Water Level Control by Fuzzy Logic and Neural. Networks

Transcription

1 Water Level Control by Fuzzy Log and Neural Lmted rulaton. For revew only. Networks Danel Wu Dept. of Systems Desgn Eng. Unversty of Waterloo Waterloo, ON NL G Fakhreddne Karray Dept. of Eletral & Computer Eng. Unversty of Waterloo Waterloo, ON NL G Insop Song Dept. of Systems Desgn Eng. Unversty of Waterloo Waterloo, ON NL G Abstrat The objetve of ths paper s to nvestgate and fnd a soluton by desgnng the ntellgent ontrollers for ontrollng water level system, suh as fuzzy log and neural network. The ontrollers also an be spefally run under the rumstane of system dsturbanes. To aheve these objetves, a prototype of water level ontrol system has been bult and mplementatons of both fuzzy log and neural network ontrol algorthms are performed. In fuzzy log ontrol, Sugeno model s used to ontrol the system. In neural network ontrol, the approah of Model Referene Adaptve Neural Network Control based on the bakpropagaton algorthm s appled on tranng the system. Both ontrol algorthms are developed to embed nto a standalone DSP-based mro-ontroller and ther performanes are ompared. Sensor Water Level Valve Water Tank Pump Valve Valve Servor Motor I. INTRODUCTION Tradtonally, aurate mathematal model-based strateges have been appled to deal wth ontrol problems. However, water level ontrol system, for example, s very omplex system, beause of the nonlneartes and unertantes of a system. Conventonal ontrol approahes are not onvenent to solve the omplextes. Fuzzy log and neural networks ontrol have emerged over the years and beome one of the most atve and frutful areas of the researh n the ntellgent ontrol applatons. There are two major dfferent types of the ontrol rules n fuzzy ontrol: the Mamdan type and the Sugeno type. The Mamdan ontrol rules are sgnfantly more lngustally ntutve whle Sugeno rules appear to have more nterpolaton power even for a relatve small number of ontrol rules. In neural network ontrol, the most ommonly used ones are supervsed ontrol, dret nverse ontrol and neural adaptve ontrol. There are many papers addressed the fuzzy or neural networks ontrol n the water or lqud level ontrol system. Nmura et al. utlzed the fuzzy log for water level ontrol n small hydro-generatng unts[]. Roubos et al. hose Sugeno fuzzy model as the model struture for a lnear model based predtve ontrol of the lqud level []. Ghwanmeh et al. showed a self-learnng fuzzy log ontrol appled to a nonlnear proess and demonstrated the robust and repeatable performane []. Naman et al. presented an adaptve modelreferene fuzzy ontroller for ontrollng the water level n a water tank []. Xao et al. provded a bakpropagaton neural network algorthm used to adjust the parameters of the PID ontroller and ontrol the lqud level of molten steel smellng DSP Controller Fg.. Confguraton of the Water Level Control System. The system onssts of the servo motor, valves, a pump, a nfra-red sensor and a DSP ontroller. non-rystallod []. In ths paper, we frst elaborate the onfguraton of the water level ontrol system. Then, we ntrodue Sugeno fuzzy ontrol [7], [8] and model referene adaptve neural network ontrol (MRANNC) [6], [9], [] strateges based on bakpropagaton algorthm. Fnally, some expermental and realtme results usng DSP ontroller are presented. II. SSTEM CONFIGURATION Fgure shows the system onfguraton. The system onssts of the servo motor, valves, a pump, a nfra-red sensor and a DSP ontroller. Water s onstantly pumped nto a vertal tube by a pump. Water an outflow from the horzontal tube. The general ontrol objetve s to reah and stablze a ertan water level n the vertal tube. As shown n the fgure, a sensor measures the water level and sends heght sgnal to the DSP mro-ontroller. The ontroller ontrols the servo motor, whh adjusts the valve to mantan a desred water level n the vertal tube. Valve onstantly opens and valve randomly opens to provde dsturbanes to the ontrol system. III. FUZZ LOGIC CONTROL In Fuzzy ontrol, two nputs for the system are hosen. They are an error (e) and an error dervatve (ė). The error s alulated by takng the dfferene between the referene Preprnt submtted to IEEE Conferene on Control Applatons. Reeved February 8,.

