Sliding Mode Indicator Model s at Thermal Control System for Furnace

Transcription

1 Proceedigs of the 7th World Cogress The Iteratioal Federatio of Automatic Cotrol Slidig Mode Idicator Model s at Thermal Cotrol System for Furace Varda Mkrttchia*, Sargis Simoya**, Aa Khachaturova***, Hasmik Yeraosya**** *All Armeia Iteret Uiversity, Sydey, P.O.Box 965, NSW 66, Australia (Tel: ; aaiu@optuset.com.au). **State Egieerig Uiversity of Armeia, Yereva, Armeia, ( ssimoya@seua.am) *** Istitute for Physical Research of NAS of Armeia,, Ashtarak-, Armeia, ( khaa@ipr.sci.am) **** PhD Departmet of All Armeia Iteret Uiversity, Yereva, Armeia, ( hhhui@freeet.am) Abstract: This paper discusses ad deals the developmet of the Slidig Mode Cotrol Idicator with the usig techique of Discotiuous Cotrol for furace i Laser Physics. To improve efficiecy of practical implemetatio, the furace cotrol system is regarded as electroic elemets havig a discotiuityswitchig mode where the slidig modes are the basic motios. Implemetatio of this approach implies the kowledge of the coditios of the occurrece of slidig mode, for which purpose a slidig mode idicator hardware ad model has bee developed by meas the LabView graphical programmig laguage uder Widows eviromet. INTRODUCTION Furace cotrol i laser physics ca be difficult, due to their itrisic oliearity. I fact, cotrol should esure system stability i ay operatig coditio ad good static ad dyamic performaces i terms of rejectio of iput voltage disturbaces ad effects of load chages (output impedece). These characteristics, of course, should be maitaied i spite of large iput voltage, output curret, ad eve parameter variatios (robustess). Cotrol withi slidig mode (SM) eables us to decrease the sesitivity to variatios of chip characteristics makig them idepedet upo the eviromet. These features make this cotrol techique a valid alterative to stadard cotrol approaches like curret-mode cotrol. The block-diagram of cotrol system with Idicator of Slidig Mode is show o Figure, where - is the error of cotrol sigal (Mkrttchia, 7). From the poit of view of mathematics, the problem may be reduced to that of fidig the area of attractio to the maifold of the discotiuity surfaces itersectio. I the described algorithm, a ew compoet called Slidig Mode Idicator is proposed. This block detects the occurrece of SM i the system. If the SM does ot occur, the idicator block deliberately geerates the SM i the system (Mkrttchia, 999-7). Ufortuately by use this desig result for chip desig eeds some developmet process ad desig ew Idicator diagram. Cotrol withi slidig mode eables us to decrease the sesitivity to variatios of chip characteristics makig them idepedet upo the eviromet. The metioed problems ca be overcome by usig asymptotic observers of state ad aticipatory devices elimiatig delays. Discotiuity of cotrol results i a discotiuity of the right-had parts of the differetial equatios describig the system s dyamic properties. Deliberate itroductio of objects ito the slidig-mode operatio will ecessitate a cotiuous moitorig of the slidig-mode occurrece ad stability (Utki, 98). Our purpose is to achieve a model suitable for the use with all types of solutio simulatio. Therefore it should be preseted as a simple equivalet circuit. The circuit elemets are derived from physical cocepts, which are more ofte tha ot lost wheever a complex model for a solutio is extracted from a optimizatio model. For the Fiite Differece Time Domai computatio of the object ports are defied o the coaxial lies as it is used i most simulators by observig wave ratios. The ports for solutio's equivalet circuit are cocetrated or iteral ports defied by voltage ad curret. The resultig S-parameters of the ports are used to extract equivalet circuit elemets leadig to well defied values with physical seses. The essetial compoets of the solutio model are the slidig-mode idicator, observer ad the aticipatory device. As already oted, the approach used is orieted toward a deliberate itroductio of slidig modes over the itersectio of surfaces o which the cotrol vector compoets udergo discotiuity. Realizatio of such a approach implies the kowledge of the coditios of the occurrece of slidig mode. Desiged for this purpose was the idicator of slidig /8/$ 8 IFAC 59.38/876-5-KR-.6

