Control Systems of a Non-stationary Plant Based on MPC and PID Type Fuzzy Logic Controller

Transcription

1 Proceedings o the International MltiConerence o Engineers and Comter Scientists 2016 Vol I,, March 16-18, 2016, Hong Kong Control Systems o a Non-stationary Plant Based on MPC and PID Tye Fzzy Logic Controller Igor S. Nadezhdin, Alesey G. Gorynov, Flavio Manenti, Anton O. Ochoa Bie Abstract Tyically, rocesses taing lace in modern indstrial lants have signiicant nonlinearity. To control so comlex dynamic rocesses sed atomatic control system (ACS) based on zzy logic s (FLC) or on the basis o a redictive model s (MPC). In this aer are comared the systems o atomatic control with dierent reglators (zzy PID reglator and MPC reglator), i introdced into the system o dierent distrbing inlences. Index Terms model redictive control, zzy logic, PID, control system. C I. INTRODUCTION rrently in the indstry, at any stage o rocessing o the material / sbstance there is a high level o atomation. The se o atomatic control systems o rodction rocesses is done in order to imrove the saety o the technological rocess, as well as imrove the economic erormance o lants and rodction as a whole. As a rle, the majority o technological rocesses (lants), occrring today in the indstry, is a comlex dynamic objects. Comlex dynamic systems are objects with nonlinear static characteristics, that is, objects that are described by dierential eqations with time-varying arameters. Exerience has shown that control o sch lants by means o traditional PID s does not rovide the reqired qality control. In order to imrove the eiciency o atomatic control system o comlex dynamic objects, researchers arond the world, doing research, trying to combine the standard PID reglator with zzy adative [1, 2]. Crrently, Manscrit received December 6, 2015; revised Janary 22, This wor was nded as art o the Federal government-sonsored rogram «Science» by Toms Polytechnic University. I. S. Nadezhdin is with the National Research Toms Polytechnic University, Institte o Physics and Technology, Deartment o Electronics and Atomation o Nclear Plants, Rssia, Toms, Lenina St 30, (corresonding athor to rovide hone: ; n9@list.r). A. G. Gorynov is with the National Research Toms Polytechnic University, Institte o Physics and Technology, Deartment o Electronics and Atomation o Nclear Plants, Rssia, Toms, Lenina St 30, ( alex1479@t.r). F. Manenti is with the Politecnico di Milano, Det. di Chimica, Materiali e Ingegneria Chimica Gilio Natta, Italy, Milano, Piazza Leonardo da Vinci, 32, ( lavio.manenti@olimi.it). A. O. Ochoa Bie is with the National Research Toms Polytechnic University, Institte o Physics and Technology, Deartment o Electronics and Atomation o Nclear Plants, Rssia, Toms, Lenina St 30, ( anthonob@t.r). there are dierent tyes o zzy s, bt the zzy based PID reglators are the most common [3, 4]. As a rle, setting a zzy is made based on the Mamdani. In this, the Mamdani is located directly in the control channel, as shown in the aers [5, 6]. For this research sing zzy PID reglator resented in this aer [7], bt withot the rocedre o identiication o arameters o the control lant. The distingishing eatre o this zzy PID is that in him sing exert grade determined coeicients PID reglator. Also, recently, or the control o comlex dynamic objects are widely sed s on the basis o a redictive model [8, 10]. For the synthesis o sch a reglator is necessary to mae a mathematical model o the control lant. Using a mathematical model o the control lant, reglator is to redict changes in the controlled variable or a certain eriod o time ahead and calclate the otimal control action, to rovide the best trajectory o the controlled variable. The rose o this aer is the comarative analysis o atomatic control systems with PID reglator based on zzy logic and reglator on the basis o a redictive model (MPC). In this case system will be introdced stewise distrbing inlences are not nown magnitde and dration. A. Control lant II. THEORETICAL PART Since in the aer discssed atomatic control system or a comlex dynamic control lant, the arameters o sch an lant can be changed dring the rocess. At the initial time control lant is described by the transer nction o the irst order (1). The dynamics o the control lant is described as a linear system with the transer nction W (s) that reresents channel and the transer nction W (s)that stand or channel : s W ( s) e, T s1 W ( s) e T s1 s In crrent o rocess, when switching lant rom one mode to another or when changing characteristics o the (1)

