2 DOF Fuzzy Gain-Scheduling PI for Combustion Turbogenerator Speed Control

Transcription

1 DOF Fuy GanSchedulng PI for Combuston Turbogenerator Speed Control Arnulfo odrguemartne*. aul Gardunoamre** *Dvson of Control Systems, Insttute of Electrcal esearch, Cuernavaca, Morelos 690 Mexco (emal: **Dvson of Control Systems, Insttute of Electrcal esearch, Cuernavaca, Morelos 690 Mexco (emal: Senor Member IEEE Abstract: Ths paper presents to realatons a DOF PI fuy ganschedulng controller for derange speed control of combuston turbogenerators. The DOF scheme allos ndependent tunng of the reference trackng and the dsturbance rejecton characterstcs for the controlled system. Then, the fuy approach extends these characterstcs all over the operatng space of the combuston turbogenerator. Both realatons can be nserted nto the speed control loop of exstng control systems thout degradng performance. Once n the loop, the controllers can be progressvely tuned onste, based on the nspecton of speed responses. The proposed DOF PI fuy ganschedulng control schemes are sutable for applcaton on actual combuston turbogenerators. Keyords: Combuston turbogenerator, DOF control schemes, Ganschedulng, speed control, Fuy systems.. INTODCTION Noadays, poer generaton by means of combuston turbogenerators (CTG) plays a major role orldde. Also, most poer plants to be bult n the next 0 years ll be combnedcycles based on CTGs due to ther advantages over other technologes. Advantages nclude lo commssonng, lo mantenance and operaton costs per unt of poer, fast startup and response to load change, capablty to use dverse fuel (desel, ol and bomass), as ell as versatlty to ntegrate hgh performance combned cycles and cogeneraton systems based on topng combuston turbne cycles, Horlock (00). CTGs operate at relatvely hgher speeds, pressures and temperatures, than other plants, as ell as, over der operaton ranges and faster changes of ponts of operaton. Moreover, operaton of CTGs s very hghly automated, ncludng the stages of startup, synchronaton, loadng n derent modes, stoppng and trppng. These characterstcs set very tght requrements for the control system; the startup very probably beng the most demandng stage for the control system Garduno and Sanche (995). At startup, the man duty of the control system s that of acceleratng the CTG from turnng gearspeed up to synchronatonspeed accordng to a predefned acceleraton pattern. Wth ths am, the speed control has to provde the correct control actons to follo, th the hghest fdelty, the establshed acceleraton pattern, avodng the occurrence of stall, surge, hgh vbraton, resonance, hgh temperature and combuston nstabltes, and to compensate the eects of dsturbances produced by normal operaton events and other external forces, n the shortest tme, savng fuel and preservng the CTG duty lfe. Current CTG speed controls bascally consst of a feedback loop, here a PI or PID algorthm provdes the control sgnal from the speed devaton beteen the speed reference and measurements Woodard (00). In general, such control algorthms cannot provde optmal response to more than one control objectve. They can be tuned for reference sgnal trackng or dsturbance rejecton requrements, but both at the same tme. Conversely, todegrees of freedom (DOF) control strateges can be used to acheve both, good trackng of reference sgnals and rejecton of external dsturbances. Nevertheless, although several DOF control schemes are avalable n the techncal lterature, there are fe references on ho to extend the benefts of DOF control schemes over de ranges of operaton, as requred by CTGs, Garduno and Lee (000, 003). In ths regard, ths paper unvels to feasble realatons of DOF PI fuy ganschedulng schemes to control CTG speed at startup, from fuel gnton up to rated speed, just before synchronaton of the poer plant to the poer grd. Secton presents the bascs conventonal and DOF speed controls. Secton 3 presents the realaton of to DOF PI fuy ganschedulng (PIFGS) controllers for CTG, odrgue and Garduno (0), here a fuy system s used to spread the benefts of a DOF PI structure all over the CTG startup operatng space by mplementng a ganschedulng strategy. The fuy system ncely solves the problems of detecton of operatng condtons, controller stchng and gan schedulng. Secton shos some smulaton experments and results that provde valuable nformaton regardng the performance of the proposed derange DOF fuy speed control schemes, as compared to the conventonal PIbased speed control schemes. Secton 5 summares ths ork and dras conclusons.