2 7th IFAC World Cogress (IFAC'8) modes. From the poit of view of mathematics, the problem may be reduced to that of fidig the area of attractio to the maifold of the discotiuity surfaces itersectio (Dubrovsky ad Kortev, 968). O the idicator iput, two sigals x ad g from the equivalet circuit are supplied. Furace Logic-switchig block. DEVELOPMENT OF SLIDING MODE INDICATOR The desiged algorithm of slidig mode idicator based o Lab View programmig is show i Fig.. Y sp + - Y E p p E С С + + g( Slidig Mode Idicator Switchig fuctio former e ( g( g( o yes Alarm mode, chagig cotrol value from М to М. +M -M X ( t ) Object of cotrol Fig.. Block-diagram of cotrol system with Idicator of Slidig Mode The idicator compares two sigals recordig the momet of chagig the sigs of fuctio t ) ad g (, see (). g ) ( t ) C t C de dt () where g( - is fuctio of idicator; - is the error sigal. I () C ad C is costat of object cotrol; g is fuctio of switchig; x is system parameter, t is time. The rule of chagig of cotrol fuctio is where K, K K... if... g( U ( () K... if... g( - fixed parameters of regulator; The goal is to fid the coefficiets for a switchig equatio of a first order lag temperature system ad the associated temperature system. The temperature sesor should be placed so it respods to chages i the actual temperature as quickly as possible. This reduces the sesor time costat. I a perfect world there would be o differece betwee the actual ad measured temperature. I this case oe could simply switch o ad off the heater at the set poit. I the real world there is a lag i the sesor respose. If oe were to switch the output usig the measured temperature without takig ito accout the sesor lag, the actual temperature would oscillate aroud the set poit. To compesate for the sesor lag we must take ito accout sesor time costat Fig.. Algorithm of developmet slidig mode idicator 3. DEVELOPMENT OF CONSTRUCTION PROCESS OF SM EXISTENCE REGION S As it kow, the motio of the system operatig i the slidig surface is ivariat to disturbaces, parameter ucertaities, couplig betwee chaels, ad oliearities see i the system. The costat coefficiets Ci of the slidig surface boudary described by (Mkrttchia, 999-7) are chose to provide the output trackig motio i slidig mode. This is accomplished through costructio of SM existece regio ad choosig the coefficiets Ci from the regio. The graphic developmet method of costructio of SM existece regio is give o Figure 3. F(p) Ã K p * L F(M) -6 F(p) Y, Fig. 3. The developmet SM existece regio for furace cotrol system O N x, p O,O Ã x, F(M) Ý 6

3 7th IFAC World Cogress (IFAC'8) The output sigals of Slidig mode idicator are show o Figure. I case of (a) the slidig mode occur i system; i case of (b) the system is out of slidig mode regio; i case of (c) the system is deliberately itroduced o slidig mode by chagig of cotrol value from M to M. 4. SYSTEM MODELING WITH SLIDING MODE The goal is to fid the coefficiets for a switchig equatio of a first order lag temperature system ad the associated temperature system. The temperature sesor should be placed so it respods to chages i the actual temperature as quickly as possible. This reduces the sesor time costat. I a perfect world there would be o differece betwee the actual ad measured temperature. I this case oe could simply switch o ad off the heater at the set poit. I the real world there is a lag i the sesor respose. If oe were to switch the output usig the measured temperature without takig ito accout the sesor lag, the actual temperature would oscillate aroud the set poit. To compesate for the sesor lag we must take ito accout sesor time costat ad estimate how fast the error betwee the set poit ad measured temperature chagig. This results i the slidig mode equatio give below with e beig the error betwee the set poit ad the measured temperature. If s> the the heater is tured o otherwise the heater is tured off. s( t ) st ) t ) The followig parameters of the plat were cosidered: G = 3.69 Plat gai i degrees per % cotrol p = 3.4 Plat time costat i miutes s = Sesor time costat i miutes T = /6 Update period i miutes. Update more ofte for less ripple i the PV. T a = 5 Ambiet temperature. Coefficiets for the simulator are as follows. A p T exp A p =.995 p B p = (-A p ) B p = 4.876* -3 T A s = exp A s =.983 s B s = - A s B s = 7 Now covert the SMC equatio to a form that ca be used by a computer. eis roughly equal to (e[]-e[-])/t. The resultig equatio is: ee s s e T Igorig scale, this simplifies to: s T s s s T s C * e[ ] e [ ] * ee. Lettig С= the equatio simplifies to ad we have С=,7. s. 5. SIMULATION USING A SYSTEM OF DIFFERENCE EQUATIONS The first equatio calculates the actual temperature. Notice that it uses the cotrol output from the iteratio before. The secod equatio calculates the measured temperature usig the sesor time costat. The ambiet temperature is take ito accout so the temperature ca decay dow to the ambiet temperature ad ot. The third equatio just calculates the error. The fourth equatio is the equatio that does the slidig mode cotrol. Notice that the cotrol output is either fully o (%) or off. There is o i betwee. x y e u A p ( x T a ) T ag * Bp * u A s ( y T a ) T ab s ( xt a ) ry... if...( C * ee )... otherwise 4. EXPERIMENTAL RESULTS, where x - is actual temperature i the plat differece equatio; y - is the measured temperature i the sesor differece equatio; e error sigal, Error = SP- PV; Slidig Mode Cotrol. s s * e ' e. If s>, the tur o the heater else tur it off. The cotrol system icludes: ove with a heater ad a thermocouple; a amplifier that has sufficiet gai (k=) so as to provide the rage of voltage eeded; the PC hardware; voltage-cotrolled power supply for the ove heater. Software support is provided by the desiged cotroller program writte i the LabView programmig laguage eviromet. The DAQ board measures output from the operatioal amplifier. The voltage from the PC hardware is the cotrol sigal that will tur ON or OFF the heatig elemet to keep temperature set programmatically ad maitai the slidig mode. The model arragemet icludig the ove used i real experimet was allowed to achieve stability of ~ C. 6

