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Inferential Control Using Nonlinear Model-Based Observer Control
. Inferential Control using Nonlinear Model-based 0 bserverControl R.W.Jones and P.J.Gawthrop ·Dept. Mechanical Engineering, Glasgow University Glasgow G12 8QQ, Scotland, U.K. Abstract Model:.based ObseriJerControl is introduced and its use in the inferential control of the vapour composition of a simula.ted lash separation process is demonstrated. As the underlying control problem is mUltivariable in nature the fundamental consideration in the control design prob- . lem is ·the choice of a control structure that allows all the practical performance criteria to ·be satisfied. By providing estimates of the unmea.surable process variables model-based observer control allows a greater range of possible control structures to be considered. The most desirable control structure doesne;,t control the inferred primary control variable directly and an inferential setpoint scheme is implemented: .
1
Introduction
Model-based Observer Control is a fundamental approach to model-based control. It's motivation comes from threeatea.s: linear state-space observer theory [8], inferential control and the application of bond-graphs to observer design [3]. In this paper we are going to use this approach to investigate thenonlinear inferential Control of a simulated multicomponent·jlash separation process. This utilisation' of inferential control, though, is just one aspect of an integrated approach to the control design problem. The funda.iD.entalproblem in process control is not the development of Inore.sophisticated algorithms but rather the establishment ofa structural framework for selecting the manipulated and measured variables [1]. The major priority being to choose a structl,lre that satisfies the overall eConomic goals of the process. By providing estimates of the unmea.surable process variables model-based observer control allows a greater range of possible control structures to be considered. · The structure assessment provided us with a desirable structure in which the primary control variable, the inferred composition of the vapour outlet stream, was not controlled directly. In the implementation of this structure the ·inferred composition is used to update the setpoint of one of the controlled variables in a cascade control scheme, to ensure that the primary control variable is regulated to its' desired value. This implicit use ·of the inferred primary variable will be caned inferential setpoint control. The ·best of the structures that controls the inferred vapour composition direcdy,stan4ard inferential control, was also identified. . . A compa.risonof both of these approaches to nonlinear inferential control is carried out by ~ examining their a.bility to regUlate the vapour composition subject to an unmeasurable distur- bance in the feed of the flash separation process. Both of these schemes are superior to the use of a composition analyzer with a 6 minute time-delay [6]. .
2
The Flash Separation Process
A schematic of an isothermal vapour-liquid flash for a continuous system is shown overleaf. F is a. multic6mponent liquid feed strea.mwhile L and V axe the outlet liquid and vapour streams respectively. A heat input, Q, into the liquid holdup in the flash drum is used to vary the rate of vapourization. The work in this paper was 8upported by SERC through the ECOSSE consortium based at Edinburgh University.
. 151
v
F
Q--+---.....,
L
Figure
1: The Flash Separation Process
The feed consists ofArklone and Genklene.Arklone is the light (more volatile) component with a boiling point of 330.8 K. The boiling point of Genklene is 347.2K. An overall mass balance gives: dM . --(·1) dt = . F. - V - L The energy balance giveS:
dB
d
t
2
_
2
_
2
_
= FL Zi(Ci.c5TJ)- V LYvi(CV6T + ~il- LLqi(Ci,6T)+Q i=1
1=1
(2)
.=1
. where 6TJ is the difference between the feed and ambient temperatures, 6T is the difference between the drum and ambient temperatures. The component mass balance gives: dm - . ._' = Fz-V .,- dt '07'"
Lq-,
(3)
The nominal system parameters can be found in [5]. The system states are the moles of Arklone (Xl) and Genklene (X2) in the drum and the drum enthalpy (X3)- The primary control variable is the. concentration of the Arklone in the vapour outlet, '1/111. The manipulated vatiablesare the heat input, Q (Ul ),the vapour flowrate, V (tL2) and the liquid flowrate, L ( U3).
