This paper describes some studies made towards the automatization of hydroturbine generators with microcomputers. The overall design will include an automata controlling the starting-up and shutting-down procedure as well as an self-tuning regulator for the speed control.  A self-tuning regulator based on the classical pole-assignment-method is studied. The algorithm uses a fast procedure for solving the polynomial equation implicit to selfturner regulator. This procedure is very simple from a computational point of view as only applications of elementary transformations on a 2 x 2 polynomial matrix are needed.The algorithm has been programmed on a Digital PDP 1103 computer and applied to some test problems

Aracil Santonja, Javier

Camacho, Eduardo F.

García Franquelo, Leopoldo

Provost, J. M. G.

Rodríguez Rubio, Francisco

idUS. Depósito de Investigación Universidad de Sevilla

IFAC International Federation of Automatic Control • SOFTWARE FOR COMPUTER CONTROL Preprints of the 3 rd IFAC IIFIP Symposium Madrid, Spain 5 . 8 October 1982 Editors G. Ferrate Barcelona, Spain E.A. Puente Madrid, Spain. Contents CONTROL SOFTWARE ENGINEERING AND MANAGEMENT III The Production of Program Families Based on Abstract Data Types A. perez Riesco and J. Yun Cabrora (E) Simulation Program (BASIM) for Personna! Compumrs R.P. OffereinsandJ.W. Moorman (NL) Control Software to Combine Batch Control with Enhanced Continuous Control HM. Henry, S. Abdelhay, G. Bailley, C. Gray and C. Cabl. (GB) INDUSTRIAL APPLICATIONS I iK 405 411 411 If StudIes for the AppHcation of an Adaptive Controller to Hydroturbine Generators F. R. Rubio, E.F. Camacho, J. Araeil, L.G. Franquelo and J.M.G. Provost (E) Fault Surveillance and Back-Up Policy for a Load-Frequency Digital Controller J.G. Ayza and J.M. Fuertes (E) 425 tI An On~ Line Algorithm for Power System Observability Determination P. Albenos and C. Alvarez (c) INDUSTRIAL APPLICATIONS II An Interactive SImulation Model of Batchwise, Chemical Production - AT 001 to (mprove the Communication between the Plant Operators and the Production Process 431 435 K. Heide, P.M. Jorgensen and H. Soeberg (DK) 443 Chemical Plant State Estimation Using Balance Models O. Aama, K. Joers, U. Silitman and 1: Tader (SU) 449 Computer Based Process Control System which is Distributed, Hierarchical and Fully Redundant E.H.L. Derksen and K. Buring (NL) 455 Implementation and Comparison of Two Extreme Types of Optimal Control H. Soeberg (OK) 463 INDUSTRIAL APPLICATIONS III Microprocessor-Based Grain Dryer Control u.J. J.aksoo, c.M. Ta/vis8fldJ.M. Ummer (SU) Automatic Sequencer for the Control of a liquid Phase Epitaxy Furnace J. L. Souza L_ (F) Control of Ceramic Furnace USing a Two Microcomputer Structure H. £1 HailarandJ.8. Pourci./{F) INDUSTRIAL APPLICATIONS IV A Adaptive Control Application to a Lathe A. Viz"" and A.M. S;inchez (E) Static Adaptive Algorithms for Computer Control of Diesel Engine Tests F. Sastran (c I Software for a Microcomputer Controlled Laser Synchronization System M. Nechmadi and D. Tabak (IL) Microprocessor Based Multifunction Telephone Terminal J. Mlflambras·Pulg and J. Rivero·Laguna (El ADDENDUM Example of CAMAC Programming in ADA J. Z.lewlki (P) 469 475 479 483 489 495 501 ~07 • STUDIES FOR THE APLICATION OF AN ADAPTIVE CONTROLLER , TO HYDROTUR/lINE (lENERATORS ' F; R • .Rubio. E.F. Camacho. J. ~I. L.G. Franqll8lo and J.M.G. Provost Department of Auromaric and Electronics •. E. T.S. EngineerIng Ind. . UnlVetslty af S!!villa. Spain. Abstract. .This,paper describes ,some studies ~~e towards tlje_ automatiza"t:iorl_ of :hy<:1r.oturb1ne' qenerators ~ith micrOCoInputer.~ ... 