Rı. Cır. •. (b) lntegrator circuit. ·1 y. CC ii-i- Z 1-----1r---. -i- V1. (c) Derivative circuit. (d) Summing cireuit. Figure 2. Basie building blocks usiııg CCIIs together with ...
I"T,,\"1I1 i. 1';o.:I\"EKSITY l''l:I;''ITK''I;
JOI:ıt.'i.-\1.UF t:l.l:(TIUC\I.~
YE.\R.
~,\("nn'
1:I.t: will be obtained as follows:
(5a)
4. THE RESULTS OFSlMULATION In order to confırm the theoretical results. the PID circuit aiven in Fiz. 4 is simulated in the SPICE prograrn by usi;g the macro-model of A0844!AO from Analog Oevices. In this circuit, supply voltages of ± i2V and in orderto illutrate the time-domain response, the step input voltage with i Volt amplitude are used, In simulation procedure. the values of the capacitors Ci and Ci>. the resister values, and the input voltages also are given in the caption of Fig. 5. The capacitance values are selected such as to have a ben er iIlustration.
(5b) (5c)
C""ttt ERDAL,
The simulation results of the output of the CCII based PID controller are given in Figure 5 (a) and Cb) respectively. In both situations, the proportional gains are taken to be zero in order noı ıd confuse the fıgures.
Ali TOKER. C",'dl!l.ACAR
.-ı New
Prupurtiuııal-llI1~m/-Dt!ril'/llil'" AlIlf Calrtılıııitıg
t.a---
-
general, it is not known in advanc •.· ho« muciı cach parameter contribuıes LO the \1111pul crr, ır. That is why this definiıion is quiıc rcusunahlc. since the dcsigncr cxpecıs the conıribuıion cır cach parameter variaıion on output dev iili ion ııı bi! equal to each other. The formulation ıır ıhcsc ıolcrances was given by Erdal .:1. a]. i ı) 1·:\5 ;1 resulı, we can deline the optimuııı paranıerer io lı: rances as
..
.--------------------------_._----, •• i;.
t
(a)
,.--------------------," - - - .. ............ - .._ ..-._ .. - . •.••.••.••••• _ •••••. __ ••• ~ •• _._ ••• , __•••••• _••••.• _ •.•••• ~ •.•••••• - •••. ,
'
'Ye
_
................. _. ..... _......•-_
.
_
_
_
_--
!
_
-
.
.
v,
,--t ••/niST«.ı,J ı"
1m;.ı",
o_o •••••••••••
: •• ~._.~
••••••••••••
, •••••
_ •••••••••••••••••••••••••••
.............. ; : -+;.. ~
...Jo.-~ 1._
;
.:.
_
"0
rolcrance.
i~ ıhc
I.,
its maximum
\ alue. i.c.
.
• •••.
••••
··i···
• ••
.
------_.- - _ .. - _.- _.-
_ ~.lıııi
i.••
where (r)E[Wı.(.):j
(b)
frequency
Figıır« 5. Resıılıs ofth« siınıılatioıı (!ll!7ı: 1'1/) controller in Fig -i of the rıD controller for step respoııse of the input wiıh iV arnpliıudc and R,=50Id2. Rıı=50kO. Cıı=O.1 ~IF and Ci as parameter from 0.5~ıF to 2pF (Rıı' i Ol..:[}. Rı=2kO. Rı=IOkO. Rrr=-5MO. RlT=-WkO.R:n= ikO) (a) Output
i=I, .... IS
where t,. is the iıh parameter
(w
~:
;..
,
output rolcrance of the controller. il i~ ıhc parameter number. Le. n= 18 for ihe ~ ivcn coııtiguration. and IOj is the angular frequency al
~~.::.:~::.:~:.:~:~~::~?~~~=.~;~ which !ST J takes ,'. ~ ..... -
27 i
IP/Dı CtIIılrIII/"r Reulization By (Isiıı;: Current C/J"'·••.vor» Opıiııııım Purıııııcter Tul••raners
waveform
(b) Output wavcforrn of the PID controller for step resporise of the input with Sm V arnplitude and R,=-50kO, Rn=50kD. Cı= i~ıF and Ciı as parameter from 5~ıF to 20~ıF (R ••~' i OkO. R1=2kn. R!=IOkO. Rır=5Mrt R:ı·;-HH,n. R..r=lkn)
band,
dcsigncr»
is
T
Hencc
i
v.
interval
maximum
and
(OE [(r)ı.ıı)~].