3
The Control Structure Assessx:nent
The Relative Gain Array (RGA), Condition Number (CN) and mi:WmumsingUlar-value, O'min, derived from linearised state-space system representations were used to provide insight into the dynamic closed-loop properties of the different control structures . . The RGA also provided insight into the interactions between individual oontrolloops [10]. Related theoretical results [4]a1so answered questions regarding system integrity when the control structures are implemented in conjunction with a decentralised controller. . Table 2 gives the principal diagonal of the RGA, the CN and O'min for a small selection of the control structures. Thebra.cketted numbers give the frequency at which the indicators were determined. For the 3-input 3-output structUres Qis paired with the first listed controlled variable, V with the second and L with the third.P is the drum pressure, T the drum temperature aildh the liquid level. Structure 4 was chosen as the preferred control structure for the flash separation process. The regulation of all the variables in the face .of process disttu'bances ·will generally produce an offset in the vapour composition. This necessitates the incorporation of an additional
152 .
Controlled Control Variables Structure ' 1 Yt/ltP;h 2 P'Y~l,h T,P,h 3 'h,P,L 4
CN (5%10....3 ) , C7m in (5%10- 3 ) 0.0179 -3.53,-3.78,0.96 .;.6~63,-7 .12,0.95 '74.9 ,0.0179 4.53,4.73,0.96 . 7.63,8.07,0.953 74.9 0;0005 366.3,393.1,0.2 513.0,550.8,,0.24 3553~5 138.76 small,smaJI,1.0 . small,small,l.O 0.2688
RGA (1%10...,6) , RGA (5%10-3 )
Table 1: RGA, CN and
D'min
for the Qontrol Structures
composition controller within a cascade c:Ontrol scheme. When implementated using the modelbased observer this gives the inferential setpoint control sCheme. Full details legarding the assessment ca.n he round in [5]. . . ' . . The choice of the best structUre which Controls the va.pourcomposition directly was straightforward. Qualitative arguments would seem to indicate structure 1 but the negative diagonal elements of the RGAimply a lack of integrity and a difficult control problem. Strll(:ture 2, was . . ' therefore chosen. .
'.
c
'
.
'
4 . Model-Based Observer Control
.
The general scheme of model-b~d observer (MHO) (Ontrol is outliriedin Figure 2. There ~ are baSically two feedback loops. in , this approach to model~based control: .. . . . 1. the observer feedback loop which a.~tempts to make the model states follow the system
states" 2. and the controller feedback loop which attempts to make the model outputs follow desired trajectories. ' . H theSe feedback loops are working well then system outputs will be driven towards their desired values. The above descriptions are nonspecific .with regard to how individual feedback loops are desi~ed andtontrol objectives area.chieved. There is the freedom to integrate within the structure any theory which will satisfy the control objectives. In particular,physlcalknowledge about the system can: be directly incorporated into the design of these feedback loops [3],[2],[7]. The inferential control of the flash separation process demonsirates one particular implementation of the approach: 1. the observer reeaback loop is based on simple linear observer design [3];
.....
2. and the inferential controller feedback loop is based on a simple cascade design that utilises two and Proportional and lntegral controllers. .
A simple observer design and the use of conventional controllers is taken to emph~is because the effect ofthe chosen control structure and the use of the MBO control approach to produce the inferential control scheme~ If we represent a nonlinear single-input single-output process 'as
%=f(%,u);
%et=O) = %0;
y=g(%)
(4).
where the input, u f R, the states, % f Rn, arid the output; 11 f R. f is a real analytic vector field .a nd 9 isa real c,malytic function on Rn. The model states, % will be updated using a model-based obse.rver of the following form:
i= jex,u.)+ K o ell ;
.
.
y= gex)
153 ,
(5)
w -~
Vi
"
··..•
.,l,
·
·······~······-4----~---;
-
MeaL
j
,, ,, ,
· ,
~.
,
____________________. ~~ __ ~ __________ J
• MOD£L.8ASEDOBSBRVEa
..