2 If e s HN OPEN valve WIDE If e s N and ė s NOT P OPEN valve A BIT If e s N and ė s P LEAVE valve ALONE If e s S and ė s N OPEN valve A BIT If e s S and ė s S LEAVE valve ALONE 6 If e s S and ė s P CLOSE valve A BIT 7 If e s P and ė s N LEAVE valve ALONE 8 If e s P and ė s NOT N CLOSE valve A BIT 9 If e s HP CLOSE valve A LOT TABLE I RULE BASE - HN Lmted rulaton. For revew only. N N S P HP - - (a) Error Membershp Funtons S P Output Funtons OPEN valve WIDE 9 e + ė OPEN valve A BIT e ė LEAVE valve ALONE e + ė + CLOSE valve A BIT e ė + CLOSE valve A LOT e + ė + TABLE II OUTPUT FUNCTIONS. sgnal and the urrent water heght. The error dervatve s alulated by subtratng a prevous error from the urrent error. The output of the system s a voltage that s sent to a servo motor to ontrol the valve. The Sugeno model s used n the system. The Sugeno model s omputatonally effent, and works well wth optmzaton and adaptve tehnques, so t s popular for ontrol problems, n partular for dynam nonlnear systems. The Sugeno fuzzy model takes the form: IF e s A AND ė s B, THEN SERVO s f(e,ė) The output funton f(e,ė) takes the form: r(t) (b) Error-Dot Membershp Funtons HN N S P HP N error_dot S Fg.. P error () Mappng Membershp Funtons and Mappng e NN ontroller u NN dentfer Nonlnear Plant e e y e yp A e + A ė + A The parameters of the output funton A, A, and A an be modfed through the mro-ontroller nterfae. The rule base used here s shown n Table I. Fve membershp funtons for the error are shown n Fgure (a), and three for the error dervatve are shown n Fgure (b). The rules mappng s shown n Fgure (). Labels n Table I and Fgure are as follows: HN=Hgh Negatve;N=Negatve;S=Small;P=Postve; HP=Hgh Postve; For the Sugeno model, output funtons must be defned. Ths wll dede how the system provdes the proper ontrol through the manpulaton of the valve. Table II shows the output funtons and nomnal tunng values that the ontroller uses on start up. Eah of these parameters an be modfed usng the user nterfae of the mro-ontroller. IV. NEURAL NETWORK CONTROL In ths paper, the Model Referene Adaptve Neural Network Control approah based on bakpropagaton algorthm s appled to mplement the water level ontrol system. Fgure Fg.. Neural Network Control n Water Level Control Systems, denotes tme delays of the nput or output sgnals. shows the ontrol struture. n Fgure denotes tme delays of the nput or output sgnals. A. Neural Network for Identfer The neural network for dentfer s desgned as a threelayer neural network. It has a nput layer, a hdden layer, and an output layer. N,N j and N k are ther output values respetvely. The neuron numbers n the hdden layers an be hosen dependng on the pratal tranng result. The neural network dentfer models are traned to learn the forward dynams of the plant. Sx nputs and one output are seleted as the dentfer model for the system. These sx nputs are the ontrol sgnals: u(t ), =..., and the prevous output sgnals: y(t j), j =... These sgnals provde the Preprnt submtted to IEEE Conferene on Control Applatons. Reeved February 8,.

