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Control structures for optimization: examples from chemical industry
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Proceedings, 10th IFAC International Symposium on Advanced Control of Chemical Processes Proceedings, 10th IFAC International Symposium on Shenyang, Liaoning, China, July 25-27, 2018 Advanced Control of Chemical Processes Shenyang, Liaoning, China, July 25-27, 2018 IFAC PapersOnLine 51-18 (2018) 429–433
ScienceDirect
Control structures for optimization: examples from chemical industry Control structures forKrister optimization: examples from chemical industry Forsman* Mohammed Adlouni* KristerSpecialty Forsman* Mohammed *Perstorp Chemicals, SE 284Adlouni* 80 Perstorp Sweden; (e-mail: [email protected]) *Perstorp Specialty Chemicals, SE 284 80 Perstorp Sweden; (e-mail: [email protected]) Abstract: We analyze and exemplify how some classical control structures can be used for optimizing a chemical process directly. Some key structures in this context are split-range control and mid-ranging Abstract: analyze and exemplifycontrol how some classical used control can bemanipulated used for optimizing control. In We applications, split-range is primarily to structures manage several variablesa chemical affecting process directly. key structures this context are reference split-rangetocontrol and objective, mid-ranging (valves) the sameSome controlled variable,inwithout explicit a control or control. In applications, split-range is primarily to used manage optimization criterion. However, the control same basic principleused can be for several directlymanipulated optimizing avariables process, (valves) affecting the same variable, explicit reference control than objective, or subprocess. In some cases controlled that scheme provideswithout a simpler and more clear to cutasolution MPC. or A optimization criterion. However, the same basic principle be used for directly optimizing process, similar observation applies to mid-ranging control (alsocan known as input resetting control,a or valve or subprocess. In some cases that scheme provides a simpler and more clear cut solution than MPC. A position control). similar observation applies to mid-ranging control (also known as input resetting control, or valve position Keywords: process control, chemical optimizing control, split-range control, mid-ranging © 2018, control). IFAC (International Federationindustry, of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. control Keywords: process control, chemical industry, optimizing control, split-range control, mid-ranging control cold liquid from the storage tank, because the first step in 1. INTRODUCTION plant 2 requires hot liquid. So by ensuring that the feed to cold liquid the asstorage tank,webecause the steam first step in 2 is asfrom warm possible, minimize usage 1. INTRODUCTION By “classical control structures” we mean such well known plant plant 2 requires hot liquid. So by ensuring that the feed to multivariable schemes as cascade control, feedforward there. By “classical control structures” such inwell known plant 2 is as warm as possible, we minimize steam usage control, ratio control, etc. Those we are mean described numerous there.optimization problem is easily solved by an SRC. The This multivariable schemes as cascade control, feedforward textbooks, e.g. Marlin (2000) and Smith and Corripio (2006), block named “SR” in (Fig. 1) implements the two look-up control, ratio control, etc. Those are described in numerous and compared to Model Predictive Control in Forsman This optimization problem is easily solved by an SRC. The tables illustrated in (Fig. 2). In words: “When the control textbooks, e.g. Marlin (2000) and Smith and Corripio (2006), (2016). In this paper we show how some classical structures block named “SR” in (Fig. 1) implements the two look-up signal u is between 0% and 50% valve v1 is fully closed, and and compared to Model Predictive Control in Forsman can be used for on-line optimization in ways that are not well tables illustrated in (Fig. 2). In words: “When the control v2 opens from 0% to 100%. If u increases further, from 50% (2016). In this paper we show how some classical structures known from literature. The most important structures in this signal u is between 0% and 50% valve v1 is fully closed, and can be used for on-linecontrol optimization ways that are not well to 100% v2 is fully open, and v1 opens from 0% to 100%.” context are split-range (SRC) in and mid-ranging control v2 opens from 0% to 100%. If u increases further, from 50% known from literature. The most important structures in this (sometimes called input resetting control or valve position to 100% v2 is fully open, and v1 opens from 0% to 100%.” context control).are split-range control (SRC) and mid-ranging control v1 (sometimes called input resetting control or valve position control). 2. SPLIT RANGE CONTROL BASICS Feed tank v 1
Storage tank