Figure 2: Model-Based Observer Control where Ko.represents the obserVer gains.lngeneral the system model will be structurally correct, (it can .be ·automatiCally generated from first principles [a]) but parameterically different. A PI observer :is required to drive the model states to the system states i.e. Ko Will be of a PI form. The controller stru.c ture used throughout the paper is a decentralised one. The deQsion about the suitability of each control structure was made this in mind. Each individual controller was tuned to give the best control performance allowed by the structure [5]. Three output variables can be measured for the llash separation proc:ess, drum temperature Yl, drum pressureY2 and the liquid level Y3. These are used in the .model~based observer to provideey • There are many possibilities for designing the observer feedback gains. Here the deSign was carried out using a linearised model about the steady-state conditions using poleplacement [8]. . . The matrices A,B and Cof the linearisedstate-space system representation are A=[-0.0013 0.0013 ~.0000123 B= 10 0.0013-0.00130.0000123 0 -,0.0045) . 1 0.0120 0.0257
-0.0056 . ~.0047 ~0:0044 ..0.0053 -0;6364~.0838]
c=
[-0.0075 -0;0160 -0.0067 -:0.0187 0.00990.0082
0.0028 0.0030 0]
5 Inferential Control of the Flash Separation For control structure 4 of the three controlled variables the logical one from which to infer the vapour composition is the drum pressure. Therefore in the cascade arrangement,required for inferential setpoint control, the inferred composition controller is the master and the pressure . controller the slav.e. For the control studies the process and model were structurally the same but parametl'ically different, a 20 % error being introduced into the modelled feed cOIIlPosition {Le.z= O.6}. This introduced steady-state and dynamic modeJJ.ing errors. The model states were initially driven to the process states using the MBO. An unmeasurable 'step disturbance, a decrease of o.of in the fraction of light component in the feed, was then introduced. For the standard inferential controller (structure 2) Ko can be chosen such .t hat all the process states are tracked closely by the model states. Figures 3 and 4 show the estimates of 3:1 and X2 for the inferential setpoint scheme after the onset of the disturbance. The dashed .lines indicate the model states and each unit on the time axis represents 10 seconds. The . tr3.cldng is quite poor 'with the estimator gains having tobedetuned to ensure stable e~timation. This degradation in perfonnance compared with the standard inferentialcontl'ol, eStimation is . because inferential setpointcontrol involves a change in the process operating r-egion. The l41earised state-'space representation used in the observer deSign is therefore inaccurate. . Figures 5,6 and 7 compare the disturbance rejection on the vapour composition, drum level and pressure using both types of inferential control. Three responses are shown. The full lines 'show the controlled response using the standard inferential controller. The dashed and dotted lines show two different controlled responses using inferential setpoint control, the difference is due to different observer ga,ins. The pressure units a.ie Pa 13:1076 •
154
·,....
6.6
.,.13
~~'.
6-'8
....
5.12 ·'-111
6-'6
'-11
6..54
-.--.- .
5.19
Io·
'.11
U1
5.77
60S
5.76
... A,..... ..,
\
So7S
~.
5.".0
400
200
--
eo
6M
100
l2IlO
1000
Figure 3: The Arldone Molar Holdup:
/7'::::-'~"'-;.,-"._..'........-:o....-?----------1 . r .'
'G.556
:
.~
Cl.5S4
1000
Figure 4: The Genklene Molar Holdup:2;2 .
:7:1
o.ssa G.SS7
60460
aur-----------------------------~ 1).111
.-
I:
CI.5S3 ·... l ·
"'"
CI.5$2
1Ei
·CI.5'1
!-!
~o
Figure 5: The Vapour Composition:
,Figure 6: The Liquid Level: h
Yvl
. The inferential set point scheme arguably gives a better performance in regulating the pri' mary variable. The pressure setpoint being increased toach.ieve this result, a procedure that coUld cause problems depending upon the safety and environmental limitations of the process equipment. The effect on the liquid level forthls scheme is minimal. The results highlight that the quality of control is related to the quality of estimation. . Figures 8,9 and 10 show the corresponding manipulated inputs~ ·l'h.ese provide insight into t.he relative ability of the two structures to handle disturbances without infringing the constraints of the physical system. Changes in the input variables Jor the inferential setpoint scheme are much smaller than the standard scheme implying that mucit larger disturbances can be rejected before the input constraints ate reached. '. '.
0.
13
~
o.,s!"",- - - : \ - -_ _ _~-_--'-~-....._,_,
1
~
;
I
0;12$
0.7 0.12
\\
.
1
-.---.-.........•.. --~--.. --.....~
...•.•...... ---,.-.-...
0.65
j
0 .11' 0.6
0.11' '0'1'0,.1 600
·100
'" 1'000
1200
Figure 7: The Drum Pressure: P
Figure 8: The Heat Input:
155
Ul
I.QS---._ _ _ _ _~~-.....,..----------
Ir O.95
,t
0.9;-
"~~'.
j
\
0.1
o·
. /~
I;
.. . . . .
2.6~
I
i ' .
.
.. .
.
.