2 Proceedings o the International MltiConerence o Engineers and Comter Scientists 2016 Vol I,, March 16-18, 2016, Hong Kong material (eedstoc) may vary the order o the transer nction, which describes the control object on the control channel W (s). In or case the dynamics o the control lant is described by the ollowing transer nctions: W ( s) s e, T1 s 1 T2 s 1 T3 s 1 W ( s) e T s1 s In addition to changing the arameters o the control lant in crrent o technological rocess in the system introdced stewise distrbing inlences o nnown magnitde and dration. B. The atomatic control system with adative zzy PID A roosed atomatic control system with zzy PID is shown in Figre 1. g ε Adative zzy Fig. 1. Adative zzy atomatic control system P Control lant P (2) y minimizing a nctional which lays the ey role rom the viewoint o the design o adative and otimal control systems. It is addressed here in the ollowing orm: min Je J Jn (3) where Je J he 2 j j he 1 h 2 j j h 1 Jn the nmber o control error oscillations in the interval he, (4). where = 1,2,, j the control error, j the control action, he the control error interval, h the control interval, j the index o time samling. For the calclation o arameters o the PID reglator is sed Mamdani with zzy rles, obtained by minimizing the nctional (3). C. The atomatic control system with MPC The atomatic control system with MPC is similar atomatic control system with adative zzy (Figre 3). (4) (5) Deicted in Figre 1 the variables have the ollowing meanings: g set oint; measrable distrbance; control action; P lant control channel; P lant distrbance channel; y controlled variable; control error is deined as = g y. Let s consider in more detail the adative zzy reglator, resented in Figre 1. Scheme adative zzy is shown in Figre 2. P Control lant g ε МРС P Fig. 3. The atomatic control system with MPC y Jn Je,T, t Fzzy rles base generator Adator-otimizer J Strctral sheme o MPC is shown in Figre 4. The strctre o the reglator incldes: a redictive model and ower otimization. ε Bloc otimization y* ε r,t i, T d PID Predictive model (a rocess model) Fig. 2. Adative zzy Adative zzy reglator consists o the ollowing blocs: a zzy rles base generator, a Mamdani zzy ott and Jn, Je and J terms calclation engines. The otimization roblem consists o maximizing or Predictive Fig. 4. Strctral scheme o MPC Main idea o model redictive control can be reresented

3 Proceedings o the International MltiConerence o Engineers and Comter Scientists 2016 Vol I,, March 16-18, 2016, Hong Kong ollowing manner: there are control action (t) and y(t) controlled variable, g(t) is the desired vale (deendence) changes in the controlled variable. Consider a system in discrete time, it is only in moments o time t= ΔT, where ΔT some samling eriod, and some integer. For convenience the grahical reresentation we will consider ΔT=1. The main eatre o model redictive control is a mathematical model o the control lant, which accrately describes its behavior. Availability o an adeqate mathematical model o control lant allows to redict the vale o the controlled variable to a certain nmber o stes orward (Figre 5). y(t) The ast g(t) Crrently Horizon rediction yt () Ftre Horizon control t where: Q and R weighting coeicients, the nmber o cycles on which bild the rediction o the behavior o the controlled variable y(t) (rediction horizon), m the length o the seqence o tre vales o the control action (t) (horizon control). Ater eeding by at control lant o the irst element calclated the otimal seqence the control action (t), at the next cloc cycle the whole rocedre is reeated again, taing into accont the the newly received inormation. So is nctioning reglator with a redictive model. III. RESULTS OF EXPERIMENTAL RESEARCH Described beore atomatic control system with dierent s have been imlemented in MATLAB/Simlin. To conigre zzy PID reglator in atomatic control systems (Figre 1) have been deined arameters control lant described by the transer nction o the irst order (1). For the synthesis o reglator with model redictive is sed the transer nction o the irst order (1), with the same arameters as or setting zzy PID reglator. In both atomatic control systems imose restrictions on the control action. At a certain moment in time has been set a desired vale or the controlled variable (setoint). The reslting setoint the transient rocesses shown in Figre 6. (t) Fig. 5. A grahical reresentation o the idea o model redictive control t The vales o the controlled variable y(t), redicted at some time t, in Figre 5 are designated ollowing manner yt (). Horizon rediction is bilt on a certain nmber o cloc cycles. The rojected trajectory o the controlled variable will deend on the tre vales o the control action (t). Essence o method consists in inding a seqence o vales o the control action (t), which will rovide the best rojected trajectories or the controlled variable y(t). The seqence length o the calclated control actions (t) is a ixed qantity and is called the horizon control. The seqence o vales o the control action is determined by solving a roblem o otimization. Choosing the best trajectory the controlled variable is determined by indicators o qality control. The aer is sed the qality indicators, which contains the sqare error between the redicted controlled variable control lant y(t) and the desired trajectory (set oint) g(t). When choosing the otimal vales o the control action (t), reglator sees to minimize the nctional sbmitted by exression o the orm: Fig. 6. The transient rocesses or set oint As can be seen rom o transient rocesses (Figre 6), both the atomatic control systems derive controlled variable to a redetermined level. Time control o the atomatic control system with zzy PID totaled 0,036 hors (128.9 seconds), bt with the MPC hor (34 seconds). Overshoot atomatic control system with zzy PID was 7.8 %, and the control system with MPC- came ot on a redetermined level withot overshoot. Also or o transient rocesses resented in Figre 6 it was calclated qadratic integral criterion (QIC) rom the ollowing exression: m1 2 2 (6) J Q y i r i R i i1 i0 t2 QIC g( t) y( t) dt t1 2 (7)