2. SPLIT RANGE “Split-range control” in itsCONTROL simplest BASICS form consists in connecting the output u of a controller to several manipulated “Split-range control” in valves, its simplest consists in variables (MVs), typically throughform a look-up table. connecting the output u of to several manipulated More generally, we will calla controller any structure where several MVs variables (MVs), typically valves, through a look-up output table. are calculated algebraically from the same controller More generally, we will call any structure where several MVs split-range control. This means that introducing SRC reduces are calculated from the same controller output the number of algebraically degrees of freedom available for control of a split-range process. control. This means that introducing SRC reduces the number of degrees of freedom available for control of a process. A classical application of SRC is in temperature control, when both heating and cooling may be needed, using A classical application of for SRC is in and temperature different process equipment cooling heating. control, when both heating and cooling may be needed, using different equipment cooling and heating. A simpleprocess example of an for SRC application motivated by economic optimization is showed in (Fig 1). The primary A simple example of SRC the application motivated by control specification is toancontrol level in the feed tank. economic optimization is showed in (Fig 1). The primary This is done by a single level controller (LC) that control specification is to vcontrol the level in the feed tank. manipulates two valves, 1 and v2. The liquid in the top This iscoming done from by athesingle controller stream, storagelevel tank through v1, is(LC) cool, that and manipulates two valves, v 1 and v2. The liquid in the top the liquid in the bottom stream is hot. The process has two stream, coming from(DoF), the storage through 1 , is cool, and degrees of freedom since tank we have twovMVs and just the in the bottom(CV), stream is hot. process has two one liquid controlled variable namely theThe level. degrees of freedom (DoF), since we have two MVs and just one (CV), the level. The controlled extra DoF variable can be used fornamely optimization: It is preferred to take the hot liquid coming directly from plant 1 before taking The extra DoF can be used for optimization: It is preferred to take the hot liquid coming directly from plant 1 before taking
Storage tank Plant 1
SR
LC
SR
LC
Feed tank
Cooler
Cooler
v2
Plant 1
v2
Plant 2
2 Fig. 1. Split-range control applied to level control Plant example.
Fig. 1. Split-range control applied to level control example. v1
v2
v1
v2 u
u
u
u
Fig. 2. SRC: Valve positions as functions of control output. Fig. SRC: positionsscheme as functions of control output. It is 2. clear thatValve this control provides a solution to the energy optimization problem while ensuring that the level in It clearvessel that this control scheme provides a solution to itthe theisfeed is controlled. It is also worth noticing that is energy optimization problem while ensuring that the level in difficult or maybe impossible to achieve the same control the feed vessel controlled.MPC, It is also worth noticing thatv it as is behavior usingistraditional considering v1 and 2 difficult or maybe impossible to achieve the same control independent MVs. behavior using traditional MPC, considering v1 and v2 as independent MVs.
2405-8963 © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2018.09.338 Copyright © 2018 IFAC 423
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There are some additional practical considerations to be made when implementing an SRC scheme like the one above. For example, if the valve characteristics are considerably different for v1 and v2, it may be advantageous to modify the lookup table so that the process gain from u to CV is reasonably constant across the operating region. If not, tuning the level controller could be unnecessarily difficult.
(“active constraint”) is, then we can make an MV-CV-pairing that ensures maximum throughput.
3. SRC FOR THROUGHPUT MAXIMIZATION
The SRC scheme described by (Fig. 5) and (Fig. 6) caters for active constraint switching. This structure can be seen as a kind of “dynamic variable pairing”.
Consider a simple process consisting only of a heat exchanger functioning as a cooler of a product stream, as in (Fig. 3). The product temperature is measured by a temperature transmitter TT. The cooling water flow through the exchanger can be manipulated by the valve v2, and the flow of product by the valve v1. So this process has two DoF.
It is not uncommon that over time a constraint switches between being active and inactive. For example, during summer the temperature of the incoming cooling water may be so high that the cooling capacity is limiting, even though that is not the case during winter.
v1 TC
u
Cooling water
v2
SR
v1
Product TT
Fig. 5. SRC for production rate maximization in cooler. v2 v2
v1
Fig. 3. Heat exchanger process. u
u
This process step is in fact the bottle neck of the plant, so it is important to ensure that it is always running at maximum capacity. It is a strict requirement that the temperature should be controlled to its setpoint. In addition to this primary control specification we want the product flow to be maximized, so then we need to use both DoF. The temperature is affected both by cooling water flow and product flow. Normally we would manipulate v2 to control temperature and keep v1 fully open in order to maximize production, as showed in (Fig. 4).