I
2.5~
I
0;15' 0.15
2.7,
2.4
\,, ,
2.3
\
2.2
G.6S
o.\~""""-~200~--@~:==600;===:;IOO;:==;iOOO;:==:juoo 2.IO~--'.200=-~~@~-~600~--IOO~~-I~OOO~-~l2OO Figure 9: The Vapour Flowrate:
6
1£2
Figure 10: The Liquid Flowrate:
U3
Di$cussion and Conclusions
The inferential setp6int sCheme while giving an improved performance 'for our case also necessitates a more rigourous approach to observer design for all the advantages of the control structure to be fully utilised. Misawaa.nd Hedrick give a comprehensive overview of the different approaches to thenonlinea.r state estimation problem in [9]. A physical model-based approach . ' for the observer design [2] is described elsewhere. In the ·implementation ofaninferenti~ setpointscheme, it is desirable that a high level of interaction exists between the inferred primary control variable and the controlled variable, otherwise the actual inferred setpoint could be physically unobtainable. Also it is required to tune one more set of control .gains than the standard control scheme. . With the ava.i.lability of an accurate process Plodel there seems no reason why the tuning procedure could not be automated. The emphasis in the paper has been on stressing the importance of the control structure and its use in conjunction with model-based observer control to generate a nonlinearinferential control scheme. The following items are the subject of current .research: .• the incorporation of physical model-based state estimation algorithms, • the development of a noIilinear model predictiv'e controller which makes explict use of the system model, ' ,
7
References
(1] A. S. Foss. AIChE, 19:209-214, 1973. [2] P. J. Gawthrop and R. W. Jones.Bond-graph-based adaptive control. In 4th IFAC Symposium on Adaptive sysiemsin Control and Signal Processing, 1992.
[3] P. J . Gawthrop, R. W. lones, and S. A. MacKenzie. Bond graph based control: A process engineering .example. In American .Control Conference, 1992, . (4] P. Grosdidietand M.Morari. Interaction measilres for systems under decentralised control. Automatica, .22(3):309-319, 1986 . [5] R.W. Jones. Control of amultlicomponent fiashseparation process. Control Group Research RepoitR-91/12, 'GlasgowUniversity, Dept. of Mechanical Engineering, 1991. [6] R.W. Jones. Nonlinear inferential control using model-based observer control. . Control Group Research Report R-91/17, Glasgow University, Dept. of Mechanical Engineering, [7] A.J. Krener and W. Respondek. Nonlinear observers with linearizableerror dynamics. SIAM..7. Control Opt., 2:197-'216, 1985.
[8] H. Kwakernaak and R. Sivan. Linear Optimal Control Systems. Wiley, 1972. [9] E. k. Misawaand J. K. Hedrick. Nonlinear observers - a state-of-the-art survey. Trans. ASME, 111:344-352, 1989.
[10] S. Slcogestad and M. Morari. Implication of large rga-elements on control performance. Ind. Eng. Chem. Res., 26(11):2121-2330, 1987. . 156
1
Introduction
Model-based Observer Control is a fundamental approach to model-based control. It's motivation comes from threeatea.s: linear state-space observer theory [8], inferential control and the application of bond-graphs to observer design [3]. In this paper we are going to use this approach to investigate thenonlinear inferential Control of a simulated multicomponent·jlash separation process. This utilisation' of inferential control, though, is just one aspect of an integrated approach to the control design problem. The funda.iD.entalproblem in process control is not the development of Inore.sophisticated algorithms but rather the establishment ofa structural framework for selecting the manipulated and measured variables [1]. The major priority being to choose a structl,lre that satisfies the overall eConomic goals of the process. By providing estimates of the unmea.surable process variables model-based observer control allows a greater range of possible control structures to be considered. · The structure assessment provided us with a desirable structure in which the primary control variable, the inferred composition of the vapour outlet stream, was not controlled directly. In the implementation of this structure the ·inferred composition is used to update the setpoint of one of the controlled variables in a cascade control scheme, to ensure that the primary control variable is regulated to its' desired value. This implicit use ·of the inferred primary variable will be caned inferential setpoint control. The ·best of the structures that controls the inferred vapour composition direcdy,stan4ard inferential control, was also identified. . . A compa.risonof both of these approaches to nonlinear inferential control is carried out by ~ examining their a.bility to regUlate the vapour composition subject to an unmeasurable distur- bance in the feed of the flash separation process. Both of these schemes are superior to the use of a composition analyzer with a 6 minute time-delay [6]. .