'The overall. desig" will,inplude 'an automata 90ntro1l1ng the star t1ng~up and shutting~doWn procedure as well as an self-tuning re gulator for the, speed coIlt"ol. ' -A self-tun1ng regulator based on the, classical pole-assignment -method is studied. The algorithm uses a fast procedure for sol-'ving the ,polynomial equation implicit to self turner regulator!" • This procedure is ve~ simple from a computational point of view as only applications of elementa~ transformations on a 2 x 2 po lynomial l1!atrix are needed. ' . -The algorithm has been programmed on, a Digital PDP 1103 computer and applied 'to ' some test'problems. K~ywords~ Ad-apt,ive: control, microprocessors I process control. ,INTRODUCTION Self~tuni;;g' reqQlators are designed -to, operate in processes that exhibit either time varying or nonlinear dyn~ mic or both. This is the 'case of hld:ro . turbine sp~ed requla.tors:where. non -iI nearities in the valves and ~ther·sys terns parts are found.'These systems a1 so, have gradual drifts 'and, delay ana-what is more 1mpo,rtant,s'10w time, changes in two of the main factors affecting the overall "syst~ c;lyn~ics; which are the water head (Elgerd, 1982) and the Mw/HZ constant of the system (stiffness) depending on the governor and ,load characteriStics (Sterling -1978). Classical analog regulators,me chanical and electronic, have been, -used to control the speed. ofhydro.tu!. hine generators.. These regulators' are tuned at installation and have to. be retuned from time to tUne. Setf-tu-1)ing regUlators seem ' to. be the ans -' -. wer ~ some of t;he problem ment,ioned. SeH-timing, regulators (AEttrom';1980) ..,:c'!< bas1c:;Uly l.1ke this, 'l'hS pmoess 'para-meters .are estimated on-line by are .... cursive least-squares estimation and these estimates are 'then used to. cal-, culate 'the regUlator parameters. . Due to the parameter changes in the -process, "the estimation i1l190r~thin needs some adapt,iye mechanism to "fo -11"" parameter changes. A way of in ~, troducing this mechanism iEt to use a ,forgetting facto.r, in such a way that the algorithm gives'more weight to -the latest measurements and therefore allows .it to follow pararnet<;r, changes. Choosing an a.ppropiate forgetting fac . tor is essential fo.r the aigorithm to ' ,work. If a large forgetting factor ~ is· chosen. The estimation algorithm ~ has a very 'poo.r speed of adaptation~_ to. parameter changes in the. modelj On the other hand, if a smaH forgetting ,factor 1schosen,the identification' algorithm is, extremely sensitive, to -d1sturbancesand susceptible to nUme-rical computationai dificulties,when "blow-up* problems in the covariance -matrix arise. The algorithm'used in this paper'works with an,'identification algo,rithm(For-teacue and, c'oworkers, 1981) with a 'va ,riablel forgetting factor that solves the problems mentioned before. \ The adaptive algorithm used is descri bed in next section, and'is based~on­a, cpntrol law ~quivalent to a linear feedbaok of the state vector and an observer. A 'method (Aracil,1974) ,ba sed on elemental transformations on a 2 <'x 2, polynomial mat~ix" is used to 4Z5 426 F.R. Rubio et aL solve the polynomial equation found in the algorithm~ The amount of computation required-for adaptive regulators,and therefore the sampling time f increases considera bly with the order of the system con~ sldered. Working with a reduced model can sometimes improve the quality of the control as sampling time can be -reduced, in this sense the paper pre-sents some results obtained. ADAPTIVE CONTROLLER. The structure chosen for the adaptive controller is the one shown in fig. 1. This control. structure corresponds -to a linear state feedback and a Luan berger observer given certain condi = tions (Elliott and Wolovich,1979). As it is known this control law will ar-bitrarily assign all close-loop sys -tern poles preserving the open loop z~ ros. • Let us suppose that Td(z) 1s the desi red close-loop transfer function. It-can be seen. from fig. 1 that Td(z) y(z)_ N(z) G(z) (1) V{z)- D(Z)G(Z)+D(Z)K(z)ffi(Z)H(Z) This equation can be transformed in Td(z) ~ N(z) (2) D(z) + F(z) when the following equations hold N(z) H(z) + D(z) K(z) ~ Y(z) (3) Y(z) ~ F(z) G(z) As degree G(z) ~ n-l, with n=degree Dlz) , the degrees of K(z) and H(z) should be equal or smaller than n-l -in order to obtain a realisable control.ler. To satisfy equation (3) polynomials K(z) and Hlz) can be obtained applying the following algorithm (Aracil,1974). 