Antenna Azimuth Position Control System Verification Dr. Jose Granda ME27 !2"2!"7 Graduate Students# Su$h%ir &undal 'ee (hao (yrone (racy
)*(+,D-C(),*# Control systems are interated into many facets of life/ ranin from nature to social issues to mechanical systems. A nature e0am1le ould %e our %odies# hen e ant to ra% an o%3ect4 our eyes ill focus on it and relay the information to our %rain4 hich ill send electrical sinals to our muscles to 1osition our arms correctly. (here are mechanical systems li$e controllin ater flo from a tan$4 and $ee1in the tan$5s ater heiht at an a11ro1riate heiht. (here are an unlimited num%er of control e0am1les in the orld4 %ut e ill focus on a 1articular electromechanical system. *orman S. *ise in6estiates the desin of a control system for an antenna in his te0t%oo$ Control Systems Enineerin. (he name of this 1ro3ect is Antenna Azimuth Position Control System. (he %asic idea is that someone4 from a control toer4 can ad3ust a sim1le 1otentiometer %y hand and ultimately mo6e a lare antenna. (his system is thorouhly analyzed %y Dr. *ise. (he system schematics are i6en and transfer functions are o%tained %y hand. (his ill 1ro6ide us su11ort durin our analysis of the Antenna Azimuth Position Control System.
,'JEC()VE# ,ur rou15s o%3ecti6e is to o%tain the same analysis results as the Control Systems Engineering te0t%oo$ on the same Antenna Azimuth Position Control System. (he te0t%oo$ uses hand analysis4 %ut e ill try to match the results usin a com%ination of Cam1G4 Matla%4 and Simulin$. (he items e ill com1are are transfer functions and ste1 res1onses. Cam1G should 1ro6ide the same results as lon as our modelin of the system is correct. (his is here the hardshi1 may lie.
S8S(EM C,*CEP(# 9e must understand the systems o1eration so an e01lanation ill follo. Poer is a11lied to a 1otentiometer. An o1erator ill rotate a 1otentiometer5s $no% a certain amount. (he 6oltae difference from the source and the ne 1osition is then measured. (hat ne 6oltae sinal ill %e sent to a 1ream1lifier. (he 1ream1lifier ill am1lify the sinal %y a ain :;<. (hen that result ill %e sent to a 1oer am1lifier. (he 1oer am1lifier is 1oered %y a much reater 6oltae to allo for sinificant ain. So the out1ut of the 1ream1lifier ill %e am1lified %y the 1oer am1lifier and that result ill %e sent to a motor. (he motor is connected to a shaft and ear =!. Gear =! is connected to a larer ear =2. Gear =2 is directly connected to the shaft of the antenna. ,nce the motor 1oers ear =! then ear =2 ill start to rotate the antenna. Gear =2 is also connected to ear =>. Gear => and ear =2 ha6e the same ratio. Gear => is connected to another 1otentiometer. (hat 1otentiometer is connected to the same 6oltae source as the first one. (he difference %eteen that 1otentiometer and the 6oltae source is then feed%ac$ to our oriinal 1ream1lifier. (hen the 1ream1lifier ill ta$e the difference %eteen the to 6oltae sinals and out1ut that result into the 1oer am1lifier. (he 1oer am1lifier then dri6es the motor to mo6e the antenna. (he 1rocess ill continue to cycle as lon as there is a 6oltae difference %eteen the to 1otentiometers in the system. A ra1hical 6ie is 1ro6ided %y the te0t%oo$.
(E?(',,; SC&EMA()C# (he antenna control system needs to %e con6erted from a 1hysical system to a %o0 diaram schematic. (his schematic is 1ro6ided %y the te0t%oo$.
&ere e can see all 1arts of our 1hysical system. (he 1otentiometer the o1erator controls is at the 6ery to1. (he sinal is sent to the 1ream1lifier then to the 1oer am1lifier. (hat result is sent to a motor @yrator then to a ear4 hich is connected to another ear to chane the 1osition of the antenna. Binally the antenna5s sinal is connected to another ear and a 1otentiometer. (he feed%ac$ is easily seen oin %ac$ from the 1otentiometer into the differential 1ream1lifier. (he feed%ac$ is crucial in determinin hether our antenna is in the correct 1osition.