2
The Flash Separation Process
A schematic of an isothermal vapour-liquid flash for a continuous system is shown overleaf. F is a. multic6mponent liquid feed strea.mwhile L and V axe the outlet liquid and vapour streams respectively. A heat input, Q, into the liquid holdup in the flash drum is used to vary the rate of vapourization. The work in this paper was 8upported by SERC through the ECOSSE consortium based at Edinburgh University.
. 151
v
F
Q--+---.....,
L
Figure
1: The Flash Separation Process
The feed consists ofArklone and Genklene.Arklone is the light (more volatile) component with a boiling point of 330.8 K. The boiling point of Genklene is 347.2K. An overall mass balance gives: dM . --(·1) dt = . F. - V - L The energy balance giveS:
dB
d
t
2
_
2
_
2
_
= FL Zi(Ci.c5TJ)- V LYvi(CV6T + ~il- LLqi(Ci,6T)+Q i=1
1=1
(2)
.=1
. where 6TJ is the difference between the feed and ambient temperatures, 6T is the difference between the drum and ambient temperatures. The component mass balance gives: dm - . ._' = Fz-V .,- dt '07'"
Lq-,
(3)
The nominal system parameters can be found in [5]. The system states are the moles of Arklone (Xl) and Genklene (X2) in the drum and the drum enthalpy (X3)- The primary control variable is the. concentration of the Arklone in the vapour outlet, '1/111. The manipulated vatiablesare the heat input, Q (Ul ),the vapour flowrate, V (tL2) and the liquid flowrate, L ( U3).
3
The Control Structure Assessx:nent
The Relative Gain Array (RGA), Condition Number (CN) and mi:WmumsingUlar-value, O'min, derived from linearised state-space system representations were used to provide insight into the dynamic closed-loop properties of the different control structures . . The RGA also provided insight into the interactions between individual oontrolloops [10]. Related theoretical results [4]a1so answered questions regarding system integrity when the control structures are implemented in conjunction with a decentralised controller. . Table 2 gives the principal diagonal of the RGA, the CN and O'min for a small selection of the control structures. Thebra.cketted numbers give the frequency at which the indicators were determined. For the 3-input 3-output structUres Qis paired with the first listed controlled variable, V with the second and L with the third.P is the drum pressure, T the drum temperature aildh the liquid level. Structure 4 was chosen as the preferred control structure for the flash separation process. The regulation of all the variables in the face .of process disttu'bances ·will generally produce an offset in the vapour composition. This necessitates the incorporation of an additional
152 .
Controlled Control Variables Structure ' 1 Yt/ltP;h 2 P'Y~l,h T,P,h 3 'h,P,L 4
CN (5%10....3 ) , C7m in (5%10- 3 ) 0.0179 -3.53,-3.78,0.96 .;.6~63,-7 .12,0.95 '74.9 ,0.0179 4.53,4.73,0.96 . 7.63,8.07,0.953 74.9 0;0005 366.3,393.1,0.2 513.0,550.8,,0.24 3553~5 138.76 small,smaJI,1.0 . small,small,l.O 0.2688
RGA (1%10...,6) , RGA (5%10-3 )
Table 1: RGA, CN and
D'min
for the Qontrol Structures
composition controller within a cascade c:Ontrol scheme. When implementated using the modelbased observer this gives the inferential setpoint control sCheme. Full details legarding the assessment ca.n he round in [5]. . . ' . . The choice of the best structUre which Controls the va.pourcomposition directly was straightforward. Qualitative arguments would seem to indicate structure 1 but the negative diagonal elements of the RGAimply a lack of integrity and a difficult control problem. Strll(:ture 2, was . . ' therefore chosen. .
'.
c
'
.
'
4 . Model-Based Observer Control
.
The general scheme of model-b~d observer (MHO) (Ontrol is outliriedin Figure 2. There ~ are baSically two feedback loops. in , this approach to model~based control: .. . . . 1. the observer feedback loop which a.~tempts to make the model states follow the system
states" 2. and the controller feedback loop which attempts to make the model outputs follow desired trajectories. ' . H theSe feedback loops are working well then system outputs will be driven towards their desired values. The above descriptions are nonspecific .with regard to how individual feedback loops are desi~ed andtontrol objectives area.chieved. There is the freedom to integrate within the structure any theory which will satisfy the control objectives. In particular,physlcalknowledge about the system can: be directly incorporated into the design of these feedback loops [3],[2],[7]. The inferential control of the flash separation process demonsirates one particular implementation of the approach: 1. the observer reeaback loop is based on simple linear observer design [3];
.....