(!Li
(:1,
iS~.('):
value at this frequency.
can easily detennine
spccificd
(oı) '5 S ".i
it should be rıored that
1')E[c,ıl.Ul:I.
the
deseribes
(1'1)
. i
•••••••
bclong
ıo
has
iıs
The dcsigncr
by plotting
iS:
ıhis interval or by using alrcudy mathernatical programs Iikc Matiab.
at
(I')):
ex isı ing
For example, assuming that the proportional !!ain, Kp=10, the integral gain, Kı =1 s'. and the derivative gain. Ki) =5 s, are gi\ CIL Therı the parameter values can be sclecıcd in Fig. 4 as follows: R" =IOKO.
Rı =2KO,
Rı =50KfL
RJ) =50KO.
=5KO.
R;T =.ıOKO,
RIl
R! =20KD.
(Sa) (gb)
Rn ~ IKn.
(gı.:)
From Figs. 5 (a) and (b). it is clear that the results are in good agreernent with the ıhcorcıical expecıations.
Cı=I~IF,
5. C.I\.LCULATING OPTIMUM PARI\.METER TOLERI\.NCES
For this example, the maximum values of the parameter sensitivities are calculatcd as follows:
The optimum parameter tolerances are defined as the tolerances contribute equally to the upper bound of the relative error of the output volıage of the controller (Itl V./V,,\) given in Fig. 4. In
ıS·~«(.ı," i. 'ing, =1.
C,'1'1I1ERDAL.
(1,=1.
C(}=IO~IF. i=I...4.
'Yk=I'
i=I, ...• 18
(SJ)
k=ı....ı.
(Se)
(9)
If it is required that 1.1V./V" i s 0.1 the parameter tolerances are to be choscn as follows:
Ali Tol'ER.
C~'dt!1
..ıC-tR
21"2
IR, IK"
lu,
.-i St'K' Pmpıırtilıl/al-/llft'::ral-Dt'ri'·Oli.'t' (P/D) Controller Reaiizaıion Br Usinı: Current Convevars And Catcıdaıing Dptimum Parameter TO/t'ralı~t'S " .
= IK: = iR_ = İCİ = Ic" = 0.55~·o. = IK:, = lıt" = 0.55%. = i~. = 0.55%. i = 1.....4.
( 10a) (IOb) (IOc)
For this panicular example, the optimum ıolerances are found to be equal to each other, however they are usually differenı in general ense. Choosing the parameter tolerances such as above, the designer can guarantee that the maximum deviation of the output voltage of the conıroller caused by the parameter variaıions due to the environrnental effects will be less than or equal ıo O. I. This rcsult can alsa be verified in SrlCE simulation. If ltiv./V"I ~ 0.01 is required the parameter ıolcrances rnusı be chosen ten times sınailer than the ones in Eq. (I O) and so forth.
6. CONCLUSIONS In this study. a CCII based PID design procedure is given and a new PID circuit is proposed. This circuiı consists of only four CClls. two urounded capaciıors. eighı resisıers. and four- voltaze buffers and iı is vay convenienı for inıeurated circuit implernentation. it is also ver)' s~itable sıable and fası control due to the enhanced properties of the current-tnöde circuits used in the design. Considering that, ıhe controller coefficients Kı,. Kı. and Ki) are depended on the time consıants and resisıor ratios they can easily ~e adjustcd ıo any desired value independently lrom each other, Furthermore, ıhe optimum parameter ıolerances are determined to keep the relative error of the output of the CClls based PI D controller due ıo parameter variations in its ıolerance region.
REFERENCES [I] Kuo, B.C., "Automatic Control Systerns ", Prenıice-Hall, Upper Saddie River, NJ.. 1997. [2] Svoboda. J. A., "Current conveyors, operarional amplifiers and nullors .•.., lEE Proceedings, Vol. 136, No. 6, pp. 317-322, December 1989.