Fig. 6. SRC; valve positions as functions of u. The above example is further elaborated and analyzed in Reyes-Lúa et al (2017). Another example, of a different type, is given by (Fig. 7). Two processes P1 and P2 are separated by a buffer tank. The level of the tank is controlled by a P-controller LC. P1 is bottlenecking the entire plant, so it makes sense to manipulate the valve v2 in order to control the buffer level, and to set v1 = 100% so that production is maximized. In this case v1 is the throughput manipulator (TPM) for the entire plant.
v1 TC
LC TPM v1
v2
P1
Set to 100% by operator
Fig. 4. Production maximization when cooling capacity is not limiting. However, it could happen that cooling capacity is limiting production rate. In that scenario we may use v1 for controlling temperature, thus connecting it to the TC, and keep v2 fully open. So if we know beforehand what the limiting quantity
Buffer 100%
P2 v2
Fig. 7. Processes separated by buffer tank. P1 bottlenecking. If instead P2 is the bottle neck, then the control structure in (Fig. 8) provides online optimization. Now v2 is TPM.
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Frequently the VPC scheme can be used for this purpose in the same cases as SRC but the resulting solution is only suboptimal, since it requires a certain back-off. In practice it may still be desirable, because it does not change the MVCV-pairing. In the above example with heat exchanger throughput maximization, the control performance, e.g. temperature variability, may be significantly better using cooling water as MV than using product flow.
LC 100%
P1
Buffer
P2
v1
TPM
Fig. 8. Same plant as in Fig. 7, but P2 is bottlenecking. If, again, we do not know beforehand if P1 or P2 is bottlenecking the plant, then the structure showed in (Fig. 9) provides on-line production rate maximization. In some sense there is no longer a TPM for the entire plant.
4. COOLING SYSTEM EXAMPLE Consider a cooling system consisting of a refrigerating type of cooling machine, pressure equalization vessel, variable speed pump and two heat exchange units with control valves as shown in (Fig. 11) of Appendix A.
SR
The system has four manipulated variables: input power to the cooling machine, pump speed and two valve positions for each of the heat exchangers.
LC
P1
Buffer
P2
v1
The cooling machine outlet temperature, the pressure upstream of the heat exchangers and the temperatures of the two cooled streams from the heat exchangers are measured and can be controlled.
v2
Fig. 9. SRC for maximizing throughput when bottleneck is moving.
The transfer function matrix for this 4x4 system is highly interacting. To decrease the interaction between the subsystems, the pressure is controlled by manipulating the pump and the coolant temperature at the cooling machine outlet is controlled by manipulating the cooling machine input power. The most straightforward control structure for the temperatures of the cooled streams exiting the two heat exchangers is to simply control each temperature by manipulating the valve that affects the coolant throughput, as in (Fig 11).
4. MID-RANGING CONTROL Mid-ranging control, or “input resetting”, or “valve position control” is a classical technique for handling a process where two MVs influence the same CV, but with different gain and dynamics. The basic idea is to use two controllers: one that controls the CV by manipulating the fast and accurate MV, and one that slowly controls the operating point of the aforementioned by manipulating the slow and coarse MV. The latter is often called a valve position controller (VPC). Its CV is the MV of the first controller. Fig. 10 shows a common way of implementing such a scheme. The most common reason for using VPC is to use the extra DoF to simultaneously address accuracy and rangeability, i.e. it is motivated by non-linearities (saturation and quantization). The setpoint for the VPC is often 50%, so that it aims at keeping the primary valve in the middle of its range, hence the name “mid-ranging”. r1 = Setpoint for y
C1
u1
+ C2 VPC
u2
Assuming that there exists a known priority between controlled temperatures, a split-range implementation could ensure that this priority is met while utilizing the cooling machine maximally. In (Fig. 12), Appendix A, this splitrange solution is illustrated. The high-priority temperature control, in this case TC1, primarily uses its own valve and secondarily limits the second temperature controller’s output (valve) through a minimum selector.
