Research Article International Journal of Current Engineering and Technology EISSN 77 46, PISSN 347 56 4 INPRESSCO, All Rights Reserved Available at http://inpressco.co/category/ijcet Design of Model Reference Self Tuning Mechanis for PID like Fuzzy Controller N. J. Patil Ȧ* Ȧ Instruentation Engineering, D. N. Patel College of Engineering, Shahada, Dist Nandurbar, India Accepted 4 March 4, Available online April 4, Vol.4, No. (April 4) Abstract This paper presents a ethod for tuning the scaling factors of PID type fuzzy controllers. The ethod tunes the input scaling factor related to change in error and the output scaling factor related to integral output of PID type of fuzzy controller using odel error, error between reference odel and process. Fuzzy Controller used is typical fuzzy PID type of controller in which the scaling factors are set at their initial values using classical approach. An adaptive echanis block based on odel error is added in the classical fuzzy controller. This block tunes one input scaling factor and one output scaling factor based on function of odel error. The algorith is tested on the second order plus delay tie processes. The results are copared with other ethods such as PID, classical FLC and tuning ethod based on relative rate observer. The ipact of the present ethod is checked using both graphical and analytical criteria. Keywords: Fuzzy, PID, Self Tuning, Tie Delay,.. Introduction Fuzzy Logic controllers are ostly used for process control applications where the syste is coplex or shows a nonlinear behavior. After the first application of fuzzy control algorith, fuzzy logic is applied quite often in ost of the control probles. Although fuzzy controller application was successful copared to classical controllers, the design procedure is dependent on the experience and knowledge of the operator and it has liitation of using heuristic rule base (E. Madani, 974). In literature, various types of fuzzy PID (including fuzzy PI and fuzzy PD) controllers have proposed. The PID type controllers have structures analogous to the conventional PID controller (Z. Woo et al, ). Fuzzy PI type control is ostly used because of the liitation of fuzzy PD type controller such as steady state error proble. Fuzzy PI controller also has disadvantage of showing poor perforance in case of higher order systes due to internal integration operation (J. Xu et al, ). For Fuzzy PID controller three diensional rule table is needed which akes the design ore coplex. So cobination of fuzzy PD and fuzzy PI is used to iprove the perforance (M. Golob, ; M. Guzelkaya, ; R. Mudi and N. Pal, ; O. Karasakal, 5). The PID type FLC can be fored either by using a cobination of one PI and one PD type FLC with two different rule base given in or by using one PD type FLC with an integrator and suation unit at the output presented in (S. Chopra et al, 8; H. Li and H. Gatland, 996). The design paraeters of fuzzy controller are classified as (M. Guzelkaya et al, 3): *Corresponding author: N. J. Patil () Structural paraeters, () Tuning Paraeters First type of paraeters covers input /output variables to fuzzy inference, fuzzy linguistic sets, ebership functions, fuzzy rules, inference echanis and defuzzification echanis. Second category includes input/ output scaling factors, and paraeters of ebership functions such as centre of ebership functions etc. Generally first types of paraeters are selected during offline design while the others can be calculated during online adjustents of the controller to iprove the perforance of process. A nonadaptive fuzzy controller is one in which these paraeters do not change once the controller is being used online. If any one of these paraeters is altered online, controller is called as adaptive fuzzy controller. Adaptive Fuzzy controller that odifies the rules is called self organizing controllers and fuzzy controllers in which scaling factors are odified are called self tuning controllers (D. Drainkov et al, 993). A class of self organizing controller is discussed in literature of Xu called as fuzzy learning controllers (L. Zhen and L. Xu, ). In this paper, we will use fuzzy PID type controller fored using one PD type FLC with an integrator at the output. In this type of FLC nuber of scaling factors required is decreased as copared to the structure of cobination of PI and PD type FLC having two different rules base. There are different tuning ethods are presented in previous literature (C. Tseng, 6; P. Mary and N. Mariuthu, 9, D. Seborg et al, 5). Here a odified ethod is presented for tuning the scaling factors of PID type FLC. This new ethod adjusts the input scaling factor related to change in error and output scaling 585 International Journal of Current Engineering and Technology, Vol.4, No. (Feb 4)
