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On-line Measurement and Control of Penicillin V Production
Copnight
© IF.-\ C
\lodellill!!; alld C.>IItrol of
Biotechnological PnKt'sst's. :\()or
ON-LINE MEASUREMENT AND CONTROL OF PENICILLIN V PRODUCTION K. Frueh, Th. Lorenz, 11,,(III1(
Ilia
J. Niehoff, J. Diekmann, R. Hiddessen and K. Schuegerl
"{,',h 11 i"/II' Chl'IIIII ', ('I//, "'"illl/'( /lt lllllll, '1'1, LII/III"(I', ,1111111111111111, '1'1', FU(;
Abstract. Penicillium chrysogenum was cultivated in a suspension of pellets of a suitable size (less than 0.4 mm in diameter) in a 98-I-airlift reactor with an outer loop and a working volume of 90 1 to produce Penicillin V during fed - batch fermentations. The measurement of several key values improved the control of the rather complex fermentation process , to attain an increased productivity of antibiotics. Physico- chemical sensors as well as automatic chemical ana lyzers were applied . A thermal mass flow meter was used for the control of the sole energy input by aeration to minimize the aeration rate. To achieve an optimal productivity, the dissolved oxygen concentration was held above a critical value. The use of a PI - controller failed to maintain the dissolved oxygen con centration necessary, because the properties of the fermentation broth were changing frequently. A self - tuning controller allowed a satisfac tory control of the penicillin process. Keywords. Process control, sensors , on -l ine computer - control, self - tun ing control, fed - batch process, tower-I oop-r eactor, penicillin.
rate and high product formation rates. During the growth phase, limitations should be avoided by monitoring the concentrations of the carbon , nitrogen and phosphor sources . Later on , the growth is limited by the carbon source (e.g. glU cose) . AMmonium or urea serve as nitrogen sources and sui fate as a sulphur source for the biosynthesis of penicillin. These sources as well as the product were mea sured. Since no specific steam- sterilizable sen sors detecting these components have been available up to now , an ultrafiltration system was developed to sample cell - free medium. It was possible to steam-steril ize this system, and it was stable for longer periods. The sample was divided to feed different automatic chemical analy zers using wet - chemical methods. If nec essary , it was diluted and treated by re agents. The reactions resulted in colored complexes whose adsorbances were measured by photometers.
INTRODUCTION It is important to monitor several key var ia bles of biotechnological processes to control and optimize the process for the minimization of production costs. Three steps are necessary to achieve these aims . ( Mo r, 1 9 8 1 ) : 1. Development of instruments to monitor the environment of cells. 2. Correlation of the different measured data. 3 . Maintaining the optimal environmental conditions by continuous analysis and feed-back control of the environment. INSTRUMENTA'i'ION AND MEASURE MENT TECHNIQUES The instruments for measuring the process variables, e.g . pH, temperature, liquid volume, overall volume of aerated medium , aeration rate, medium recirculation rate through the outer loop, 02-and C02-concentrations in the outlet gas and the dis solved oxygen concentration have been known for many yea rs. Most of these sensors are steam-sterilizable and their signals a r e stable for longe r periods. In addition, it is also necessary to measure the concentrations of some substrates in the fermentation broth, to avoid unde sired limitations or catabo lite repreSSions during the d ifferent phases of the process.
A U T
0 A N
A L
PHOSPHATE SULFATE Air -
UREA
loft reactor
PENICILLIN
Y AMMONIUM
Z DOC
E R
The penicillin ferm entat i on process can be devided into three phases : a g r owth phase with a high growth rate and a negligible product formation rate, a transition phase, and a production phase with a low growth
GLUCOSE Ultrafiltration I Pro~ __ /
Fig. 1.
75
Automatic chem i ca l analyzer
76
K . Fru e h 1'1 al.
The sensors which meas u red the ammon i um and d i sso l ved organic carbon (DOC) concen t rat i ons we r e based o n p H- electrodes de t ect i ng ammon i a and C02 . Contro l led by a computer program , the chemical analyzers were rinsed by base , ac i d or buffe r s o l u t i ons , and the sisnals were actualized by a u tomatic recalibration of the i nstru men t s .
base (KOH) by the pH control , urea was u sed as a nitrogen source. I f the urea concentrat i on was held at a certain level, no acid or base wa s needed to keep the pH at the desired value , and the pellet mor phology of the mo l d was stable. By moni tor i ng the ammon i um concentration , nitro gen l i mitRtion was avoided. I n the production phase, the active ce l l mass should be kept constant. This i s the main p r erequisite to maintain an optimal production rate. Since it was not possible to determine the active biomass continu ously , the CPR was used as a measure for the active cell concen t rat i on, because the metabolism of the cells does not change and the CPR remains constant during that t i me.