3 urrent and prevous two ontrol sgnals, and also norporate n the hstoral trend from the last three tme steps of the output of the system. A set of orrespondng nput-output tranng patterns s seleted from the open-loop ontnuous sgnal response of the system. The ontrol nput sgnal s dretly added to servo motor of the system and system output sgnal s refleted wth the sensor, whh s atual water level. In tranng a neural network to learn a forward dynam model of a plant, the bakpropagaton error sgnal between the output and the hdden layer s expressed as N Lmted rulaton. For revew only. Fg.. wj N j Nk w kj NN Contorller N wj N j Nk w kj NN dentfer The Conneton Between the Controller and the Identfer δ k = T k N k () where T k s the target pattern and Nk s the atual output of the dentfer, and between the hdden and nput layers, t s expressed as δ j = f (net j ) δ k w kj () k Here, f (net j ) s the dervatve of the atvaton funton f(net j ) where f(net j ) = + exp( net j ) The weghts between the nput and hdden layers are updated as w j (t + ) = η δ j N + α w j (t) () and the weghts between the hdden and output layer are updated as () w kj (t + ) = η δ k N j + α w kj (t) () where N and N j are the outputs of the nput and hdden layers, respetvely, η s the learnng rate, and α s the momentum oeffents. The onstants η, α are all hosen emprally. B. Neural Network for Controller The neural network ontroller s reated dretly based on the neural network dentfer. Its desgn s fully norporated the learnng strategy nto the traned dentfer. The weghts of the neural network dentfer are onstantly verfed aganst the atual plant output. Ths ensures that the weghts allow the neural network dentfer to properly predt atual plant output. The neural network dentfer s used as means to bakpropagate the performane error to get the equvalent error at the output of the neural network ontroller. The auray of the plant model s rtal n ensurng that the ontroller s aurate as well. The error between the plant output and the dentfer output s also heked for the auray level of the dentfer. Ths error s used to bakpropagate and adjust the weghts of the dentfer to provde the most aurate representaton of the plant. The neural network for ontroller s also desgned as a three-layer neural network. It has a nput layer, a hdden layer, and an output layer. N, N j and N k are ther output values respetvely. The neuron numbers n the hdden layers an be hosen also dependng on the pratal tranng result. To llustrate the dervaton of the error sgnals for the neural network ontroller, Fgure provdes the onnetons between the ontroller and dentfer networks. The adaptaton of the weghts of the neural network ontroller between the hdden and output layers an be derved as follows: wkj E = η (6) where w kj E = (y p r) (7) where y p and r are the atual and desred plant output. The supersrpt denotes the varables belongng to the neural network ontroller and supersrpt denotes the varables belongng to the neural network dentfer. Usng han rule, equaton (6) an be expanded as follows: so where and wkj E = η net k net k w kj w kj = η δ k N j (8) δ k = E net k N j = net k w kj δk s the error sgnal between the hdden and output layers of the neural network ontroller. Lnear funtons are used at the nput and output neurons of the neural networks between the ontroller and dentfer. Therefore, δk an be represented as follows: δ k = E N k = E net = E N where net and N are the nput and output of the dentfer nput layer neurons. Further usng han rule Hene, δk = E net net j j N E net j = δ j (9) () Preprnt submtted to IEEE Conferene on Control Applatons. Reeved February 8,.

4 NN In n n j n k η α Identfer 6..8 Controller..6 TABLE III PARAMETERS SETUP. Lmted rulaton. For revew only.... Plant Dsturbane Tranng Data U and so, net j N = w j δ k = δ j w j () Fg.. Plant Dsturbane Tranng Data, U s an nput sgnal and s a output of the sensor The error sgnal between the nput and hdden layer of the neural network ontroller an be derved as follows:. Plant Test Data U δ j = E net j = E N j N j net j (). By usng han rule and where so, E N j = E net net k k Nj N j net j = f (net j) f (net j) = N j ( N j ) δ j = N j ( N j ) ( δ k w kj) () The weghts of the neural network dentfer an be further mproved onlne f neessary. Ths an be reahed by bakpropagaton of the followng error equaton through the neural network dentfer at every sample. y p and y are the outputs of the atual plant and neural network dentfer, respetvely. e = (y p y ) () V. EXPERIMENTAL RESULTS