[3] Wilson, B .. "Recent developrnents in current conveyor and current-mode circuits". Proceeding of lEE pt, G. Vol. 137, (2). 1990. pp.63-77. [4] Roberts, G. W .• Sedra, A. S .. "All current-rnode frequency selective circuits", Elecıronics Leııers. Vol. 25. 1989, pp.759-761. [5] Toumazou. C .. Lidgey F. J .. and Haigh D. G., =Analog IC Design: The Current-Mode . Approach", Peter Peregrinus, 1990. [6] Erdal, C .• Toker. A .•and Acar. C .. "Current conveyor based proportional-inregralderivative (PID) conıroller and cakularing optimum parameter ıolerances". Proceedings C?(' OPT/Af 10(J(). International Corference un Opıinıizaıion of Elearical and Elecıroııic Equipnıents. Brasov, Vol. lll, pp. 575-578. [7] Smith. K. C. Sedra. A., HA secondgenetation current conveyor and its applications", IEEE Trans. iili Circııit Theory, Vol. 17. 1970. pp.132-134. [8] Patranabis D., Ghosh D. K., "Integrator and differentiators with current conveyors". IEEE Trans. On Circııits and Systems, Vol. CAS-31. No. 6. June 1984 [9] Erdal. C. Toker. A .. and Acar, C. "OT A-C based proponional-integral-deri"ati"e (PIO) controller and calculating optimum parameter tolerances", Turkish Journal Of Elearical Engineering & Computer Sciences. Elektrik; Vol. 9. No. i. 2001.(1t is accepted and it will be published) (10] Aronheim. P., "Transfer function synthesis using a current conveyor ". iEEE Trans. On Circuiıs and Sysıems, Vol. CAS-2 I, pp. 312-313, March 1974. {I I] Tek. H., Anday, F., "Voltage transfer function synthesis using current conveyors", Electronics Leuers, Vol. 25, No 23, November 1989.
C~\'{11ERDAL, Ali TOKER,
Cerdet ACAR
"-A N~ Proporfioııa/-/lllt!::ra/-Daivaıiv~ (P/D) Controller Realization By Using Current CDırr~yors And Calcutating Optimum Paramda Tolerances
Biography
273
of Cevat Erdal
Cevat Erdal was bom in Bergama. Turkey. 1948. He received both the B.Sc. and M.Sc. degrees in electrical engineering from the Faculty of Eleettical and Electronics Eng., Istanbul Technical University. Turkey in 1973 . He received the Ph. D. degree in 1987 from the Institute of Science and Technology of the same university. He is currentlyan assistant professor in Control Engineering Dept. He is also the author or co-author of about 28 papers published in scientific reviews or conference proceedings. His main research interests are transducers, process control and design of new controllers.
Biography
of Ali Toker
Ali Toker was bom in IstanbuL. Turkey. 1951. He received the B.Sc. and M.Sc. degrees in eleettical engineering from the Faculty of Electrical and Electronics Eng., Istanbul Technical University, Turkey in i973 and 1975. respectively, He received the Ph. D. degree in 1986 from the Institute of Scierıce and Technology of the same university. He is currentlyan associate professor in electronics. ıeaching graduaıe and undergraduate courses. He is also the author or co-author of about 50 papers published in scientific reviews or conference proceedings. His main research interests are design of currenı-mode circuits and analog signal processing applications.
Biography
of Cevdet Acar
Cevdet Acar was born in Hopa. Turkey, 1943. He received his B.Sc .. M.Sc. and Ph.D. degrees from Istanbul Technical University in i965, i967 and 1972. respectively. In 1970 he joined the Electronics and C ommunication Engineering Department of Istanbul Technical University. Since i988 he is a professor of circuit and systeıns in the same department. His research interesrs incJude design of active network synthesis, analog signal processing. and sensitivity and tolerarıce analysis. He is the author or the co-am hor of more than 60 journal papers published in international journals, more than 20 confererıce papers presented in international confererıces and '2 books related to the above mentioned areas.
Cevat ERDAL. Ali TOKER, Cevdet ACAR