4 7th IFAC World Cogress (IFAC'8) 5. CONCLUSIONS This paper formulates usig the methods of slidig mode cotrol. The Slidig Mode Idicator is desiged based o results obtaied i the sphere of discotiuous system desig. The experimetal results of applyig the desiged Slidig Mode Idicator illustrated the improvemet of the achieved performace applied to the furace cotrol system desig applicatio i Laser Physics. A additioal compoet of the slidig mode cotrol system the slidig mode idicator is proposed i the paper. The SM idicator allows for moitorig the existece of SM i the system ad eforcig the SM via modificatio of the parameters if the SM fails. The applicatio of the slidig mode idicator is demostrated o the cotrol system for furace i laser physics. Ñèãíàë óïðàâëåíèÿ Cotrol sigal Ñêîëüçÿùàÿ Slidig mode ïîâåðõíîñòü, surface S a) à) Number Êîëè åñòâî of poits òî åê S = Ñèãíàë óïðàâëåíèÿ Cotrol sigal Ñèãíàë Cotrol óïðàâëåíèÿ sigal Slidig Ñêîëüçÿùàÿ mode ïîâåðõíîñòü, surface S Ñêîëüçÿùàÿ ïîâåðõíîñòü, S Slidig mode surface á) b) c) Number of poits Êîëè åñòâî òî åê ñ) Êîëè åñòâî òî åê Number of poits 6 Fig. 4. The output sigal of developmet SM Idicator REFERENCES Basi, M.V. et al. (4). Robust itegral slidig mode regulator with delayed cotrol iput. Proceedigs of the III Iteratioal coferece o System Idetificatio ad Cotrol Problems, SICPRO 4, Moscow,

5 7th IFAC World Cogress (IFAC'8) Dubrovsky, E.N. ad A.V. Kortev (968). Adaptive variable structure systems of automatic cotrol with bouded cotrol actio. I: Variable structure systems ad their applicatio i problems of flight automatio (B.N. Petrov ad S.V. Emelyaov. (Ed.)), Nauka, Moscow. Mkrttchia, V.S. (999). Special-Purpose Devices Usig Techiques of Discotiuous Cotrol ad Settig Adjustmet (DC & SA) i Cotrol Applicatios. Proceedigs of the 999 IEEE Iteratioal Coferece o Cotrol Applicatios, Kohala Coast-Islad of Hawai I, Hawaii s, USA, Mkrttchia, V.S. ad A.A. Khachaturova (4). Slidig mode cotrol system for laser spectroscopy of alkali metal vapours. Proceedigs of the III Iteratioal coferece o System Idetificatio ad Cotrol Problems, SICPRO 4, Moscow, Mkrttchia, V.S. ad Khachaturova (5). Slidig Mode Thermal Cotrol System for Furace i Laser Physics". Proceedigs of the 6th IFAC World Cogress, Praha, 5, pp Mkrttchia, V.S. ad Boiko (7). Desig of Slidig Mode Idicator. Proceedigs of the America Cotrol Coferece. ACC 7. New York, Utki, V.A. ad A. V. Utki (4). Idetificatio liear system via slidig mode techique. Proceedigs of the III Iteratioal coferece o System Idetificatio ad Cotrol Problems, SICPRO 4, Moscow, Utki, V.I. (98). Slidig Modes i Problems of Cotrol ad Optimizatio (i Russia), Nauka, Moscow. 63