The neural network ontrol algorthm were frst traned and tested wth C language wth a normal PC. Then, the algorthm were ported to DSP-based ontroller and tested. A. Tranng and Testng for Neural Network Control ) Parameters Setup: In order to have quker alulaton wthout sarfng performane, some parameters were setup as shown n Table III. In Table III, n,n j and n k denote the number of nodes n the nput layer, hdden layer and output layer, respetvely, η and α denote learnng rate and momentum term, respetvely Fg. 6. Plant Test Data ) Identfer Tranng and Testng: The traned dentfer wll be used as a representaton of the system plant to effetvely reate a ontroller for the system. Then, the offlne tranng of the ontroller wll be feasble to reah.. Tranng Data An open loop system was used to obtan a system response urve for the plant response to a random nput sgnal. Fgure shows the nput sgnal used for tranng of the NN dentfer. Ths was done by sendng a voltage sgnal through a potentometer nto the servo motor, and t ontrols the valve. By reatng a random nput ontrol sgnal and measurng the sensor output whle a random and a onstant dsturbane exsts. A set of data was reated and ndated the behavor of the plant response to a haraterst nput sgnal. It was desgned to fall wthn the operatng range of the sensor. As shown n the fgure, the nput sgnal u vares between values of V and V.. Testng Data One the tranng porton of the Identfer s ompleted, t needs to be verfed wth the tranng results. A seleton of smlar data was reated for testng the traned network. Fgure 6 shows a set of testng data used for the Identfer.. Identfer Tranng Identfer tranng resulted to a level of error of 7.98 after, epohs. At the ut-off of, epohs, the dentfer was stll onvergng on an error, but extremely slowly. Then, ths level of an error was used to move onto Preprnt submtted to IEEE Conferene on Control Applatons. Reeved February 8,.

5 Identfer Tranng Error Error Lmted rulaton. For revew only. Controller Tranng Data Desred Error (V) Water Level (m) Epoh Test Fg. 7. Identfer Tranng Error Fg. 9. Controller Tranng Data. Identfer Test Data U -PRED Controller Test Data Test Data... Water Level (m). -. Epoh Fg.. Controller Testng Data Fg. 8. Identfer Testng Results ontroller tranng. Fgure 7 shows the trend of dereasng error n the dentfer tranng.. Identfer Testng The error seen as a result of testng s shown n Fgure 8. Sne the level of error seen s on the same sale of that for the tranng, then movng to ontroller tranng beame the next step. It s beleved that a more rgorous tranng ould result n better error and better performane for ontroller tranng and fnal mplementaton. ) Controller Tranng and Testng: In order to effetvely reate a ontroller for the system, the exstng system was analyzed n an off-lne setup. The goal n the projet s to develop a ontroller through smulaton and use more omputer resoures n a hghly effetve manner. It proved far more effetve to desgn the tranng and testng n an off-lne format.. Tranng Data Fgure 9 shows the referene sgnal used for tranng of the neural network ontroller. It was desgned to mantan a level wthn the operatng range of the sensors. A random sgnal was reated that would provde the ontroller wth typal values that a user ould hoose durng normal operaton. These values were held wthn the deal operatng range for whh the dentfer was traned.. Testng Data Fgure shows a set of testng data used for the neural network ontroller. As an be seen, ths pattern s somewhat smlar to that seen n the tranng. As was the ase n the dentfer, one the tranng porton of the ontroller s ompleted, t needs to verfy that tranng. A set of data was seleted for testng the ontroller tranng. Sne the tranng data used was desgned to be a omponent of typal operatonal values, a smlar set of data was reated for testng the traned network.. Controller Tranng In Fgure, onvergene towards the goal of small error s learly seen n the ontroller tranng algorthm. However, the error does not reah the desred ut-off. Despte ths, the weghts traned as a result of ths tranng provde a very good response when the testng data s used to evaluate the ontroller weghts.. Controller Testng As shown n Fgure, the weghts for both the dentfer and ontroller had been traned to a level that provded an aeptable level of predton, and showed that the ontroller was workng as expeted. Error (V) Controller Tranng Error Fg.. Epoh Controller Tranng Error Error Preprnt submtted to IEEE Conferene on Control Applatons. Reeved February 8,.