P1 Small influence
r2 = Setpoint for u1
Since the available cooling power in the cooling machine is limited, it could occur that the temperatures of one or both cooled streams from the heat exchangers cannot be kept at setpoint level due to too large cooling in the heat exchangers.
y
P2 Large influence
Fig. 10. Block diagram for a mid-ranging structure. However, the same idea is also useful in optimizing control: the VPC could be used for ensuring that the back-off from an active constraint is at a prescribed level. This idea has been described by Shinskey (1998) and others.
The prioritizing split-range structure is extendable and could be used when more heat exchangers are added to the system. This solution handles the case when the high-priority temperature control is deviating from its setpoint due to too high coolant temperature, not the case where the valve saturates due to insufficient differential pressure. The simple pressure control from (Fig. 11) and (Fig. 12) has a constant setpoint. Of course, a high pressure could be chosen as to keep the differential pressure from being limiting, however there is an energy optimization to consider. It is wasteful to have a high pressure and small valve openings at the heat exchangers.
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A structure that optimizes the pump speed to save energy is a VPC acting on the maximum valve opening of the two (or more) heat exchanger valves, as shown in (Fig 13). The setpoint to the VPC should be close to 100% yet retain room for control.
Systems, including Biosystems (DYCOPS-CAB), pp 514519. Marlin, T.E. (2000). Process Control. Second edition. McGraw-Hill. Reyes-Lúa, A., et al. (2017). Optimal Operation with Changing Active Constraint Regions using Classical Advanced Control. Submitted to IFAC AdChem 2018. Shinskey, F.G. (1998): Process Control Systems. 3rd edition. McGraw-Hill. Smith, C.A. and Corripio, A. (2006). Principles and Practice of Automatic Process Control. Third Edition. Wiley.
REFERENCES Forsman, K (2016). Implementation of advanced control in the process industry without the use of MPC. Proc. 11th IFAC Symposium on Dynamics and Control of Process
Appendix A. COOLING SYSTEM FIGURES
Cooling machine
TC3
Pressure equalization vessel TC1
TC2
PC
VSD
Fig. 11: Cooling system: completely decentralized control.
Cooling machine
TC3
Pressure equalization vessel TC1
SR
TC2
PC
VSD
Fig. 12: Cooling system: SRC used for optimization.
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Cooling machine
TC3
Pressure equalization vessel TC1
SR VPC
MAX
TC2
MIN
PC
VSD
Fig. 13: Cooling system: SRC in combination with VPC and selectors, used for optimization.
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Proceedings, 10th IFAC International Symposium on Advanced Control of Chemical Processes Proceedings, 10th IFAC International Symposium on Shenyang, Liaoning, China, July 25-27, 2018 Advanced Control of Chemical Processes Shenyang, Liaoning, China, July 25-27, 2018 IFAC PapersOnLine 51-18 (2018) 429–433
ScienceDirect
Control structures for optimization: examples from chemical industry Control structures forKrister optimization: examples from chemical industry Forsman* Mohammed Adlouni* KristerSpecialty Forsman* Mohammed *Perstorp Chemicals, SE 284Adlouni* 80 Perstorp Sweden; (e-mail: [email protected]) *Perstorp Specialty Chemicals, SE 284 80 Perstorp Sweden; (e-mail: [email protected]) Abstract: We analyze and exemplify how some classical control structures can be used for optimizing a chemical process directly. Some key structures in this context are split-range control and mid-ranging Abstract: analyze and exemplifycontrol how some classical used control can bemanipulated used for optimizing control. In We applications, split-range is primarily to structures manage several variablesa chemical affecting process directly. key structures this context are reference split-rangetocontrol and objective, mid-ranging (valves) the sameSome controlled variable,inwithout explicit a control or control. In applications, split-range is primarily to used manage optimization criterion. However, the control same basic principleused can be for several directlymanipulated optimizing avariables process, (valves) affecting the same variable, explicit reference control than objective, or subprocess. In some cases controlled that scheme provideswithout a simpler and more clear to cutasolution MPC. or A optimization criterion. However, the same basic principle be used for directly optimizing process, similar observation applies to mid-ranging control (alsocan known as input resetting control,a or valve or subprocess. In some cases that scheme provides a simpler and more clear cut solution than MPC. A position control). similar observation applies to mid-ranging control (also known as input resetting control, or valve position Keywords: process control, chemical optimizing control, split-range control, mid-ranging © 2018, control). IFAC (International