N. J. Patil Design of based Self Tuning Mechanis for PID like Fuzzy Controller for Tie Delay Systes factor related to integral coefficient in siilar anner to the ethods given in (P. Mary and N. Mariuthu, 9, D. Seborg et al, 5). Rest of the paper is organized in following sections. In section presents tuning echanis based on odel error for scaling factors. In section 3 coparative results using tuning echanis with conventional PID, classical PID, self tuning fuzzy fro previous literature are given. Conclusions on the proposed ethod are given in section 4.. Model Reference Self Tuning Fuzzy PID Controller The fuzzy PID controller used for this work is shown in Fig.. The output of fuzzy PI and PD controller is given by (Z. Woo et al, ) U ( U(k ) ΔU( FPI U ( GCU Δu( FPD Where U FPI ( and U FPD ( are output fuzzy PI and fuzzy PD controller, GCU is scaling factor for fuzzy PD controller, u( is output of fuzzy controller. r( Z e( GE E( u( GU FLC ce( GCE CE( GCU u( U Z UPD ( U PI ( U PID( PROCESS Fig. PID like Fuzzy Controller (Z. Woo et al, ) Inputs of fuzzy controller are scaled using scaling factors also known as fuzzy gains as: E( GE e( ; CE( GCE ce(; ΔU( GU Δu( Where e(, ce(, GE, GCE are error, change in error and scaling factor related to error and change in error respectively. The output of fuzzy PID controller is given as U ( U ( U ( FPID FPI FPD U(k ) ΔU( GCU Δu( U(k ) GU Δu( GCU Δu( f(ge,gce,gu,gcu) The tuning of scaling factors related to integral coefficient, GU and derivative (change in error) coefficient, GCE has ore effect on the perforance of the syste. Here we introduce a reference odel in structure of fuzzy controller to generate odel error given by e y y p (4) () y p ( () (3) y ( represents the desired perforance and e ( represents the difference between actual process value and expected value of output. By considering the fact we will use the following ethod and define the factors as functions of error as follows: f e ( ) k (5) e where α i, β i are constant values. These constants are needed due to initial and interediate conditions. When odel error is iniu or zero i.e. e ( = eans y p ( = y ( then, f () (6) ) For positive odel error, e ( > eans y p ( < y ( then the above equation becoes, f ( ) ) For positive odel error, e ( < eans y p ( > y ( then the above equation becoes, f ( ) ) The basic idea of tuning the scaling factor is to ultiply by aount f( and to the initial tuning values by sall aount to increase or decrease the according value of process output. This will generate the relationship for adaptive echanis as follows GU( GU f (9) GCE( GCE Fro above equation, it is observed that we are aking the two scaling factors function of odel error. This will force the overall syste to behave like a reference odel. r( e( GE E( u( GU FLC ce( GCE CE( GCU u( Z REFERENCE MODEL y ( y p ( e ( ADAPTIVE MECHANISM U Z UPD ( U PI ( f( U PID( PROCESS Fig. Model reference self tuning adaptive fuzzy PID controller The function related to integral factor i.e. f( decreases as the odel error decreases while the function related to y p ( (7) (8) 586 International Journal of Current Engineering and Technology, Vol.4, No. (Feb 4)