Vo c~O CPR
CPR
v.1
i
(1)
CO - production rate 2 gas inlet rate gas outlet rate
c~02
CO 2 - concentration in gas inlet stream
c
I'
- v.1 c~O 2
V
0
I
2
0
co 2
V L
V0 2 - concentration in gas outlet streaJ:l liquid volume
The CPR was kept constant by varying the feeding r ate of the sugar solution manu a l ly . Automatic control will become pos sible , if the consumption of carbon can be predicted by a model. SELF - TUNING CONTROL
Fig. 2.
Airlift - loop- reactor 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
air inlet oxygen probe pH- probe temperature control microfluor i meter sampl i ng probe level meter foam detectors oute r loop ve l oc i ty meter air fo r gas ana l ysis cooli n g water mechanical foam breaker press u re meter (liqu i d vo l ume) inocu l um connection
CORRELATI ON OF THE MEASUREME NTS AND MANUA L CONTROL Some of t hese measure ments we r e co rr e la ted , e . g . the urea concent r at i on and t he pH- v al ue o r the C02 product i on r a t e (C PR ) and the penici lli n produc ti v i ty . At the end of the grow t h phase , t he p r o t e i ns of the nut r ient we r e exha u sted a nd the p H dropped . To avo i d the add i t i o n o f
S i nce energy input occurs by aeration alone , it is important for the minimiza t i on of the production costs to aerate only as much as is necessary to maintain a certain level of dissolved oxygen con centrat i on (DOT) and to achieve a suffi cient mixing of the fermentation broth. Efforts to control DOT by means of the aeration rate with a conventional PI- con tro l ler fai l ed, because the system para meters often changed during fermentation, and t he con t roller had to be retuned fre q uent l y . By us i ng a self - tuning controller, it was possible to overcome this problem. I ts app l ication also had the advantage that i t was possible to manage nonlinearities of the system by using local linearizat i on in wh i ch the model parameters change wi th the set - point. I t is assumed that the process can be des cribed by the following linear difference equation of the order m: y(k)+a y(k - 1)+ ... +amy(k - m)= 1 = b u(k -1- d)+ .. . +bmu(k - m-d)+v(k) 1
(2 )
u(k) and y(k) a r e th e s amp l ed p r ocess in put a nd ou t p u t S i g n a l s and v(k) i s a dis c r e t e wh i te noise . The p r ocess dead - t i me d i s exp r essed in mul t i ples o f the sampl i ng t i me To. The z - t r ansfo r m of equation (2) i s :
On·line \l eas urc lll c nt and Control
y (z)
(3 )
with the polynomials A (z -1 )
the minimum variance controller is mul tip l ied by a proportional integral action term of the following transfer function : GpI
1 +
(z)
=
(4 )
B (z -1 )
(5 )
D(z -1 )
(6 )
Now the model order m and dead - time d have to be determined. Simulations (Kurz , 1980) have shown that the process order llb does not need to be known exact l y . Parameteradaptive controllers are insensitive to a wrong model order within: mp -1 -< m -< mp +2
(7 )
The main problem in controlling DOT by aeration is the unknown time - varying dead time . This however can be overcome by using dead - time est imat ion wit h an a l go rithm , e . g . RLSVT (Kurz , 1979). The RLSVT algorithm basically consists of the well - known recursive least squares algorithm in which a forgettinq factor A is introduced . By using A < 1 slowly , time varying process parameters can be t r acked. An upper limit d max of the process deadtime has to be known a prior i, and the number of parameters of the B polynomia l (eq . 5) is increased by d max : ~ -1 ~ - 1 ~ - (m+d ) B(z ) = b z + ... + b m+ d z max ,( 8) 1 max which results in a process model : y (z)
1- ( 1- 0)z - 1 -1 1-z
(15)
The parameter- adaptive controller combined in this way was applied for DOT control using a process model of the third order. I t showed good performance and sta bi li ty . However, several precautions had to be taken . When there are no disturbances or set pOint changes for longer periods , the co variance matrix of the estimator will in crease because of the forgetting factor. This results u ltimate ly in excessive changes of paramete r estimates (Astroem, Wes terberg , Wi t tenmark , 1978) . Therefore , whenever DOT was within one percent of the set - point, the forgetting factor was set to 1. Sudden changes of the process - e . g . through the addition of an antifoam ag ent could result in estimating a system with a negative gain and cause the control l er to react the opposite way. The estimated parameters were thu s checked, if they de scribe a system with a positive gain , otherwise parameter estimates of the pre ceding sample interval were taken . Fi nally , a level meter was used to preven t the a irli ft react or from flooding . When ever a critical upper level was reached , the set - point was reduced automatically. When the level dropped below a defined lower level , the set - point was increased by gradual steps until the origina l set point was reached, or the level was in betwee n th e l ower and the upper level .