1. Using Euclid's algorithm calcula-te Plz) and Q{z) such that Nlz) P(z) + D{z) Q(z) = 1 (4) 2. Form the polynorndal matrix, 3. -P(z) 1/J (Z] (5) Q(z) 1fi (z) \ \ Reduce the degree of j and j adding column 1 mUltiplfed by 2~ constant to column 2 until it is no longer possible to decrease both or either of them.· rocess M(z)/D{z) o t. Figure 1. structure of the Adaptive Controller. Notice that 1 is always possible if N(z} and D(z) are prime. As transfor mations described in 3 do not change -the determinant of J(z) we have. (6) as plz) and Q(z) satisfy (4). Therefore the polynomials K(z) and H(z) are respectively j22(z) an -jll(z). Most of the success of an adaptive con troller depends on how well the identI fier behaves. It is well known that -the forgetting factor has great influen ce in the behaviour of the identifier -and serious problems can be found when a constant forgetting factor is used, especially in steady-state regulation where old information is continually £orgotten and very 1itt1e dynam~c in-formation is coming in from the pro -cess which may in turn lead to an eX Application of an Adaptive Controller to Hydroturbine Generators. 4Z7 ponential growth of the covariance rna trix making the identifier very sensi tive to noise. There are various ways of avoiding the problems mentioned before. Some of them act directly on the covariance m~ trix making sure that it is always bounded .. Other methods consist of using a variable forgetting factor which in turn may be changed by different me -thods. We have used a variable forgetting 'factor. which is updated with an alg", r1thm (Fortescue, 1981).which takes in-to account the following fact: the error between the output of the pro -cess and the one of the estimated sys tern will tell us something about the-behaviour of the identifier." A small error can be obtained if either: the process has not been excited; the pa-rameter values are nearly correct· or the identifier is sensitive enough to reduce this error. When we have -a chan ge in the process "p"arameter, the pro=-cess and identifier will give a diffe rent output and the error will be la! ge. In the first case a reasonable strate gy would be to retain as much inforrn~ tion as possible by choosing a ~or getting factor close to one. In the second case the algorithm should for-get'the measurements correspondlng to the l10ldfl process. This can be accom-plished by choosing a low forgetting factor. A measurement of the informa tion content of the filter can be de~ fined as the weighted sum of the squ~ res of the errors, which can be expre ssed in a recursive way as: -" (t)=A(t)L(t-l)+ 1_~(t_k_1)TK(t)~(t)2 where A(t) is the forgetting factor, K(t) is the gain of the filter and ~T(t) contains the last n+1 measure-ments of the input and output of the process. The forgetting factor is then calcula-ted in such a way that the estimation is based on the same amount of infor-mation"That is" keeping E (t) constant. It can be seen that this is accompli-shed by' A (t) 1 - l/N (t) where N (t) = Lo/[l-i> (t-k-l) TK(t) ] e{t) 2 the identification algorithm can be expressed as : 1. 'Y'(t) = $(t-k-l)T()'(t-1) 2. e(t) = y(t)- 'Y'tt) 3. K(t)=P(t-l)<jl (t-k-1)/[1+<jl (t-k-1) T P(t-l) $(t-k-ll] .... .... 4. 0(t) =8(t-1) + K(~) e(t) 5. A(t) = 1- [1- <jl(t-k-l)T K(t)]e(t)2/ EO if A(tkAminsetA(t)=Amin 6. p(t) = [l-K(tl $(t-k-1)~P(t-l)/ A(t) -IMPLEMENTATION OF THE ADAPTIVE CONTRO LLER. Two systems based on microprocessors, have been used for the i~plementation of the adaptive controller. The first one (center) is dedicated to the com-putation of the algorithm described -in the previous sections; the second One (peripheral) is dedicated to actu~ te on the process with the set point received from the center and to scan the process qutput and send it to the center. This structu~e can be seen in fig. 2. Trans. Figure 2. System Configuration The main computer is liberated ~ ~ 'tasks of controlling the analog input output interface. This structure allows the system to be used for the control of a distributed process,connecting to the central computer various peri-pheral computers through series tran~ mission lines~ The communication protocol is of the question from the center-Janswer fromr the peripheral type in such a way that the peripheral will be quiet until an order has been sent. A time out has been used in order to avoid that both computers remain aimu1taneously:in a waiting state. 