2. and the inferential controller feedback loop is based on a simple cascade design that utilises two and Proportional and lntegral controllers. .
A simple observer design and the use of conventional controllers is taken to emph~is because the effect ofthe chosen control structure and the use of the MBO control approach to produce the inferential control scheme~ If we represent a nonlinear single-input single-output process 'as
%=f(%,u);
%et=O) = %0;
y=g(%)
(4).
where the input, u f R, the states, % f Rn, arid the output; 11 f R. f is a real analytic vector field .a nd 9 isa real c,malytic function on Rn. The model states, % will be updated using a model-based obse.rver of the following form:
i= jex,u.)+ K o ell ;
.
.
y= gex)
153 ,
(5)
w -~
Vi
"
··..•
.,l,
·
·······~······-4----~---;
-
MeaL
j
,, ,, ,
· ,
~.
,
____________________. ~~ __ ~ __________ J
• MOD£L.8ASEDOBSBRVEa
..
Figure 2: Model-Based Observer Control where Ko.represents the obserVer gains.lngeneral the system model will be structurally correct, (it can .be ·automatiCally generated from first principles [a]) but parameterically different. A PI observer :is required to drive the model states to the system states i.e. Ko Will be of a PI form. The controller stru.c ture used throughout the paper is a decentralised one. The deQsion about the suitability of each control structure was made this in mind. Each individual controller was tuned to give the best control performance allowed by the structure [5]. Three output variables can be measured for the llash separation proc:ess, drum temperature Yl, drum pressureY2 and the liquid level Y3. These are used in the .model~based observer to provideey • There are many possibilities for designing the observer feedback gains. Here the deSign was carried out using a linearised model about the steady-state conditions using poleplacement [8]. . . The matrices A,B and Cof the linearisedstate-space system representation are A=[-0.0013 0.0013 ~.0000123 B= 10 0.0013-0.00130.0000123 0 -,0.0045) . 1 0.0120 0.0257
-0.0056 . ~.0047 ~0:0044 ..0.0053 -0;6364~.0838]
c=
[-0.0075 -0;0160 -0.0067 -:0.0187 0.00990.0082
0.0028 0.0030 0]
5 Inferential Control of the Flash Separation For control structure 4 of the three controlled variables the logical one from which to infer the vapour composition is the drum pressure. Therefore in the cascade arrangement,required for inferential setpoint control, the inferred composition controller is the master and the pressure . controller the slav.e. For the control studies the process and model were structurally the same but parametl'ically different, a 20 % error being introduced into the modelled feed cOIIlPosition {Le.z= O.6}. This introduced steady-state and dynamic modeJJ.ing errors. The model states were initially driven to the process states using the MBO. An unmeasurable 'step disturbance, a decrease of o.of in the fraction of light component in the feed, was then introduced. For the standard inferential controller (structure 2) Ko can be chosen such .t hat all the process states are tracked closely by the model states. Figures 3 and 4 show the estimates of 3:1 and X2 for the inferential setpoint scheme after the onset of the disturbance. The dashed .lines indicate the model states and each unit on the time axis represents 10 seconds. The . tr3.cldng is quite poor 'with the estimator gains having tobedetuned to ensure stable e~timation. This degradation in perfonnance compared with the standard inferentialcontl'ol, eStimation is . because inferential setpointcontrol involves a change in the process operating r-egion. The l41earised state-'space representation used in the observer deSign is therefore inaccurate. . Figures 5,6 and 7 compare the disturbance rejection on the vapour composition, drum level and pressure using both types of inferential control. Three responses are shown. The full lines 'show the controlled response using the standard inferential controller. The dashed and dotted lines show two different controlled responses using inferential setpoint control, the difference is due to different observer ga,ins. The pressure units a.ie Pa 13:1076 •
154
·,....
6.6
.,.13
~~'.
6-'8
....
5.12 ·'-111
6-'6
'-11
6..54
-.--.- .
5.19
Io·
'.11
U1
5.77
60S
5.76
... A,..... ..,
\
So7S
~.