2 . DOF CONTOL SCHEMES. Conventonal Speed Control Strategy Typcal CTGs consst of fve major components that operate contnuously to produce electrc poer (Fg. ). The startng devce can be an electrc motor to ntally move the CTG. The compressor takes n atmospherc ar, compresses t and sends t to the combuston chamber. Pressured ar s mxed th fuel and burned to produce the hot flue gas that s delvered to the turbne movng blades through expanson noles. The exhausted flue gas s released to the atmosphere and the rotatonal mechancal energy s transmtted to the electrc generator, hch converts t nto electrc energy. Startng devce fuel ar ntake Compressor Compressor dscharge Combustón chamber Turbne Hot gas Exhaust gas Fg.. Major components of a typcal CTG. electrc generator Essentally, the control system structure of a typcal CTG contans to control crcuts: the nlet gude vanes (IGV) poston control crcut to regulate ar flo and a dual speed and poer control crcut to regulate fuel flo. In the former crcut, flue gas temperature, compressor dscharge pressure and turbne speed are permanently montored to set safety lmts to the fuel valve demand sgnal to ensure CTG physcal ntegrty (Fg. ). At startup, the control system actvates the closed loop speed control at the tme of fuel gnton up to rated speed. At the tme of synchronaton to the poer grd, the closed loop poer control s actvated. These control loops are usually based on PI or PID control algorthms.. Structure of DOF Speed Controllers In general, DOF controllers have a structure th separately actng control trajectores or degreesoreedom (Fg. 3), here s the speed reference, Y s the speed measurement, E s the speed error, C fb s the feedback controller, fb s the feedback control sgnal, C s the feedforard controller, s the feedforard control sgnal, and s the total control sgnal. The feedforard controller C solves the speed reference trackng problem and the feedback controller C fb regulates speed and solves the dsturbance rejecton problem. To realatons of DOF PI controller structures are presented n hat follos. In the frst DOF PI controller structure, the feedback controller C fb s based n a generaled PI controller: K fb ( s) = K fb ( Y ( s) ) ( b( s) Y ( s) ) () s here K fb s the proportonal gan, K s the ntegral gan, the eghtng coecents a=0 and b= and fb s the correspondng feedback control acton. C ps rpm MW temperature comp dscharge pressure speed poer temperature supervson surge supervson speed supervson speed/poer control f(.) IGV demand Fg.. Speed/poer control scheme for a CTG. E C C fb fb Fg. 3. DOF controller structure. < fuel valve demand The feedforard controller C s based on a P controller: ( s) = = s C s K here K s the proportonal gan and s the feedforard control acton. The change of the control acton beteen to consecutve samplng nstants, k and k, s gven by: fb = K r ( k ) K K Te( k ). u k = u k u k fb here r(k) = r(k) r(k) s the change n the reference sgnal, y(k) = y(k) y(k) s the change n the output sgnal, e(k) = r(k) y(k) s the error sgnal, K and K fb are proportonal gans for the reference and output, respectvely, and K s the ntegral gan. Note that hen K and K fb are equal, the generaled PI algorthm reduces to the conventonal PI algorthm. The fnal control sgnal s obtaned recursvely as: ( ) u k = u k u k () Y A dscretetme recursve verson of the generaled PI control la s shon n Fg.. r( k) r ( k ) e( k ) K T K K fb Fg.. Frst DOF PI controller structure. () (3) u ( k) u ( k ) u ( k ) u( k )

3 In the second DOF PI controller structure, the feedback controller C fb s the same as n the frst case: K fb ( s) = K fb ( y( s) ) ( b( s) Y ( s) ) (5) s No the feedforard controller C drectly uses the reference value r(k) at each samplng nstant k, hle n the frst DOF PI control structure the feedforard controller uses the change n the reference sgnal r(k): ( s) = = (6) s C s K here K s the proportonal gan and s the feedforard control acton. Thus, the fnal control acton generated by ths control structure s gven by: = fb = K r ( k ) K K Te( k ) u k u k u k fb here r(k) s the reference sgnal, y(k) = y(k) y(k) s the change n the output sgnal, e(k) = r(k) y(k) s the error sgnal, K and K fb are proportonal gans for the reference and output, respectvely, and K s the ntegral gan. A dscretetme recursve verson of ths generaled PI control la s shon n Fg. 5. r( k) r ( k ) e( k ) K T K K fb u ( k) u ( k) fb u k u( k ) Fg. 5. Dscretetme verson of second DOF PI control structure. 3. DOF PI FZZY GAIN SCHEDLING CONTOL Bascally, the DOF PIFGS controller s created from a seres of DOF PI controllers orkng n parallel. Each of these controllers corresponds to one partton of the operatng space (CTG startup speed range). Each controller s tuned to satsfy the trackng and rejecton requrements of ts partton, and put nto servce accordng to plant operatng condtons. Hence, the DOF PI controllers are assembled by means of a fuy system. Fufcaton mplements the mechansm to detect the plant current operatng condtons. Inference rules mplement the generaled PI local controllers, one per rule. Then, the nference process mplements the stchng logc and the nterpolaton or gan schedulng functon. The PIFGS controller s a TakagSugenoKan (TSK) fuy system th four nputs and one output. The frst nput enters the schedulng varable, α. The remanng nputs enter sgnals r(k), e(k) and y(k), requred by the dgtal generaled PI to calculate the control sgnal. The output of the TSK fuy system s the change n the control sgnal u(k). Structure of the PIFGS controller and the TSK fuy system are depcted n Fg. 6. The TSK fuy system has the follong man (7) characterstcs. Schedulng varable membershp functons are trapeodal and trangular. Sngleton fufcaton s used to smplfy calculatons by the nference mechansm. Inference mechansm s based on ndvdual rules. Output s the eghted average combnaton of all rule outputs. For type DOF PIFGS controller each rule of the fuy system mplements a DOF PI controller th the frst structure. Therefore, rules have the form: ( k ) = K r( k ) K K Te( k ) (8) fb here =,,..., s the rule number, A s the fuy set defnng the th partton of the operatng space, K, K fb and K are the generaled PI parameters or gans of the th rule or controller, and u (k) s the control sgnal generated by the th rule or controller. r( k) schedulng varable e( k) y( k) r( k) rule base f α s, ( k ) = K r( k ) K K Te( k ) then u fb u = = fuyfcaton nference combnaton Fg. 6. Structure of DOF PIFGS controller. ( k) u( k) The total control sgnal change, generated by the TSK fuy system s the eghted average of the control sgnals generated by each rule or controller: u k = = = u k here the eghts are calculated as the product of the membershp values of the nputs beng fufed. Snce only the frst nput s beng fufed: = µ A ( α ) (0) From (3), (9) and (0), the control sgnal change u(k) s: u ( k ) = = µ A ( α ) K r( k ) K K Te( k ) = µ A fb ( α ) Fnally, the control sgnal s obtaned recursvely: ( ) y( k) (9) () u k = u k u k () Smlarly, for type DOF PIFGS controller each rule mplements a DOF PI controller th the second structure: u r ( k ) = = ( K r ( k )) = (3)