N. J. Patil Design of based Self Tuning Mechanis for PID like Fuzzy Controller for Tie Delay Systes derivative factor increases i.e. which is directly proportional to GU and GCE thus decreasing GU and increasing GCE and vice versa. The overall block diagra using above tuning schee is depicted in Fig.. It is well known that in PID type controller when the integration factor is weak the syste response will probably slow. But when the integration factor is too strong then it will ake the syste unstable. Fro the above discussion it is said that the response of syste can be fastened to have better rise tie which can be achieved by having large integration and sall derivative at initial stages and to avoid instability and oscillations the factors are reversed in later stages which can be achieved by using relation (9). Values of α, β < as these are scaling factors for error and α, β > as they are constants used for avoiding the situations at initial and positive and negative odel error values. For this study these factors are α =., β =, α =.7, and β =4.5. The equivalent PID and fuzzy control coponents according to (M. Guzelkaya et al, 3) are represented by GE ; K GCE D ; KP GU K ; P K GCU I KP () The ebership functions for error, change in error, and controller output are shown in Figure 3 and rule base used is given in Table. f (E, CE, U) f ( ) and ). 3. There are three possibilities. If process output is sae as odel output y y p i.e. if odel following is perfect then f ( ) ) Go to step 4 If process output is lagging odel output y y p then f ( ) ) Go to step 4 (c) If process output is leading odel output y y p then f ( ) g ( ) Go to next step 4. Update the scaling factors GCE and GU using GCE ( ) GCE ) GU( ) GU f ( ) 5. While in this selection of α i, β i is depends on the initial values of scaling factors (GE, GCE, GU and GCU) coputed using the relations given in eq. () fro PID paraeters. NB NM NS ZE PS PM PB 3. Siulation Results.66.33.33.66 E, CE, U Fig.3 Input Output Mebership Functions (D. Drainkov et al, 993) Table Fuzzy Rule Table (D. Drainkov et al, 993) E/CE NB NM NS ZE PS PM PB NB NB NB NB NB NM NS ZE NM NB NB NB NM NS ZE PS NS NB NB NM NS ZE PS PM ZE NB NM NS ZE PS PM PB PS NM NS ZE PS PM PB PB PM NS ZE PS PM PB PB PB PB ZE PS PM PB PB PB PB Self tuning procedure. Copute odel error e ( using eq. (4) i.e. e y y p.. Generate odel error based adaptation functions This section provides the results of the proposed self tuning ethod copared with PID, classical fuzzy, self tuning schee based on relative rate observer fuzzy logic controller (RROFLC, (M. Guzelkaya et al, 3)) and proposed schee Model Reference Self Tuning Adaptive Fuzzy Controller (MRSTAFC) is given. IAE is used as perforance index. Siulations are done on a second order plus dead tie (SOPDT) process odels with different cobinations of paraeters given in (D. Seborg et al, 5). 3. The reference odel is used to indicate the required perforance which follows desired specifications such as tie constants, gain etc. In this work we used the second order odel with transfer function of the for () (3s s ) Exaple Let us consider second order plus delay tie syste fro Woo s literature (Z. Woo et al, ) 587 International Journal of Current Engineering and Technology, Vol.4, No. (Feb 4)
N. J. Patil Design of based Self Tuning Mechanis for PID like Fuzzy Controller for Tie Delay Systes G( s) e. 5s ( s )(s ) The values of GE, GCE, GU and GCU are,.5, and. respectively. The response with various controllers is illustrated in fig. 4. Analytical coparison for various controllers is given in Table. It is clear that the syste response is better with odel reference self tuning fuzzy controller (MRSTFC) as copared to the other controllers. The sudden set point change applied after the syste is settled at 5 sec to check the robustness. In this case also the response given by MRSTFC is better as copared to the other controllers. Also it is observed that it is tracking the reference odel..4..6. STFC (Woo et. al., ) RROFC (Guzelkaya et. al., 3) 5 5 75.4. STFC (Woo et. al., ) RROFC (Guzelkaya et. al., 3) MRSTFC (Modified ).4. STFC (Woo et. al., ) RROFC (Guzelkaya et. al., 3).6.6...4..6 5 5 75 STFC (Woo et. al., ) RROFC (Guzelkaya et. al., 3). 