(he 1arameters of the system are i6en to us %y the te0t%oo$. 9e ill use the same 1arameters hen com1arin results. (a%le !# Schematic Parameters
A*A8S)S# 9e ill start %y %rea$in don hat 1arts of the system to analyze. (here are three main 1arts# differential 1ream1lifier4 1oer am1lifier4 and motor 1lus ears. D)BBE+E*()A P+EAMP)B)E+#
(he %oo$ is 6ery straiht forard a%out this 1art. (hey assume that the am1lifier ne6er reaches saturation and the dynamics of this 1art are nelected. (his is %ecause the res1onse of this 1art is ty1ically much faster than the res1onse of the 1oer am1lifier. (he transfer function of this 1art is :;< hich is 3ust the ain. ,ur 1ream1lifier is modeled in Cam1G#
(he te0t%oo$5s transfer function and ste1 res1onse is shon %elo#
,ur transfer function and ste1 res1onse is shon %elo#
(he to transfer functions and ste1 res1onses are the same. (his as an easy 1art %ecause all that is ha11enin is a constant ain is a11lied to a sinal.
P,9E+ AMP)B)E+#
(he 1oer am1lifier ta$es the out1ut of the 1ream1lifier and am1lifies the sinal to send to our motor. (he o1am1 circuit is slihtly different than the 1ream1lifier. 9e had 1ro%lems ith deri6ati6e causality in our Cam1G model so e had to add a C element. (he %ond ra1h is shon %elo#
(he te0t%oo$5s transfer function and ste1 res1onse is shon %elo#
,ur transfer function and ste1 res1onse is shon %elo#
(he transfer function and ste1 res1onses for %oth the te0t%oo$ and our results match closely. 9e had to ad3ust resistor and ca1acitor 6alues in order to o%tain the matchin transfer functions. (his means that our 1oer am1lifier should %e modeled correctly.
M,(,+ A*D ,AD#
(he motor and load setu1 has %een done se6eral times. (he schematic is in the Cam1G user manual. 9e started ith that one %ut added an additional (B so that e can account for our system5s feed%ac$. (he Cam1G model is shon %elo#
(he te0t%oo$5s transfer function and ste1 res1onse is shon %elo#
,ur transfer function and ste1 res1onse is shon %elo#
9e 1ut the transfer function the %oo$ calculated into Simulin$ and ot a 1lot. (hen e too$ ours and entered it into Simulin$ and came u1 ith almost the same e0act 1lot. (he slo1e of the line is different due to the ain of the system.
C,MPE(E S8S(EM#
*o e must com%ine all three 1arts and o%tain the system5s res1onse. Birstly4 our antenna system Cam1G is shon %elo#
(he te0t%oo$5s transfer function and ste1 res1onse is shon %elo#
,ur transfer function and ste1 res1onse is shon %elo#
,nce aain4 e used simulin$ to com1are the results reardin the hole system. -sin simulin$ the transfer function and 1lot ere 6ery similar. ,ur 1ro%lem as matchin u1 the Matla% 1lots.
C,D)*G ,ne of the ma3or issues e had ith this 1ro3ect as the Matla% codin. 9e entered in all the initial conditions that ere in the te0t%oo$4 and then entered in a 6alue for the yrator4 hich as not i6en. After that e ould et errors and 1ro%lems ith our results mostly for the Motor analysis and o6erall system analysis. Binally e fiured out that e need to chane matrices dimensions in order to o%tain 2nd and >rd order transfer function euations. Still e don5t understand the matla% code ell enouh to match u1 our calculated transfer function to that one in the %oo$.
C,*C-S),* ,6erall this 1ro3ect as 6ery interestin. )t incor1orated understandin of se6eral disci1lines. A system as i6en to us that had already %een analyzed %y hand. 9e first had to read a%out the system and conce1tually fiure out ho it as or$in. (o start the analysis e had to %rea$ the system u1 into a fe sections/ the differential 1ream1lifier4 1oer am1lifier4 and motor. (hen e continued to model each section ith Cam1G %ondra1hs. Cam1G hel1ed us o%tain transfer functions and ste1 res1onses. 9e also used simulin$ to 6erify these results. -ltimately e com1ared the te0t%oo$s results ith ours and found that they ere close on some 1arts and not so close on others. 9e56e s1ent many hours on these 1ro%lems4 %ut are una%le to mani1ulate the Matla% code or system characteristics to o%tain the results e ant. ,ne other as1ect of this 1ro3ect e s1ent a lot of time ith is 1hysically %uildin the antenna control system on a %read%oard. (his as 6ery interestin to see the second order"feed%ac$ system at or$. 9e had to research all the electrical com1onents of the model and connect e6erythin toether. After %loin u1 se6eral )Cs e came u1 ith a or$in 1hysical model. 9e ha6e 6ideo ta1ed the system in action and included it in the folder that e ill turn in. oo$in %ac$ e should ha6e started the 1ro3ect a little sooner4 %ut e56e learned a lot in a short time4 and are confident that e understand the %asics of Cam1G"Matla%"Simulin$ 6ery ell.
