A Computer Control System to Regulate the Temperature of a Microwave Cavity

Transcription

1 A Comuter Cotrol System to Regulate the Temerature of a Microwave Cavity BRET F. DRAAYER, JAI N. DAHIYA Physics Deartmet Southeast Missouri State Uiversity Oe Uiversity Plaza, Cae Girardeau, MO USA Abstract: - May materials exhibit sigificat chages i dielectric roerties over very small temerature sas due to hase chages. Commoly, the dielectric roerties of a substace are iferred as these hase chages occur by lacig the substace i a microwave cavity ad bombardig it with radiatio while measurig how the resoat radiatio field is effected. However, tryig to measure chages i dielectric roerties i this maer requires recise cotrol over the temerature of the cavity. This aer describes a simle arragemet for regulatig the temerature of a microwave cavity usig a comuter ad iexesive, off-the-shelf equimet. Key-Words: - Feedback, PID Cotroller, Sectroscoy, Dielectric, Resoace, Comuter Cotrol. 1 Itroductio It is commo to use a microwave resoat cavity as a tool to study the microwave dielectric resose of materials as a fuctio of frequecy ad temerature. Whe used i for these uroses, the resoat cavity is usually oerated i the TE011 mode, which is the most sesitive mode for measurig the electric ermittivity of a material. A microwave resoat cavity dislays the same resoat characteristics as a tued circuit; the basic differece betwee the two is that the curret ad voltage of the tued circuit are relaced by electromagetic fields. As a waveguide forms the aalogy for a trasmissio lie i ordiary circuit theory, so a hollow cavity forms the aalogy for a circuit elemet. Due to the low resistace i a resoat cavity, it is ossible to obtai large values for the quality factor, or Q-factor, which is why microwave cavities are used to measure subtle variatios i the electrical characteristics of materials. Whe a samle of a material is laced i a microwave cavity, it erturbs the electric or magetic field i the cavity deedig o what mode the cavity is i, ad from this either the electric ermittivity or magetic ermeability ca be determied. Usig a resoat cavity has become a stadard techique i the study of dielectric relaxatio behavior of differet materials [1-4]. Of articular iterest is the dielectric behavior of olar molecules from the solid to the liquid hase. For olar molecules, the dielectric costat dros abrutly ear a hase trasitio temerature. I some olar molecules, like water ad itrobezee, the dro is so raid that it is very difficult to record the exact temerature at the hase chage. Cosequetly, characterizig the dielectric roerties of a substace as a fuctio of temerature requires the ability to maitai a stable temerature while resoace measuremets are beig made. 2 Problem Formulatio It is fairly easy to alter the temerature of a microwave cavity by umig either heated or cooled air through it. However, exercisig recise cotrol over the temerature is much more difficult. Curretly, the temerature of the microwave cavity used to gather the data i this aer is cotrolled by circulatig air through it that has bee cooled by liquid itroge i a thermal bath. A valve is used to adjust the amout of air that asses through the system ad thus the amout of coolig that takes lace. Without the temerature cotrol system, it is difficult to get meaigful data of dielectric roerties at a hase trasitio temerature because the temerature drifts raidly. Adjustig the airflow maually is almost imossible because the