(9 )
The impulse response of the estimated mo del (eq . 9) is obtained and used to ca lculate the dead - time and paramete r values for the process model (eq . 3) . To contro l DOT , the RLSVT method is now combined with an extended min i mum variance contro l ler , which minimizes the criterion:
11
RESULTS F i gure 3 shows the aeration rate and DOT during 2 4 hours of run 8407. The set - point was at 75 % DOT.
( 10) The weighting r on the input was proposed by Clarke and Hastings - James (1971) and prevents excessive input changes that sometimes occured with the origina l min i mum variance controller (Astroem 1970). The controller transfer funct i on is g i ven by : (1 1 )
-
:;:
.
,g
R
<
~
:;;
~ :i' or ~ ~ or :;: ~
t, I 10
12
l
Iq
I
I 16
18
I 20
I
I
11
22
2 <1
In I
wit h the polynomials: 1
o
+ 11z-1+ ... + 1
1 + f
1
z
- 1
+ ... +
m-z
z-(m-1)
Fig. 3 .
Control of DOT by aeration
(12) (13)
which are obtained from
To avoid offsets for set -po int changes,
Th e disturbances were caused by addition of urea (marker 1, 2) or precurse r (marke r 4 ) , or by oil (marker 3 , 5 , 6 , 7) Th e r e is a general increase in the aera tion rate in that phase of fermentation, because the oxygen transfer coeff i cient from the gas into the liquid phase became smaller during the transition phase , when oil was added as a substrate .
78
K. Frue h ('/ Il l .
Because o f the s e d i stu r ba n ces , it was not poss i b l e to cont r o l the carbondiox i de production rate b y means of the feed i ng r ate of the sugar su l ot i on. To ove r come this problem , a way of run ning the fermentat i on has to be found were the glucose solution wi ll be the only energy source. Furthermo r e , the urea - and phenoxyacetate solut i ons have to be added more frequently i n smaller q u ant i ties . CONCLUSIONS A self - tuning contro ll er was applied to control dissolved oxygen by means of the aeration rate in an airlift reac t or . During several fermentat i ons i t was very reliable in keeping the desired set - po i nt. Its applicability to DOT- control in other fermentations is presently explored . The add i tional wet - chemical measurements imp r oved the insight in the rather complex fermentation p r ocess and an exten sion of the automatic control is planned . ACKNOWLEDGEMENTS The authors thank Prof. M. Thoma and Dr . A. Munack , Institut fuer Regelungs technik , Un i versitaet Hannover , for their support. REFERENCES Ast r oem , K.J ., B. Westerberg, B. Witten mark (1978) . Self - tuning Contro l lers Based on Pole - p l acement Design. Dept . of Automatic Control , Lund Institute of Technology , Lund , Sweden , Report: LUTFD2/(TFRT- 3 14 8)/1 - 52/( 1978) . Astroem , K. J . (1970). Introduction to Stochastic Control Theory . Mathemat i cs in Science and Engineering , Vol . 70 , Academic P r ess . Clarke , D.W. , R. Hastings - James ( 197 1 ) . Design of d i gita l contro ll er for ran domly disturbed systems. Proc . l EE 118 . Kurz , H. (1979) . Digita l Paramete r- Adap tive Control of Processes with Un known Constant or Time - varying Dead Ti me . 5th I FAC - Symposium on I dent i f ication and Parameter Estimation , Darmstadt . Kurz , H. (1980) . Erprobung und Vergleich von parameteradap t iven Rege l a l go r i t h men bei verschiedenen Prozessen . Regelungstechnik , 28 , 2-1 0 . Mor , J . R. (198 1 ) : A rev i ew of inst r umen tal analysis in fermentat i on techno logy. 3rd I nte r nat i ona l Co n ference on Computer App li cat i on in Fermen t a tion Technology , Mancheste r, Engla nd.