4 Proceedings o the International MltiConerence o Engineers and Comter Scientists 2016 Vol I,, March 16-18, 2016, Hong Kong Calclation reslts are shown in Table 1. TABLE I INTEGRAL QUALITY INDICATORS Reglator Fzzy PID Qadratic integral criterion 1, МРС 7, Ater analyzing the qality indicators can be seen that best the transition rocess or set oint system atomatic control with MPC rovides. Then, at time 0.14 hors, the system been introdced 30% stewise distrbance. The obtained the transient rocesses are resented in Figre 7. Analyzing the obtained vales o the indicators qality o transient rocesses can be conclded that the zzy PID is a little better comensate the distrbance. Then at time 0.28 hors been introdced 50 % stewise distrbance, and changed the order o the transer nction describing the object on the control channel rom the irst to the third order (2). At moment in time 0.38 hors, been introdced one more 50% o the ste wise distrbance, while controlled variable is not yet stabilized. The obtained in reslt this extremal distrbance the transient rocesses are resented in Figre 8. Fig. 8. The transient rocesses or 50% o a ste distrbance and changing the arameters o the control lant Fig. 7. The transient rocesses or 30% o a ste distrbance For o transient rocesses (Figre 7) were identiied qality indicators o transient rocesses atomatic control system or the distrbing inlence. Time control o atomatic control system with zzy PID was hors (99 seconds), and with MPC reglator hor ( seconds). To estimate the maximm deviation o the controlled variable rom the steady-state vale calclated relative maximm deviation sing the ollowing exression: y g max 100[%] (8) where y max the maximm deviation o the controlled variable, g setoint or the controlled variable. Calclation reslts are shown in Table 2. Also or o transient rocesses resented in Figre 6 it was calclated qadratic integral criterion (QIC) sing the exression (7). TABLE II QUALITY INDICATORS TRANSIENT PROCESSES Reglator Fzzy PID The relative maximm deviation, σ (%) Qadratic integral criterion 9,48 1, МРС 8,92 1, For obtained transient rocesses (Figre 8) were also identiied qality indicators transient rocesses. Time control o atomatic control system with zzy PID was hor (858 seconds) and with the MPC hor (1021 seconds). Calclated relative maximm deviation o the controlled variable rom the setoint according to the exression (8), as well as to determine the qadratic integral criterion (QIC) o transient rocesses sing the exression (7). Calclation reslts are shown in Table 3. TABLE III QUALITY INDICATORS TRANSIENT PROCESSES Reglator Fzzy PID The relative maximm deviation, σ (%) Qadratic integral criterion 50,68 1, МРС 50,22 1, From the obtained indicators o qality o transient rocesses it is obvios that better comensate or distrbing inlences atomatic control system with zzy PID. At moment in time 0.83 hors in the system been introdced 30 % o the distrbance, while lant on the control channel described transer nction by the third order. Becase both s have been conigred to the control lant o the irst order, the qality o control deteriorated somewhat comared with the exerience shown in Figre 6. The obtained the transient rocesses are shown