2 temerature is very sesitive to chages i airflow, ad comesatig for a icrease i temerature by oeig the valve maually ofte results i the temerature becomig cooler tha desired. To overcome this roblem, we will discuss how to build a feedback cotrol system usig just four ieces of equimet a comuter, a thermocoule, a electroic valve, ad a iterface device that allows the comuter to read the cavity s temerature ad adjust the valve. Figure 1 shows the exerimetal setu. 3 Problem Solutio The electroic valve was urchased from Hass Maufacturig, ad it ca be cotrolled with either a aalog curret or voltage. I the voltage cotrol mode, the size of the valve s oeig is regulated i direct roortio to the voltage alied to it. At oe volt the valve is comletely shut off, ad at five volts the valve is fully oe. I betwee oe volt ad five volts, the valve oes icremetally i 255 stes for a ste size of 4V/255 = 15.7mV. It is iterestig to ote that the aalog voltage sulied to the valve was roduced by a D/A coverter with 8-bit resolutio ad a outut rage betwee zero ad five volts, for a ste size of 5V/255 = 19.6mV. Due to the discreacy i ste size betwee the A/D ad D/A coverters, every 4 th ste o the valve is theoretically skied ad the valve oes i two icremets for a oe-icremet icrease i the voltage roduced by the comuter. Although this imlies that we are ot usig the full 8-bit resolutio of the valve, the resolutio is still high eough (7½ bits = 192 stes) to rovide accurate temerature regulatio. To moitor the temerature of the microwave cavity, we used a off-the-shelf iterface from Comuter Boards Icororated to read the voltage of a T-tye thermocoule. The iterface rovides for adjustable gai ad has cold juctio comesatio, which meas it ca comesate for the temerature offset due to the thermocoule-to-iterface cotact. A more comlete descritio of the thermocoule ad iterface ca be foud i [5]. Due to the resolutio of the iterface s A/D coverter ad the rage of temeratures ivolved, the thermocoule reorts temeratures i 1/8ºC icremets with a error of ±1/16ºC, which allows for very accurate temerature readigs. 3.1 Cotroller Descritio Figure two is a block diagram of the valve, thermal bath, ad microwave cavity oerated i oe-loo. It shows that the outut of this system, i.e., the temerature of the cavity (T c ), deeds o the iut airflow, f(t), ad a umber of variables, x 1, x 2, x, as idicated by the fuctio G(x 1, x 2, x ). Imortat variables that affect cavity temerature iclude heat absortio due to imerfect isulatio, air loss through leaks, the amout of liquid itroge i the thermal bath ad the liquid itroge evaoratio rate, just to ame a few. Ufortuately, we oly have good cotrol over oe of these variables the airflow. Other variables fluctuate as the airflow ad other factors chage, but we do ot have good kowledge of these relatioshis ad how they affect cavity temerature. I other words, we do ot have accurate kowledge of G(x 1, x 2, x ), ad thus caot redict how the temerature will vary as the airflow rate chages. Moreover, we caot accurately model the system i the time domai, ad hece we have o aalytical meas of determiig a trasfer fuctio for the system i the Lalace domai. Noetheless, the situatio is far from hoeless. We ca characterize the system s resose to various stimuli, such as a ste fuctio, to gai isight ito the system s behavior. I so doig, we ca cotrol the temerature i the cavity desite havig a icomlete uderstadig of the hysical rocesses that dictate temerature. To regulate the temerature of the cavity accurately, it is helful to embed the coolig system ito a feedback cotrol system, as show i Figure 3. Feedback allows the actual temerature of the cavity to be comared to the desired temerature, ad to make adjustmets based o the differece, or error, e(t). Essetially, the magitude of the error determies the stregth with which a cotoller laced i series with the coolig system acts to correct the differece. Big differeces result i big correctios, ad small differeces result i small correctios. The sig of the error esures that the correctio is alied i such a way so as to reduce the differece. If the desired temerature is cooler tha the actual temerature, airflow through the valve is icreased to lower the discreacy. The toology of the cotroller is comosed of three searate arts a roortioal comoet, a itegral comoet, ad a differetial comoet, which is why this toology is deoted as a PID cotroller. With this cotroller i lace, the airflow, f(t), is give by:

3 de( t) f ( t) = K e( t) + K i e( t) dt + K d. (1) dt The roortioal comoet, rereseted by K e(t), icreases airflow i direct roortio to e(t). As the actual temerature aroaches the desired temerature, the outut rereseted by the roortioal term decreases, causig a decrease i airflow. However, i the absece of the itegral ad derivative comoets, there is o hoe of the error becomig zero because o error imlies zero airflow. But we kow that the cavity is costatly absorbig heat sice it is ot erfectly isulated; therefore, the airflow rate will decrease util equilibrium is reached ad coolig matches heat absortio. Ay decrease i temerature beyod this equilibrium caot be sustaied due to the decrease i airflow. Thus, the roortioal comoet ca ever reduce the error to zero by itself, which is why it is combied with a itegral ad differetial comoet i the PID desig. Essetially, the itegral comoet will maitai airflow through the system eve as the error goes to zero. Although the itegral comoet ca theoretically reduce steady-state error to zero, it also makes the system slow to react to chages i desired temerature, ad ofte results i overshoot whe the temerature goes from oe stable temerature to aother. To overcome this roblem, the derivative comoet is icluded, ad its fuctio is to act as a ower surge by reiforcig the roortioal comoet whe the actual temerature is movig away from the desired temerature, which hels comesate for the sluggishess caused by the itegral comoet; moreover, it ooses the roortioal comoet whe the actual temerature is movig towards the desired temerature, ad thus hels elimiate overshoot behavior. 3.2 Comuter Imlemetatio Thus far, we have viewed the cotroller as oeratig i cotiuous time, with measuremets ad adjustmets beig made at every istat i time. However, comuters are discrete by their very ature, ad usig a comuter i a cotrol system therefore imlies that readigs ad adjustmets will occur icremetally i time, ad with fiite resolutio. Fortuately, comuters are fast eough ad iterface equimet is accurate eough that the discrete ature of comuter cotrol is ot a major roblem for most alicatios, ad the ramificatios of fiite digital recisio will ot be addressed further i this aer. Noetheless, to accurately reflect the digital ature of the cotrol system, we must chage the differetial cotrol equatio (eq. 1) to a differece equatio. Aroximatig the itegral term i (1) with a sum ad the derivative term with the differece betwee the most recet samle ad the revious samle, (1) becomes: f ( T ) = K e( T ) + K e( j T ) = 1 (2) + K d [ e( T ) e(( 1) T)], where T is the samlig iterval ad is a iteger that reresets the samle umber. For the uroses of comuter codig, it is coveiet to exress (2) as a sigle summatio. Of course the itegral term is already i the form of a sum. If, i the roortioal ad differetial terms, e( t) is rereseted as j= 1 i j 1 e ( t) = e( j t) e( k t), k = 1 ad we let e( t) be deoted as e, the (2) becomes: where f = j = 1 α = K α e + β e (3) j j 1 + δ e j 2, K d + Ki t + t 2K d β = K, ad t K δ = d t Note that (3) aturally leds itself to a iterative comuter rocedure. The PID cotroller algorithm is easily imlemeted by readig the temerature of the cavity, fidig the differece betwee the actual temerature ad desired temerature, formig the sum i (3), ad storig the curret error ad sum for the ext iteratio. All that remais to secify is how to determie values for K, K i, ad K d. 3.3 Determiatio of PID Parameters A ituitive rocedure for determiig PID arameters is to adjust the roortioal term, K, util a reasoable ste resose is roduced. Next, adjust the itegral term, K i, to miimize steady state error..,