© IF.-\ C
\lodellill!!; alld C.>IItrol of
Biotechnological PnKt'sst's. :\()or
ON-LINE MEASUREMENT AND CONTROL OF PENICILLIN V PRODUCTION K. Frueh, Th. Lorenz, 11,,(III1(
Ilia
J. Niehoff, J. Diekmann, R. Hiddessen and K. Schuegerl
"{,',h 11 i"/II' Chl'IIIII ', ('I//, "'"illl/'( /lt lllllll, '1'1, LII/III"(I', ,1111111111111111, '1'1', FU(;
Abstract. Penicillium chrysogenum was cultivated in a suspension of pellets of a suitable size (less than 0.4 mm in diameter) in a 98-I-airlift reactor with an outer loop and a working volume of 90 1 to produce Penicillin V during fed - batch fermentations. The measurement of several key values improved the control of the rather complex fermentation process , to attain an increased productivity of antibiotics. Physico- chemical sensors as well as automatic chemical ana lyzers were applied . A thermal mass flow meter was used for the control of the sole energy input by aeration to minimize the aeration rate. To achieve an optimal productivity, the dissolved oxygen concentration was held above a critical value. The use of a PI - controller failed to maintain the dissolved oxygen con centration necessary, because the properties of the fermentation broth were changing frequently. A self - tuning controller allowed a satisfac tory control of the penicillin process. Keywords. Process control, sensors , on -l ine computer - control, self - tun ing control, fed - batch process, tower-I oop-r eactor, penicillin.
rate and high product formation rates. During the growth phase, limitations should be avoided by monitoring the concentrations of the carbon , nitrogen and phosphor sources . Later on , the growth is limited by the carbon source (e.g. glU cose) . AMmonium or urea serve as nitrogen sources and sui fate as a sulphur source for the biosynthesis of penicillin. These sources as well as the product were mea sured. Since no specific steam- sterilizable sen sors detecting these components have been available up to now , an ultrafiltration system was developed to sample cell - free medium. It was possible to steam-steril ize this system, and it was stable for longer periods. The sample was divided to feed different automatic chemical analy zers using wet - chemical methods. If nec essary , it was diluted and treated by re agents. The reactions resulted in colored complexes whose adsorbances were measured by photometers.
INTRODUCTION It is important to monitor several key var ia bles of biotechnological processes to control and optimize the process for the minimization of production costs. Three steps are necessary to achieve these aims . ( Mo r, 1 9 8 1 ) : 1. Development of instruments to monitor the environment of cells. 2. Correlation of the different measured data. 3 . Maintaining the optimal environmental conditions by continuous analysis and feed-back control of the environment. INSTRUMENTA'i'ION AND MEASURE MENT TECHNIQUES The instruments for measuring the process variables, e.g . pH, temperature, liquid volume, overall volume of aerated medium , aeration rate, medium recirculation rate through the outer loop, 02-and C02-concentrations in the outlet gas and the dis solved oxygen concentration have been known for many yea rs. Most of these sensors are steam-sterilizable and their signals a r e stable for longe r periods. In addition, it is also necessary to measure the concentrations of some substrates in the fermentation broth, to avoid unde sired limitations or catabo lite repreSSions during the d ifferent phases of the process.
A U T
0 A N
A L
PHOSPHATE SULFATE Air -
UREA
loft reactor
PENICILLIN
Y AMMONIUM
Z DOC
E R
The penicillin ferm entat i on process can be devided into three phases : a g r owth phase with a high growth rate and a negligible product formation rate, a transition phase, and a production phase with a low growth
GLUCOSE Ultrafiltration I Pro~ __ /
Fig. 1.
75
Automatic chem i ca l analyzer
76
K . Fru e h 1'1 al.
The sensors which meas u red the ammon i um and d i sso l ved organic carbon (DOC) concen t rat i ons we r e based o n p H- electrodes de t ect i ng ammon i a and C02 . Contro l led by a computer program , the chemical analyzers were rinsed by base , ac i d or buffe r s o l u t i ons , and the sisnals were actualized by a u tomatic recalibration of the i nstru men t s .
base (KOH) by the pH control , urea was u sed as a nitrogen source. I f the urea concentrat i on was held at a certain level, no acid or base wa s needed to keep the pH at the desired value , and the pellet mor phology of the mo l d was stable. By moni tor i ng the ammon i um concentration , nitro gen l i mitRtion was avoided. I n the production phase, the active ce l l mass should be kept constant. This i s the main p r erequisite to maintain an optimal production rate. Since it was not possible to determine the active biomass continu ously , the CPR was used as a measure for the active cell concen t rat i on, because the metabolism of the cells does not change and the CPR remains constant during that t i me.