Federationindustry, of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. control Keywords: process control, chemical industry, optimizing control, split-range control, mid-ranging control cold liquid from the storage tank, because the first step in 1. INTRODUCTION plant 2 requires hot liquid. So by ensuring that the feed to cold liquid the asstorage tank,webecause the steam first step in 2 is asfrom warm possible, minimize usage 1. INTRODUCTION By “classical control structures” we mean such well known plant plant 2 requires hot liquid. So by ensuring that the feed to multivariable schemes as cascade control, feedforward there. By “classical control structures” such inwell known plant 2 is as warm as possible, we minimize steam usage control, ratio control, etc. Those we are mean described numerous there.optimization problem is easily solved by an SRC. The This multivariable schemes as cascade control, feedforward textbooks, e.g. Marlin (2000) and Smith and Corripio (2006), block named “SR” in (Fig. 1) implements the two look-up control, ratio control, etc. Those are described in numerous and compared to Model Predictive Control in Forsman This optimization problem is easily solved by an SRC. The tables illustrated in (Fig. 2). In words: “When the control textbooks, e.g. Marlin (2000) and Smith and Corripio (2006), (2016). In this paper we show how some classical structures block named “SR” in (Fig. 1) implements the two look-up signal u is between 0% and 50% valve v1 is fully closed, and and compared to Model Predictive Control in Forsman can be used for on-line optimization in ways that are not well tables illustrated in (Fig. 2). In words: “When the control v2 opens from 0% to 100%. If u increases further, from 50% (2016). In this paper we show how some classical structures known from literature. The most important structures in this signal u is between 0% and 50% valve v1 is fully closed, and can be used for on-linecontrol optimization ways that are not well to 100% v2 is fully open, and v1 opens from 0% to 100%.” context are split-range (SRC) in and mid-ranging control v2 opens from 0% to 100%. If u increases further, from 50% known from literature. The most important structures in this (sometimes called input resetting control or valve position to 100% v2 is fully open, and v1 opens from 0% to 100%.” context control).are split-range control (SRC) and mid-ranging control v1 (sometimes called input resetting control or valve position control). 2. SPLIT RANGE CONTROL BASICS Feed tank v 1
Storage tank
2. SPLIT RANGE “Split-range control” in itsCONTROL simplest BASICS form consists in connecting the output u of a controller to several manipulated “Split-range control” in valves, its simplest consists in variables (MVs), typically throughform a look-up table. connecting the output u of to several manipulated More generally, we will calla controller any structure where several MVs variables (MVs), typically valves, through a look-up output table. are calculated algebraically from the same controller More generally, we will call any structure where several MVs split-range control. This means that introducing SRC reduces are calculated from the same controller output the number of algebraically degrees of freedom available for control of a split-range process. control. This means that introducing SRC reduces the number of degrees of freedom available for control of a process. A classical application of SRC is in temperature control, when both heating and cooling may be needed, using A classical application of for SRC is in and temperature different process equipment cooling heating. control, when both heating and cooling may be needed, using different equipment cooling and heating. A simpleprocess example of an for SRC application motivated by economic optimization is showed in (Fig 1). The primary A simple example of SRC the application motivated by control specification is toancontrol level in the feed tank. economic optimization is showed in (Fig 1). The primary This is done by a single level controller (LC) that control specification is to vcontrol the level in the feed tank. manipulates two valves, 1 and v2. The liquid in the top This iscoming done from by athesingle controller stream, storagelevel tank through v1, is(LC) cool, that and manipulates two valves, v 1 and v2. The liquid in the top the liquid in the bottom stream is hot. The process has two stream, coming from(DoF), the storage through 1 , is cool, and degrees of freedom since tank we have twovMVs and just the in the bottom(CV), stream is hot. process has two one liquid controlled variable namely theThe level. degrees of freedom (DoF), since we have two MVs and just one (CV), the level. The controlled extra DoF variable can be used fornamely optimization: It is preferred to take the hot liquid coming directly from plant 1 before taking The extra DoF can be used for optimization: It is preferred to take the hot liquid coming directly from plant 1 before taking