5 Proceedings o the International MltiConerence o Engineers and Comter Scientists 2016 Vol I,, March 16-18, 2016, Hong Kong in Figre 9. Fig. 9. The transient rocesses or 30% o a ste distrbance and the new arameters o control lant As seen in Figre 9, obtained the transient rocesses characterized by the resence o oscillations o the controlled variable. For reresented o the transient rocesses determine the direct indicators o qality. Time control o atomatic control system with zzy PID was hor (704 seconds) and with the MPC was hor (379 seconds). Similar to revios exeriments, calclated relative to the maximm deviation o the controlled variable rom the set oint sing the exression (8), as well as to determine the qadratic integral criterion (QIC) o transient rocesses sing the ollowing exression (7). Frthermore, in order to evalate the oscillatory transient rocesses was calclated degree o daming vibrations according to the ollowing exression: А A А 1 2 (9) 1 where: А 1 and А 2 amlitde two adjacent vibrations directed in the same direction. Calclation reslts are shown in Table 4. TABLE IV QUALITY INDICATORS TRANSIENT PROCESSES Reglator The relative maximm deviation, σ (%) Qadratic integral criterion The extent o daming, ψ Fzzy PID МРС 16,62 16,26 1, , ,48 0,72 The calclated qality indicators o transient rocesses (Figre 9) nmerically conirm that the atomatic control system with the MPC has a mch better qality control. IV. DISCUSSION OF THE RESULTS Comaring the transient rocesses shown in Figres 5-8 and analyzing qality indicators calclated or these o transient rocesses deine the that rovides the best qality control. In the derivation o the controlled variable to a redetermined level the best indicators qality o transient rocesses rovides the control system with MPC. When sing the MPC is no overshoot o the controlled variable (Figre 5), and the time reglation is 3.8 times less than sing zzy PID. However, when in a system occrs 30% o stewise distrbance the transient rocesses were obtained (Figre 7) which show that time reglation o zzy PID reglator in 1.15 times less than sing the MPC, as well as the qadratic integral criterion is 1.1 times less. Bt a relative maximm deviation when sing the zzy PID reglator more is 1.1 times. As can be seen, the control system with the zzy PID rovides the transient rocesses with the best qality indicators. Then, in the system been introdced 50% o the distrbance, and change the arameters o the control lant and the order o the transer nction, which describes the lant on the control channel with irst order or a third (2). According to the obtained the transition rocess (Figre 8) determined that the control system with the zzy PID rovides is 1.2 times less time reglation, bt has by 0.5 % more relative maximm deviation. Qadratic integral criteria calclated or o transient rocesses (Figre 8) are resented in Table 3, and they do not dier signiicantly. In this case, the control system with zzy PID slightly better lills distrbing inlences. Then or control lant with new arameters o been introdced 30% o the distrbance. From the resented in Figre 9 o transient rocesses determined that the control system with the MPC rovides the best qality indicators (Table 4). Time reglation control system with MPC is 1.86 times less than that the control system with the zzy PID. As well as a relative maximm deviation is 1.02 times less and qadratic integral criterion is 1.37 times less. In addition, the MPC rovides is 1.5 times higher degree o daming o oscillations controlled variable than the zzy PID. Ths, by comaring and analyzing the reslts obtained when modeling o atomatic control system with two dierent s (zzy PID and MPC ), can not be selected any single. Searately, let s note advantages and disadvantages o the sed s. The advantages o the considered zzy PID reglator is the ossibility its realization sing standard indstrial comonents. For this reqires a PID and indstrial, in which DLL library will be imlemented adater otimizer. The need to in accrate and adeqate mathematical models o the control lant is ossible to carry to the disadvantages o the MPC. The irst is not always ossible to mae an adeqate mathematical model o the

6 Proceedings o the International MltiConerence o Engineers and Comter Scientists 2016 Vol I,, March 16-18, 2016, Hong Kong control lant and secondly, than more comlex mathematical model o control lant, the more comting ower is reqired to imlement the MPC. V. CONCLUSION This aer devoted to the synthesis and comarison o atomatic control systems with zzy PID with MPC. When comaring the qality indicators obtained transient rocesses, ailed to mae an nambigos choice in avor o one o the comarable reglators. Noted advantages and disadvantages the considered reglators. ACKNOWLEDGMENT This wor was nded as art o the Federal governmentsonsored rogram «Science» by Toms Polytechnic University. REFERENCES [1] M. Gzelaya, I. Esin, E. Yesil, Sel-tning o PID-tye zzy logic coeicients via relative rate observer, Engineering Alications o Artiicial Intelligence, Vol. 16, , [2] N. Siddiqe, Fzzy control, Stdies in Comtational Intelligence, Vol. 517, , [3] A. Fereidoni, M.A.S. Masom, M. Moghbel, A new adative conigration o PID tye zzy logic, ISA Transactions, Vol. 56, , [4] L. Y. Ang, F. A. Jaar, Simlation analysis o non-linear zzy PID temeratre, Alied Mechanics and Materials, Vol , , [5] I. Eer, Y. Torn, Fzzy logic control to be conventional method, Energy Conversion and Management, Vol. 47, , [6] I. Pana, S. Dasa, A. Gta, Tning o an otimal zzy PID with stochastic algorithms or networed control systems with random time delay, ISA Transactions, Vol. 50, , [7] F. Manenti, F. Rossi, A. G. Gorynov, V. F. Dyadi, K. A. Kozin, I. S. Nadezhdin, S. S. Mihalevich, Fzzy adative control system o a non-stationary lant with closed-loo assive identiier, Resorce- Eicient Technologies, vol. 1, , Jl [8] F. Manenti, Considerations on nonlinear model redictive control techniqes, Comters and Chemical Engineering, vol. 35, , [9] D. Jolevsi, O. Bego, Model redictive control o gantry/bridge crane with anti-sway algorithm, Jornal o Mechanical Science and Technology, vol. 29, , [10] M. Nayhose, A. Tran, J.S.I. Kwon, M. Crose, G. Orolas, P.D. Christoides, Modeling and control o ibroen crystal growth and size distribtion, Chemical Engineering Science, vol. 134, , 2015.