Vo c~O CPR
CPR
v.1
i
(1)
CO - production rate 2 gas inlet rate gas outlet rate
c~02
CO 2 - concentration in gas inlet stream
c
I'
- v.1 c~O 2
V
0
I
2
0
co 2
V L
V0 2 - concentration in gas outlet streaJ:l liquid volume
The CPR was kept constant by varying the feeding r ate of the sugar solution manu a l ly . Automatic control will become pos sible , if the consumption of carbon can be predicted by a model. SELF - TUNING CONTROL
Fig. 2.
Airlift - loop- reactor 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
air inlet oxygen probe pH- probe temperature control microfluor i meter sampl i ng probe level meter foam detectors oute r loop ve l oc i ty meter air fo r gas ana l ysis cooli n g water mechanical foam breaker press u re meter (liqu i d vo l ume) inocu l um connection
CORRELATI ON OF THE MEASUREME NTS AND MANUA L CONTROL Some of t hese measure ments we r e co rr e la ted , e . g . the urea concent r at i on and t he pH- v al ue o r the C02 product i on r a t e (C PR ) and the penici lli n produc ti v i ty . At the end of the grow t h phase , t he p r o t e i ns of the nut r ient we r e exha u sted a nd the p H dropped . To avo i d the add i t i o n o f
S i nce energy input occurs by aeration alone , it is important for the minimiza t i on of the production costs to aerate only as much as is necessary to maintain a certain level of dissolved oxygen con centrat i on (DOT) and to achieve a suffi cient mixing of the fermentation broth. Efforts to control DOT by means of the aeration rate with a conventional PI- con tro l ler fai l ed, because the system para meters often changed during fermentation, and t he con t roller had to be retuned fre q uent l y . By us i ng a self - tuning controller, it was possible to overcome this problem. I ts app l ication also had the advantage that i t was possible to manage nonlinearities of the system by using local linearizat i on in wh i ch the model parameters change wi th the set - point. I t is assumed that the process can be des cribed by the following linear difference equation of the order m: y(k)+a y(k - 1)+ ... +amy(k - m)= 1 = b u(k -1- d)+ .. . +bmu(k - m-d)+v(k) 1
(2 )
u(k) and y(k) a r e th e s amp l ed p r ocess in put a nd ou t p u t S i g n a l s and v(k) i s a dis c r e t e wh i te noise . The p r ocess dead - t i me d i s exp r essed in mul t i ples o f the sampl i ng t i me To. The z - t r ansfo r m of equation (2) i s :
On·line \l eas urc lll c nt and Control
y (z)
(3 )
with the polynomials A (z -1 )
the minimum variance controller is mul tip l ied by a proportional integral action term of the following transfer function : GpI
1 +
(z)
=
(4 )
B (z -1 )
(5 )
D(z -1 )
(6 )
Now the model order m and dead - time d have to be determined. Simulations (Kurz , 1980) have shown that the process order llb does not need to be known exact l y . Parameteradaptive controllers are insensitive to a wrong model order within: mp -1 -< m -< mp +2
(7 )
The main problem in controlling DOT by aeration is the unknown time - varying dead time . This however can be overcome by using dead - time est imat ion wit h an a l go rithm , e . g . RLSVT (Kurz , 1979). The RLSVT algorithm basically consists of the well - known recursive least squares algorithm in which a forgettinq factor A is introduced . By using A < 1 slowly , time varying process parameters can be t r acked. An upper limit d max of the process deadtime has to be known a prior i, and the number of parameters of the B polynomia l (eq . 5) is increased by d max : ~ -1 ~ - 1 ~ - (m+d ) B(z ) = b z + ... + b m+ d z max ,( 8) 1 max which results in a process model : y (z)
1- ( 1- 0)z - 1 -1 1-z
(15)
The parameter- adaptive controller combined in this way was applied for DOT control using a process model of the third order. I t showed good performance and sta bi li ty . However, several precautions had to be taken . When there are no disturbances or set pOint changes for longer periods , the co variance matrix of the estimator will in crease because of the forgetting factor. This results u ltimate ly in excessive changes of paramete r estimates (Astroem, Wes terberg , Wi t tenmark , 1978) . Therefore , whenever DOT was within one percent of the set - point, the forgetting factor was set to 1. Sudden changes of the process - e . g . through the addition of an antifoam ag ent could result in estimating a system with a negative gain and cause the control l er to react the opposite way. The estimated parameters were thu s checked, if they de scribe a system with a positive gain , otherwise parameter estimates of the pre ceding sample interval were taken . Fi nally , a level meter was used to preven t the a irli ft react or from flooding . When ever a critical upper level was reached , the set - point was reduced automatically. When the level dropped below a defined lower level , the set - point was increased by gradual steps until the origina l set point was reached, or the level was in betwee n th e l ower and the upper level .