Storage tank Plant 1
SR
LC
SR
LC
Feed tank
Cooler
Cooler
v2
Plant 1
v2
Plant 2
2 Fig. 1. Split-range control applied to level control Plant example.
Fig. 1. Split-range control applied to level control example. v1
v2
v1
v2 u
u
u
u
Fig. 2. SRC: Valve positions as functions of control output. Fig. SRC: positionsscheme as functions of control output. It is 2. clear thatValve this control provides a solution to the energy optimization problem while ensuring that the level in It clearvessel that this control scheme provides a solution to itthe theisfeed is controlled. It is also worth noticing that is energy optimization problem while ensuring that the level in difficult or maybe impossible to achieve the same control the feed vessel controlled.MPC, It is also worth noticing thatv it as is behavior usingistraditional considering v1 and 2 difficult or maybe impossible to achieve the same control independent MVs. behavior using traditional MPC, considering v1 and v2 as independent MVs.
2405-8963 © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2018.09.338 Copyright © 2018 IFAC 423
Shenyang, Liaoning, China, July 25-27, 2018 Krister Forsman et al. / IFAC PapersOnLine 51-18 (2018) 429–433
430
There are some additional practical considerations to be made when implementing an SRC scheme like the one above. For example, if the valve characteristics are considerably different for v1 and v2, it may be advantageous to modify the lookup table so that the process gain from u to CV is reasonably constant across the operating region. If not, tuning the level controller could be unnecessarily difficult.
(“active constraint”) is, then we can make an MV-CV-pairing that ensures maximum throughput.
3. SRC FOR THROUGHPUT MAXIMIZATION
The SRC scheme described by (Fig. 5) and (Fig. 6) caters for active constraint switching. This structure can be seen as a kind of “dynamic variable pairing”.
Consider a simple process consisting only of a heat exchanger functioning as a cooler of a product stream, as in (Fig. 3). The product temperature is measured by a temperature transmitter TT. The cooling water flow through the exchanger can be manipulated by the valve v2, and the flow of product by the valve v1. So this process has two DoF.
It is not uncommon that over time a constraint switches between being active and inactive. For example, during summer the temperature of the incoming cooling water may be so high that the cooling capacity is limiting, even though that is not the case during winter.
v1 TC
u
Cooling water
v2
SR
v1
Product TT
Fig. 5. SRC for production rate maximization in cooler. v2 v2
v1
Fig. 3. Heat exchanger process. u
u
This process step is in fact the bottle neck of the plant, so it is important to ensure that it is always running at maximum capacity. It is a strict requirement that the temperature should be controlled to its setpoint. In addition to this primary control specification we want the product flow to be maximized, so then we need to use both DoF. The temperature is affected both by cooling water flow and product flow. Normally we would manipulate v2 to control temperature and keep v1 fully open in order to maximize production, as showed in (Fig. 4).
Fig. 6. SRC; valve positions as functions of u. The above example is further elaborated and analyzed in Reyes-Lúa et al (2017). Another example, of a different type, is given by (Fig. 7). Two processes P1 and P2 are separated by a buffer tank. The level of the tank is controlled by a P-controller LC. P1 is bottlenecking the entire plant, so it makes sense to manipulate the valve v2 in order to control the buffer level, and to set v1 = 100% so that production is maximized. In this case v1 is the throughput manipulator (TPM) for the entire plant.
v1 TC
LC TPM v1
v2
P1
Set to 100% by operator
Fig. 4. Production maximization when cooling capacity is not limiting. However, it could happen that cooling capacity is limiting production rate. In that scenario we may use v1 for controlling temperature, thus connecting it to the TC, and keep v2 fully open. So if we know beforehand what the limiting quantity
Buffer 100%
P2 v2
Fig. 7. Processes separated by buffer tank. P1 bottlenecking. If instead P2 is the bottle neck, then the control structure in (Fig. 8) provides online optimization. Now v2 is TPM.
424
Shenyang, Liaoning, China, July 25-27, 2018
Krister Forsman et al. / IFAC PapersOnLine 51-18 (2018) 429–433
Frequently the VPC scheme can be used for this purpose in the same cases as SRC but the resulting solution is only suboptimal, since it requires a certain back-off. In practice it may still be desirable, because it does not change the MVCV-pairing. In the above example with heat exchanger throughput maximization, the control performance, e.g. temperature variability, may be significantly better using cooling water as MV than using product flow.