428 F. R. Rubio et al. The peripheral station is nor.mally waiting for a byte from the center. When the byte is received, it puts it through one of the output channels,rea ding the process output and sending --it to the center. .An analog computer and an electromecha niea! system have been connected to = the system to test the behaviour of -the algorithm with various type of pro ceSses. The results obtained are des--cribed in next section~ APPLICATION TO SOME TEST PROBLEMS. The adaptive controller described abo ve has been applied to the control 07 some test problems. The first process chosen has been a second order system simulated in the analog computer with a transfer function The system haa been ·controlled, with the algorithm described in the pre -vious sections, setting the poles of the desired transfer function to ob-tain a system without dscilations and a rising time of 1.5 seconds 5 The gain K of fig. 1 is calculated at -each sl!ep in the algorithm to obtain a desired static gain. Fig. 3 shows the behaviour of the sy! tern with a sampling time of 0.5 se -canda and using a second order model for the identifier. It can be seen hoW the adaptation mechanism works in the starting up procedure and when a sudden change is produced in the pro-cess transfer function. Table I shows the mean square error -between the process output and the theoretical One for different values of the sampling time and using a first and a second order model for the con-troller. TABLE 1. MEAN SQUARE ERROR (MSQ) sampling time ist order 2nd order 1.5 sec 0.255 0.314 1 sec 0.242 0.217 0.5 sec 0.192 0.139 0.25 sec 0.123 As it can ,be seen in table 1 the MSQ decreases with the sampling time and the results obtained using a first Or dar model for the identifier are be ~ tter than'the ones obtained with a se cond order model iT the sampling time is reduced. This can be helpful when implement.ing adaptive controllers with microprocessors, as the algorithm des cribed is very simple in the Case ol-a first order model. .6 al 10 0 sec. -.6 -4 . Figure 3. Response of a second order system. Fig. 4 shows the process output for a first and second order model with the sampling time of 0.5 and 1 second re~ pectively. One of the main problems with adapti-ve controllers is the oscillatory be-haviour during the starting-up period. This behaviour is due to the fact th~ in those moments the identifier is working with very little.information and the process parameters., and there-fore the control polynomials ( K(z)and H(z)) are subject to sudden changes. One way of avoiding this problem i8 not allowing sudden changes of the par!!. meter of the control polynomials. This can be accaopl1shed by: where P is the new set of parameter~ P is tNe old set and ~ is a constant tRat can take values between 0 ( no adaptati.on) and 1 .. The va1ue of (] can be calculated as a function of the cQvariance of the estimates. Applica.tion of a~ Adaptive Controller to Hydroturbine Generators 429 4 -4 4 -4 4 -4 fl'O 1'-50 f fL'O I systan output (1 stolXler) 10 Z50 sec. systsn outplt (2nd olXler) '250 desired output I t "ov . .st F19ure 4. C!1l"par1son of a.. and :P order controller A suitable function can b~, " & exp(~"otrace(covariance» Fig. 5 shows the output of the system A process consisting '0£ a DC motor,me chanical gear, servoamplifier andjth[ co has been chosen as a second exam -pie. The main characteristic of this system is ita non l1nearities due to a dead zone produced by static fric -tions. A second and first order model have -been used to control the speed of this system. A square wave signal has been used as reference for the speed. The output of the ~ystem and some of the estimated paranetexs are shown in fig. 6. The sudden changes of the parame -ter correspond to the crossing of the dead zone by the process. 