(9 )
The impulse response of the estimated mo del (eq . 9) is obtained and used to ca lculate the dead - time and paramete r values for the process model (eq . 3) . To contro l DOT , the RLSVT method is now combined with an extended min i mum variance contro l ler , which minimizes the criterion:
11
RESULTS F i gure 3 shows the aeration rate and DOT during 2 4 hours of run 8407. The set - point was at 75 % DOT.
( 10) The weighting r on the input was proposed by Clarke and Hastings - James (1971) and prevents excessive input changes that sometimes occured with the origina l min i mum variance controller (Astroem 1970). The controller transfer funct i on is g i ven by : (1 1 )
-
:;:
.
,g
R
<
~
:;;
~ :i' or ~ ~ or :;: ~
t, I 10
12
l
Iq
I
I 16
18
I 20
I
I
11
22
2 <1
In I
wit h the polynomials: 1
o
+ 11z-1+ ... + 1
1 + f
1
z
- 1
+ ... +
m-z
z-(m-1)
Fig. 3 .
Control of DOT by aeration
(12) (13)
which are obtained from
To avoid offsets for set -po int changes,
Th e disturbances were caused by addition of urea (marker 1, 2) or precurse r (marke r 4 ) , or by oil (marker 3 , 5 , 6 , 7) Th e r e is a general increase in the aera tion rate in that phase of fermentation, because the oxygen transfer coeff i cient from the gas into the liquid phase became smaller during the transition phase , when oil was added as a substrate .
78
K. Frue h ('/ Il l .
Because o f the s e d i stu r ba n ces , it was not poss i b l e to cont r o l the carbondiox i de production rate b y means of the feed i ng r ate of the sugar su l ot i on. To ove r come this problem , a way of run ning the fermentat i on has to be found were the glucose solution wi ll be the only energy source. Furthermo r e , the urea - and phenoxyacetate solut i ons have to be added more frequently i n smaller q u ant i ties . CONCLUSIONS A self - tuning contro ll er was applied to control dissolved oxygen by means of the aeration rate in an airlift reac t or . During several fermentat i ons i t was very reliable in keeping the desired set - po i nt. Its applicability to DOT- control in other fermentations is presently explored . The add i tional wet - chemical measurements imp r oved the insight in the rather complex fermentation p r ocess and an exten sion of the automatic control is planned . ACKNOWLEDGEMENTS The authors thank Prof. M. Thoma and Dr . A. Munack , Institut fuer Regelungs technik , Un i versitaet Hannover , for their support. REFERENCES Ast r oem , K.J ., B. Westerberg, B. Witten mark (1978) . Self - tuning Contro l lers Based on Pole - p l acement Design. Dept . of Automatic Control , Lund Institute of Technology , Lund , Sweden , Report: LUTFD2/(TFRT- 3 14 8)/1 - 52/( 1978) . Astroem , K. J . (1970). Introduction to Stochastic Control Theory . Mathemat i cs in Science and Engineering , Vol . 70 , Academic P r ess . Clarke , D.W. , R. Hastings - James ( 197 1 ) . Design of d i gita l contro ll er for ran domly disturbed systems. Proc . l EE 118 . Kurz , H. (1979) . Digita l Paramete r- Adap tive Control of Processes with Un known Constant or Time - varying Dead Ti me . 5th I FAC - Symposium on I dent i f ication and Parameter Estimation , Darmstadt . Kurz , H. (1980) . Erprobung und Vergleich von parameteradap t iven Rege l a l go r i t h men bei verschiedenen Prozessen . Regelungstechnik , 28 , 2-1 0 . Mor , J . R. (198 1 ) : A rev i ew of inst r umen tal analysis in fermentat i on techno logy. 3rd I nte r nat i ona l Co n ference on Computer App li cat i on in Fermen t a tion Technology , Mancheste r, Engla nd.