5 5 Fig. 5 Response for Exaple () Exaple 3 Consider the higher order process with transfer function 7 3 ( s )( s 3) 3.. Fig.4 Response for Exaple () Exaple Consider the second order plus dead tie process with repeated roots es (s ) 5 5 The initial fuzzy settings are obtained as GE, GCE, GU and GCU are, 5,.43 and.54 respectively. The perforance with various controllers is illustrated in fig. 5. It is observed that the perforance of the self tuning adaptive fuzzy controller is better than the other ethods. The initial fuzzy settings are obtained as GE, GCE, GU and GCU are,,.38 and.68. The perforance with various controllers is illustrated in fig. 6. It is observed that the perforance of the self tuning adaptive fuzzy controller is better than the other ethods. Table Controller Perforance Coparison Process 3 Perforance Index IAE Controller Change in Given Set point Set point FPID.68 4.94 RROFLC.3 3.48 STFC.863 3.63 MRSTFC.34.683 FPID 6.7.6 RROFLC 3.954 7.574 STFC 4.95 9.65 MRSTFC 3.643 6.535 FPID.758 6.458 RROFLC.757 5. STFC.758 4.993 MRSTFC.48 4.37 588 International Journal of Current Engineering and Technology, Vol.4, No. (Feb 4)
N. J. Patil Design of based Self Tuning Mechanis for PID like Fuzzy Controller for Tie Delay Systes.4..6 STFC (Woo et. al., ) RROFC (Guzelkaya et. al., 3) than the classical self tuning fuzzy and other controllers. This ethod ay be extended for tuning of other two factors but it will increase the coplexity of controller rather than iproving results. The other ethod is to use function of change in error instead of using function of error as it gives rate of change of error. This ay iprove the perforance of the overall syste. References. 5 5 75..6.. 5 5 Fig. 6 Response for exaple (3) 4. Conclusions STFC (Woo et. al., ) RROFC (Guzelkaya et. al., 3) In this paper a self tuning ethod based on odel error to tune the coefficients of fuzzy PID controller is proposed. The tuning schee is based on the function of odel error. The scaling factors related to derivative coefficient and integral coefficients are tuned using adaptive echanis to iprove the perforance of the syste. The tuning perfored is online i.e. when the process is running. Due to odel error the adaptive echanis tunes the scaling factors such that the overall syste behaves like a reference odel. It is concluded that ethod for tuning of scaling factors based on odel error function is found efficient Madani E. (974), Application of fuzzy logic algoriths for control of siple dynaic plant, proc. of Institute of Electrical Engineers, (), pp. 585588 Woo Z., Chung H., and Lin J. (), A PID type fuzzy controller with self tuning scaling factors, Fuzzy sets and systes, 5(), pp. 3 36. Xu J., Hang C., and Liu C. (), Parallel structure and tuning of a fuzzy PID controller, Autoatica, 36(5), pp. 673684. Golob M. (), Decoposed fuzzy proportional integral derivative controllers, Applied soft coputing, (3), pp. 4. Guzelkaya M., Eksin I., and Gurleyen F. (), A new ethodology for designing a fuzzy logic controller and PI, PD blending echanis, Journal of intelligent and fuzzy systes, (), pp. 8598. Mudi R., and Pal N. (), A self tuning fuzzy PI controller, Fuzzy sets and systes, 5(), pp. 37338. Karasakal O., Yesil E., Guzelkaya M., and Eksin I. (5), Ipleentation of a New Self Tuning Fuzzy PID Controller on PLC, Int. Journal of Electrical Engineering, 3(), pp. 77 86. Chopra S., Mitra R., and Kuar V. (8), Auto tuning of fuzzy PI type controller using fuzzy logic, International Journal of Coputational Cognition, 6(), pp. 8. Li H., and Gatland H. (996), Conventional fuzzy control and its enhanceent, IEEE trans. on systes, an and cybern. part B, 6(5), pp. 79797. Guzelkaya M., Eksin I., and Yesil E. (3), Self tuning of PID type fuzzy logic controller coefficients via relative rate observer, Engineering applications of artificial intelligence, 6(3), pp. 7 36. Drainkov D., Hellendoorn H., and Reinfrank M. (993), An introduction to fuzzy control, USA, SpringerVerlag. Zhen L., and Xu L. (), Fuzzy learning enhanced speed control of an indirect field control induction achine drive, IEEE Transactions on Control Systes Technology, 8(), pp. 7 78. Tseng C. (6), Model reference output feedback fuzzy tracking, IEEE trans. on fuzzy systes, 4(), pp. 587. Mary P., and Mariuthu N. (9), Design of selftuning fuzzy logic controller for the control of an unknown industrial process, IET control theory and applications, 3(4), pp. 48436. Seborg D., Edgar T., and Mellichap D. (5), Process dynaics and control, Wiley Blackwell, UK. 589 International Journal of Current Engineering and Technology, Vol.4, No. (Feb 4)