4 f ( k ) u = = ( ) K y k K Te k fb = Wth u f (k) obtaned from: ( ) f f f () u k = u k u k (5) Fnally, the control sgnal s obtaned as: u k = u k u k (6) r f The frst relevant ssue to desgn the PIFGS controller s to select the schedulng varable, hch must be strongly related to the change of the CTG operatng condtons. In ths case, the speed reference sgnal s chosen. The speed control range spans from 96 rpm through 500 rpm. The second desgn ssue s that of parttonng the operatng space, hch must be made on the analyss of operatng condtons and control requrements throughout startup. In ths ork, t s proposed to defne parttons usng a set of ponts of operaton that are selected by ther mpact on the CTG speed response. Advantages of ths approach nclude no need of a mathematcal model of the plant; partton can be done by nspecton of the speed response usng experence. As a frst approxmaton, consder the ponts marked n Fg. 7 and lsted n Table. Partton of operatng space s done th fuy sets. For smplcty trapeodal or trangular fuy sets are chosen, th centre and base corners at the ponts of nterest (Fg. 8). Thus detecton of the operatng condtons s gven by the degree of membershp of the schedulng varable to each one of the fuy sets or parttons defned ths ay. µ(α) A A A 3 A α Schedulng varable (rpm) Fg. 8. Defnton of fuy sets for operatng space partton. Subsequently, a DOF PI controller s assgned to each partton through the nference rules of the fuy system. From (8) and the defnton of fuy sets, A, n Fg. 8, the follong nference rules are obtaned: 3 ( k ) = K r( k ) K fb K Te( k ) ( k ) = K r( k ) K fb K Te( k ) 3( k ) = K 3 r( k ) K fb3 K 3Te( k ) ( k ) = K r( k ) K K Te( k ) fb (7) Inference rules for the second structure of PIFGS controller are as follos: 3 ( k ) = K r( k ) K fb K Te( k ) ( k ) = K r( k ) K fb K Te( k ) 3( k ) = K 3r( k ) K fb3 K 3Te( k ) ( k ) = K r( k ) K K Te( k ) fb. SIMLATION EXPEIMENTS (8) Feasblty demonstraton of both PIFGS controllers s carred out by means of smulaton experments th the mathematcal model of a MW CTG n a graphcal smulaton envronment n a personal computer. Experments consst n performng CTG startup smulatons th each of the conventonal PI and both PIFGS controllers, all of them n dscretetme versons. Speed trackng performance s evaluated th the IAE (ntegral of absolute error) and CE (control eort) performance ndexes. Frst, responses th the type DOF PIFGS controller are compared to the responses th a conventonal PI controller. Fg. 9 shos startup speed responses obtaned th both the conventonal PI and the type DOF PIFGS (tral and error, and automatc tunng). Complementarly, Fg. 0 shos the control sgnals ssued by the three controllers. The DOF PIFGS controller tuned by tral and error has smaller ampltude oscllatons at the major nterest regons. Ths provdes softer control actons and less thermal stress. Fg. 7. CTG startup th PI control shong relevant ponts of operaton. Table. Ponts of operaton selected to defne parttons Pont Event Speed (rpm) Actvaton of acceleraton 96 pattern Startng engne out of servce 36 3 IGVs openng and bleedng 830 valves closng Change of slop for synchronaton speed 500 Fg. 9. Speed response of PI and PIFGS th parttons.