6 .. Controller Test Data R Lmted rulaton. For revew only. Neural Network Control Results Setpont Sensor.8.6 Water Level (m) Tme (s) Fg.. Controller Testng Fg.. Onlne Neural Network Control Result Fuzzy Control Result Sensor Setpont omparsons between the two ontrol shemes based on the expermental results. Water Level FLC NNC Plant Math Model Unneessary Unneessary Computaton Lght Heavy Trakng Performane Good Better Dsturbane Rejeton Good Better TABLE IV COMPARISON BETWEEN THE FUZZ CONTROL AND NEURAL NETWORK CONTROL BASED ON THE EXPERIMENTAL RESULTS Tme (s) Fg.. Onlne Fuzzy Control Result B. Experments on mro-ontroller The fuzzy and neural network ontrol algorthms were ported to a stand-alone VRP MTSC mro-ontroller. The man board of mro-ontroller s based on Texas Instruments TMSC DSP wth a CAN bus ommunaton port that faltates the ommunaton wth a PC for montorng onlne parameters. The ontrol algorthms were developed wth C language, ompled wth TI Compler and run from the mroontroller. To provde an objetve omparson between the fuzzy and neural network ontrol algorthms, two tests were arred out n the VRP MTSC DSP mro-ontroller. Fgure shows fuzzy ontrol result and Fgure shows the neural ontrol result. VI. CONCLUSION Ths paper proposed two ontrol shemes for the water level ontrol system. From the results of the expermental studes, the followng summary an be obtaned. For the fuzzy ontrol, n order to ensure the best performane, a number of fators and values need to be onlne determned heurstally or by tral and error, for example, the membershp funtons. For neural network ontrol, the learnng parameters and pror well-tranng s essental for the suess of the ontrol. One traned, the neural network does not requre for tunng. Table IV shows a summary of REFERENCES [] Nmura, T. and okoyama, R., Water level ontrol of small-sale hydrogeneratng unts by fuzzy log, Proeedngs of IEEE Int l Conferene on Systems, Man and Cybernets, pp. 8, 99. [] Roubos,J.A., Babuska,R., Brujn,R.M. and Verbruggen,H.B., Predtve Control by Loal Lnearzatn of a Takag-Sugeno Fuzzy Model, IEEE Transatons, 998. [] Ghwanmeh,S.H., Jones,K.O. and Wllams,D., On-lne Performane Evaluaton of a Self-Learnng Fuzzy Log Controller Appled to Non- Lnear Proesses, IEEE Transatons, 996. [] Naman,A.T., Abdulmun,M.Z. and Arof,H., Development and Applaton of a Gradent Desent Method n Adaptve Model Referene Fuzzy Control, TENCON Proeedngs. Intellgent Systems and Tehnologes for the New Mllennum, pp. 8,. [] Xao,., Hu,H., Jang,H., Zhou,J.and ang,q., A Adaptve Control Based Neural Network for Lqud Level of Molten Steel Smeltng Nonrystllod Flmsy Alloy Lne, Pro. of t h World Congress on Intellgent Control and Automaton, Chna,. [6] Narendra, K.S. and Parthasarathy, K., Identfaton and Control of Dynamal Systems Usng Neural Networks, Neural Networks, IEEE Transatons on,vol., No.,Mar,99. [7] Takag,T. and Sugeno,M., Fuzzy Identfaton of System and ts Applaton to Modelng and Control, IEEE Transatons on Systems, Man and Cybernets, Vol., No., 98. [8] Murakam,K. and Sugeno,M., An Expermental Study on Fuzzy Parkng Control Usng a Model Car, Industral Applaton of Fuzzy Control, North Holland, 98. [9] amada, T.and abuta, T., Dynam system dentfaton usng neural networks, Systems, Man and Cybernets, IEEE Transatons on, Vol., Issue,Jan/Feb, 99 [] Mstry, S.I.and Nar, S.S., Identfaton and Control Experments Usng Neural Desgns, IEEE Control Systems Magazne, Vol., Issue, Jun, 99. Preprnt submtted to IEEE Conferene on Control Applatons. Reeved February 8,.