5.".0
400
200
--
eo
6M
100
l2IlO
1000
Figure 3: The Arldone Molar Holdup:
/7'::::-'~"'-;.,-"._..'........-:o....-?----------1 . r .'
'G.556
:
.~
Cl.5S4
1000
Figure 4: The Genklene Molar Holdup:2;2 .
:7:1
o.ssa G.SS7
60460
aur-----------------------------~ 1).111
.-
I:
CI.5S3 ·... l ·
"'"
CI.5$2
1Ei
·CI.5'1
!-!
~o
Figure 5: The Vapour Composition:
,Figure 6: The Liquid Level: h
Yvl
. The inferential set point scheme arguably gives a better performance in regulating the pri' mary variable. The pressure setpoint being increased toach.ieve this result, a procedure that coUld cause problems depending upon the safety and environmental limitations of the process equipment. The effect on the liquid level forthls scheme is minimal. The results highlight that the quality of control is related to the quality of estimation. . Figures 8,9 and 10 show the corresponding manipulated inputs~ ·l'h.ese provide insight into t.he relative ability of the two structures to handle disturbances without infringing the constraints of the physical system. Changes in the input variables Jor the inferential setpoint scheme are much smaller than the standard scheme implying that mucit larger disturbances can be rejected before the input constraints ate reached. '. '.
0.
13
~
o.,s!"",- - - : \ - -_ _ _~-_--'-~-....._,_,
1
~
;
I
0;12$
0.7 0.12
\\
.
1
-.---.-.........•.. --~--.. --.....~
...•.•...... ---,.-.-...
0.65
j
0 .11' 0.6
0.11' '0'1'0,.1 600
·100
'" 1'000
1200
Figure 7: The Drum Pressure: P
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Di$cussion and Conclusions
The inferential setp6int sCheme while giving an improved performance 'for our case also necessitates a more rigourous approach to observer design for all the advantages of the control structure to be fully utilised. Misawaa.nd Hedrick give a comprehensive overview of the different approaches to thenonlinea.r state estimation problem in [9]. A physical model-based approach . ' for the observer design [2] is described elsewhere. In the ·implementation ofaninferenti~ setpointscheme, it is desirable that a high level of interaction exists between the inferred primary control variable and the controlled variable, otherwise the actual inferred setpoint could be physically unobtainable. Also it is required to tune one more set of control .gains than the standard control scheme. . With the ava.i.lability of an accurate process Plodel there seems no reason why the tuning procedure could not be automated. The emphasis in the paper has been on stressing the importance of the control structure and its use in conjunction with model-based observer control to generate a nonlinearinferential control scheme. The following items are the subject of current .research: .• the incorporation of physical model-based state estimation algorithms, • the development of a noIilinear model predictiv'e controller which makes explict use of the system model, ' ,
7
References
(1] A. S. Foss. AIChE, 19:209-214, 1973. [2] P. J. Gawthrop and R. W. Jones.Bond-graph-based adaptive control. In 4th IFAC Symposium on Adaptive sysiemsin Control and Signal Processing, 1992.
[3] P. J . Gawthrop, R. W. lones, and S. A. MacKenzie. Bond graph based control: A process engineering .example. In American .Control Conference, 1992, . (4] P. Grosdidietand M.Morari. Interaction measilres for systems under decentralised control. Automatica, .22(3):309-319, 1986 . [5] R.W. Jones. Control of amultlicomponent fiashseparation process. Control Group Research RepoitR-91/12, 'GlasgowUniversity, Dept. of Mechanical Engineering, 1991. [6] R.W. Jones. Nonlinear inferential control using model-based observer control. . Control Group Research Report R-91/17, Glasgow University, Dept. of Mechanical Engineering, [7] A.J. Krener and W. Respondek. Nonlinear observers with linearizableerror dynamics. SIAM..7. Control Opt., 2:197-'216, 1985.
[8] H. Kwakernaak and R. Sivan. Linear Optimal Control Systems. Wiley, 1972. [9] E. k. Misawaand J. K. Hedrick. Nonlinear observers - a state-of-the-art survey. Trans. ASME, 111:344-352, 1989.
[10] S. Slcogestad and M. Morari. Implication of large rga-elements on control performance. Ind. Eng. Chem. Res., 26(11):2121-2330, 1987. . 156