5 Fg. 0. Control sgnals of PI and PIFGS controllers. Table II reports IAE and CE ndexes to have a better apprecaton of controller performance. The DOF PIFGS controller has better IAE performance than the conventonal PI control for both manual and automatc tunng. Also, tral and error tunng provded better response than automatc tunng. Ths result s relevant n the sense that onste manual tunng can provde results as good as those gven by the optmaton routnes. Table. Speed response performance Controller IAE EC PI conventonal PIFGS th parttons, tral and error tunng PIFGS th parttons, automatc tunng Even better performance may be obtaned th the DOF PI FGS controller consderng more parttons, hch can be defned by nspecton of the CTG speed response. Cases th 6 parttons are consdered for both DOF PIFGS structure controllers. From Fg. 9 extra ponts of operaton are selected beteen Ponts and, and 3 and, as lsted n Table III. Ths table also lsts the parameter values of the generaled PI controller for each partton. Table 3. Selected operatng ponts and controller parameters of type DOF PIFGS th 6 parttons Pont Speed K K fb K (rpm) esponses of both DOF PIFGS controllers th 6 parttons are closedup n Fgs. and. Fg. shos responses at the begnnng of the startup ramp. Fgs. and, sho that both controllers have smlar responses. Fg. 3 shos the control sgnals ssued by both controllers, here t s seen that both sgnals are very smlar too. Fg.. Speed response of PIFGS type and type th 6 parttons. Fg.. Speed response of PIFGS type and type th 6 parttons. Fg. 3. Control sgnals of both PIFGS type and type controllers. To better apprecate the performance of the controllers, Table IV reports the IAE and CE ndexes. Clearly, response of DOF PIFGS type controller, outperforms that of the DOF PIFGS type controller. Table. Speed response performance DOF PIFGS Controller IAE EC Type, 6 parttons, tral and error tunng Type, 6 parttons, tral and error tunng

6 Fnally, smulaton experments th the DOF PIFGS type controller th 7 parttons ere made. From Fg. and table III an extra pont of operaton s selected beteen current Ponts 5 and 6, as lsted n Table V. Ths table also lsts the parameter values of the controller for each partton. Fgs. and 5 sho startup speed responses obtaned th both the conventonal PI and the DOF PIFGS type th 7 parttons. It s clear ho the DOF PIFGS type controller th 7 parttons outperforms the conventonal PI controller. Fg. 6 shos the control sgnals ssued by the to controllers. The DOF PIFGS shos much smaller ampltude oscllatons at the begnnng of the startup ramp and a lttle less at the end, compared to the control sgnal th a conventonal PI controller. Table 5. Selected operatng ponts and controller parameters of type DOF PIFGS th 7 parttons Pont Speed K K fb K (rpm) Fg.. Speed response of PI and PIFGS type th 7 parttons. Table 6 reports the IAE and CE ndexes. Clearly, response of DOF PIFGS type controller, outperforms that of the PI conventonal controller. Table 6. Speed response performance Controller IAE EC PI conventonal PIFGS th 7 parttons, automatc tunng CONCLSIONS Ths paper unveled to PIFGS structure controllers to govern the speed response of a CTG durng startup. esults of smulaton experments demonstrate that both PIFGS algorthms can mprove performance of speed control ell beyond that obtaned th the conventonal PI algorthm. Also, applcaton of PIFGS to actual CTG can be easly carred out onste startng th the current controller settngs. Both DOF controllers are sutable for applcaton n actual CTGs. EFEENCES Gardunoamre. and Sanche M. (995). Control system modernaton: Turbogas unt case study. Vol., pp Proc. IFAC Symposum on control of poer plants and poer systems. Gardunoamre. and Lee K.Y. (000). Wderange operaton of a poer unt va feedforard fuy control. Vol. 5, No., pp. 6. IEEE Transactons on energy converson. Gardunoamre. and Lee K. Y. (003). Poer plant PID schedulng control over full operatng space. Proc. th Intellgent systems applcaton to toer systems conference. Horlock J. H. (00). Combned poer plants: Includng combned cycle gas turbne (CCGT) plants, Kreger Publshng. odrguemartne A. and Gardunoamre. (0). PI fuy ganschedulng speed control at startup of a gas turbne poer plant. Vol. 6, No., pp IEEE Trans. energy converson. Woodard Governor Co., (00). 30DGT Dgtal electronc load sharng and speed control for small gas turbnes. Manual 6B. Fg. 5. Speed response of PI and PIFGS type th 7 parttons.