5.6 2. 4 sec. e -2. 2 systsn output 190 with a sampling time of 0.5 seconds - -2 des:i:red output when this "mechanism is introduced.As 2 it can be seen, the startin9 up proc~ dure is improved. -4 4 -4 y(t) (system output) yd(t) (desired output) Figure 5.Modified adaptation mechanism 190 2 Figure 6. Speed control of a DC ~otor As a third example we have chosen a -model of ~ hydroturbine generator. and the hydraulic amplifier. This pro cesS mspands to a step change in. the valve position with a momentary power decrease and can be modelled with a third order nonminimum phase system. The results obtained. using a first and second order controller are shown in fig. 7. As it can be Seen the algorithm can -not control the system with a first order model. This is due to the fact 43() F.R. Rubio et al. that the identifier gets the parame _ ters corresponding to the momentary _ drop of the output when a step change is produced in the input * As the algorithm used does not change the zeros of the process, the overall system is a nonminimum phase and this behaviour can be Seen in fig. 7. Note that the zero can not be cancelled as it is outside the unit circle. This _ problem is solved in practice by a dOuble feedback o£ speed an -valve po-sition. 8 4 -4 4 4 a 4 systEm output (2nd order) r .\. 10 sec. desired output (2nd ~ sy~output (1 "~) ( J V de8~ output (1 order) /' \.... Figure 7. Adaptive control of a nonminimun phase system. ~ <50 ~ .50 250 250 An automata for controlling the star-ting-up and· shutting down procedure -of this process is also be~n~ desig--ned. This· automata is .bein'! llI\plemen-ted with a Motorola 6800 ml:roproc7--ssor~ More than a hundred d191tal 1n-put-output signals must be handled. The automata should transfer control t.o the adaptive regulator once the tuE., bine is started. CONCLlISIONS The paper presents some studies made with adaptive controllers. An algo -rithm using Euclid's algorithm and el~ mentary transformation on a 2 x 2 p~ lynomial matrix have been used to s~ ve the polynomial equation implicit to pole placement adaptive controller. The algorithm has been tested on sev~ ral systems using first and second order models. It can be seen in two of the examples chosen that the re -suIts obtained with a first order m~ del with smaller sampling time are s~ milar to those obtained with a second order model. This fact can be of in-terest when implementing adaptive co~ trollers with ·microprocessors. A smoother way of adaptation to s~lve some of the problems of the start2ng up period of an adaptive controller has been used and we feel that this heuristic aproach should work well in practice. REFERENCES Arac1l, J. (1974). A Note on the De--sign of S.l.S.O. Systems. Revue R. A.I.R.O. N"Avril; pp. 119-125. kstrom, K.J. (1980). Self-tuning Reg~ lators Design Principles and Appl~ cations. Applications of Adaptive ContrOl. Ed. Academic Press. Inc. pp. 2-68. . Eldger, 0.1. (1982). Electric Energy Systems Teory. Mc Graw Hill. Elliott,H. and W.A. vlolovich. (1979). Parameter Adaptive Identification and Control.IEEE trans. on Automa-tic Control. Vol AC-24 N"4. pp.592 -599. Fortescue, T.R.,L.S. Kerahenbaum and B.E. Ydstie. (1981). Imp1ementa--tion of Self-tuning Regulators --with Varlable Forgetting Factors. Automatica. Vol 17. N°6. pp. 831-835. Sterling, M.J.H. (1978). Power System Control. Ed. lEE. 

Studies for the application of an adaptative controller to hydroturbine generators

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Studies for the application of an adaptative controller to hydroturbine generators

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idUS. Depósito de Investigación Universidad de Sevilla