4 Fially, adjust the derivative term, K d, util oscillator behavior is removed. However, this trial ad error method ca be time-cosumig, ad other good methods do exist. We used the Ziegler-Nichols oe-loo method [6]. I this method, the system is subjected to a abrut chage i iut, i.e., a ste iut, ad the outut is recorded as a fuctio of time. For this exerimet, the voltage cotrollig the valve was icreased from 1100mV to 1300mV, ad the temerature of the cavity was measured every two secods. Figure four is the resultig lot of cavity temerature versus time. To aly the oe-loo Ziegler-Nichols method, we eed to the lag time, L, the size of the iut ste,, ad the maximum sloe of the chagig outut, M. The lag time is the time iterval betwee alyig the ste iut ad the oset of chages i the outut. From Figure 4, it is see that L equals aroximately 75 secods. The iut ste, which should be measured i digital uits, is simly the chage i voltage divided by the ste size of the valve, or = 200 mv/19.6 mv = 10 digital uits. From Figure 4, the maximum sloe of the chagig outut is foud to be M = 4 C/335s = digital temerature uits er secod. With L,, ad M, kow, we ca calculate the PID arameters accordig to: K = = 1.42, LM K Ki = =.01, 2L L & K d = K = Exerimetal Results Due to uexected roblems with the microwave sectrometer, we were uable to take data o some materials of iterest usig the cotrol system. O the other had, relimiary tests idicate that the cotrol system works very well for maitaiig a stable cavity temerature. We aticiate takig data i the ear future ad resetig results at the MCP 2000 Coferece. Exerimetal results of the dielectric measuremets will be show i a follow-o aer. 4 Coclusios Off-the-shelf equimet to cotrol a variety of hysical rocesses is iexesive, ad easy to fid ad oerate. Therefore, digital systems to cotrol eve simle rocesses are comig ito widesread use. I this aer, we have exlaied the oeratio of the PID cotroller i a ituitive fashio, ad have tried to show that it is simle to imlemet the PID algorithm o a comuter eve with a icomlete uderstadig of the system to be cotrolled. We have also show that the temerature of a microwave cavity ca be stabilized usig a simle feedback cotrol system so that subtle dielectric measuremets ca be made with much greater accuracy tha is ossible without the cotrol system. Refereces: [1] J. N. Dahiya, S. K. Jai, ad J. A. Roberts, Phase Trasitio Studies i Polar ad No-Polar Liquids at Microwave Frequecies, Joural of Chemistry ad Physics,Vol. 74, No. 6, 1981, [2] J. N. Dahiya, Microwave Dielectric Resose of Selected Polymers, Joural of Materials Educatio, Vol 17., No. 5&6, 1995, [3] K. H. Hog ad J. A. Roberts, Microwave Proerties of Liquids ad Solids Usig a Resoat Microwave Cavity as a Probe, Joural of Alied Physics, Vol. 45, No. 6, 1974, [4] J. Roberts ad F. Aag, Dielectric Relaxatio i a Water over the Frequecy Rage 13 f 18 GHz Usig a Resoat Microwave Cavity Oeratig i the TM 010 Mode, Joural of Microwave Power ad Electromagetic Radiatio, Vol. 28, No. 4, 1993, [5] B. Draayer ad J. Dahiya, A Comuterized Microwave Sectrometer for Dielectric Relaxatio Studies, NASA Coferece Publicatio, Vol , November 1998, [6] B. D. Hall, Alicatio of PID Cotrol to a Thermal Evaoratio Source, Physics Exerimets Usig PCs, H. M. Staudemaier (Editor), Sriger Verlag, 1993,

5 Thermocoule Electroic Valve Microwave Cavity Air Pum Thermal Bath Figure 1: Exerimetal setu. f(t) Coolig System G(x 1, x 2,..., x ) T c(t) Figure 2: Coolig system i block diagram form. PID Cotroller Coolig System T D + e(t) f(t) G(x 1, x 2,..., x ) T c(t) Figure 3: Coolig system embedded i a feedback loo with a PID cotroller.

6 Ste Resose (200 mv) Degrees Celsius tem time secods Figure 4: Ste Resose of the system oerated i oe-loo.