=0.125 Tu Kp=0.45Ku Kc=To/Kp tc Ti=0.85 Tu Ti=To

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30 SIMULATION RESULTS USING NEURAL NETWORK BASED ON SELF-TUNING OF PID CONTROLLER (Neuro PID Control)

31 THE PROPOSED METHOD USING NEURAL NET HAS BEEN VERIFIED BY ADJUSTING THE PARAMETER VALUES OF PID CONTROLLER, IT GIVES SMOOTH PLANT OPERATION.AS SHOWN IN FIGURE BELOW

32 FLANKWEAR(mm) TIME(Sec.) Response of NeroPID control (S.p=0.06) INPUT OF THE CUTTING SPEED FLANKWEAR(m/sec) TIME (Sec.) Output of Neuro PID (I/ P to the plant)

33 0.2 FLANK WEAR(mm) TIME(Sec.) Response of NeroPID control (S.p=0.1) INPUT OF THE CUTTING SPEED FLANKWEAR(m/sec) TIME (Sec.) Output of Neuro PID (I/ P to the plant)

34 SIMULATION RESULTS USING FUZZY LOGIC BASIS FUNCTION OF PID CONTROLLER

35 Response of FLC PID Controller (set point =0.06) Output of FLC (input to the Plant)

36 Response of FLC PID Controller (set point =0.1) Output of FLC (input to the Plant)

37 Type of controller Set point for flank wear SETTLING TIME(Sec.) % OF OVER SHOOT ISE IAE PI NEURO PID FLC

38 CONCLUSION By comparing the responses of Neuro PID and FLC controller with PI controller controller It is observed that there is an improvement in settling time and percentage of overshoot. It is concluded that the FLC and Neuro PID controller are the best suitable for tool wear control than PI control

39 PUBLICATIONS Mr.Polaiah Bojja Mr.Abraham Dr.S.Vardarajan Dr.M.N.Giri Prasad Experimental Comparison of Adavance Control Strategies Which Uses pattern recognition Technique for Non-Linear System proc. IEEE Trans on Computer comp, Feb 2010, PP: Polaiah Bojja, Abraham, S.Vardarajan,.M.N.Giri Prasad Neural Network Based Self-Tuning Of PID Controllers Which Uses Pattern Recognition Technique For Nonlinear System i-manager's Journal on Future Engineering and Tech.,Vol.5, No.2, Nov 09-Jan 2010, PP:25-3[ISSN: ] Polaiah Bojja, Abraham, S.Vardarajan,.M.N.Giri Prasad Self-Tuning Of Robust PID Controller Using Neural Network & Fuzzy Logic Controller For Non-Linear System-Simulation Study Intr. Journal of Systems and Technology(IJST), Vol.3, No.1, June July 2010, [ISSN: ].

40 Polaiah Bojja, Abraham, S.Vardarajan,.M.N.Giri Prasad Evaluation and Development of Advance Control Strategies Which Uses Pattern Recognition Technique for Nonlinear System" Int. Jr. Compute and Technology Engineering, December Y.KOREN, Flank Wear Model of Cutting Tools Using Control theory, Journal of Engineering for Industry, Vol:1., 1978, p Saiful Akhyar and Sigery Omatu Self-Tuning PID Control by Neural Networks,Proce. Of 1993International Joint Conference on Neural Networks, p Prof. C.C.Teng, A Surgey of PID controller Design Based on Gain and Phase Margins, Inter. Journal of Computational Cognition,2004,Vol.No:2,No:3, pages

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