LC 100%
P1
Buffer
P2
v1
TPM
Fig. 8. Same plant as in Fig. 7, but P2 is bottlenecking. If, again, we do not know beforehand if P1 or P2 is bottlenecking the plant, then the structure showed in (Fig. 9) provides on-line production rate maximization. In some sense there is no longer a TPM for the entire plant.
4. COOLING SYSTEM EXAMPLE Consider a cooling system consisting of a refrigerating type of cooling machine, pressure equalization vessel, variable speed pump and two heat exchange units with control valves as shown in (Fig. 11) of Appendix A.
SR
The system has four manipulated variables: input power to the cooling machine, pump speed and two valve positions for each of the heat exchangers.
LC
P1
Buffer
P2
v1
The cooling machine outlet temperature, the pressure upstream of the heat exchangers and the temperatures of the two cooled streams from the heat exchangers are measured and can be controlled.
v2
Fig. 9. SRC for maximizing throughput when bottleneck is moving.
The transfer function matrix for this 4x4 system is highly interacting. To decrease the interaction between the subsystems, the pressure is controlled by manipulating the pump and the coolant temperature at the cooling machine outlet is controlled by manipulating the cooling machine input power. The most straightforward control structure for the temperatures of the cooled streams exiting the two heat exchangers is to simply control each temperature by manipulating the valve that affects the coolant throughput, as in (Fig 11).
4. MID-RANGING CONTROL Mid-ranging control, or “input resetting”, or “valve position control” is a classical technique for handling a process where two MVs influence the same CV, but with different gain and dynamics. The basic idea is to use two controllers: one that controls the CV by manipulating the fast and accurate MV, and one that slowly controls the operating point of the aforementioned by manipulating the slow and coarse MV. The latter is often called a valve position controller (VPC). Its CV is the MV of the first controller. Fig. 10 shows a common way of implementing such a scheme. The most common reason for using VPC is to use the extra DoF to simultaneously address accuracy and rangeability, i.e. it is motivated by non-linearities (saturation and quantization). The setpoint for the VPC is often 50%, so that it aims at keeping the primary valve in the middle of its range, hence the name “mid-ranging”. r1 = Setpoint for y
C1
u1
+ C2 VPC
u2
Assuming that there exists a known priority between controlled temperatures, a split-range implementation could ensure that this priority is met while utilizing the cooling machine maximally. In (Fig. 12), Appendix A, this splitrange solution is illustrated. The high-priority temperature control, in this case TC1, primarily uses its own valve and secondarily limits the second temperature controller’s output (valve) through a minimum selector.
P1 Small influence
r2 = Setpoint for u1
Since the available cooling power in the cooling machine is limited, it could occur that the temperatures of one or both cooled streams from the heat exchangers cannot be kept at setpoint level due to too large cooling in the heat exchangers.
y
P2 Large influence
Fig. 10. Block diagram for a mid-ranging structure. However, the same idea is also useful in optimizing control: the VPC could be used for ensuring that the back-off from an active constraint is at a prescribed level. This idea has been described by Shinskey (1998) and others.
The prioritizing split-range structure is extendable and could be used when more heat exchangers are added to the system. This solution handles the case when the high-priority temperature control is deviating from its setpoint due to too high coolant temperature, not the case where the valve saturates due to insufficient differential pressure. The simple pressure control from (Fig. 11) and (Fig. 12) has a constant setpoint. Of course, a high pressure could be chosen as to keep the differential pressure from being limiting, however there is an energy optimization to consider. It is wasteful to have a high pressure and small valve openings at the heat exchangers.
425
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A structure that optimizes the pump speed to save energy is a VPC acting on the maximum valve opening of the two (or more) heat exchanger valves, as shown in (Fig 13). The setpoint to the VPC should be close to 100% yet retain room for control.
Systems, including Biosystems (DYCOPS-CAB), pp 514519. Marlin, T.E. (2000). Process Control. Second edition. McGraw-Hill. Reyes-Lúa, A., et al. (2017). Optimal Operation with Changing Active Constraint Regions using Classical Advanced Control. Submitted to IFAC AdChem 2018. Shinskey, F.G. (1998): Process Control Systems. 3rd edition. McGraw-Hill. Smith, C.A. and Corripio, A. (2006). Principles and Practice of Automatic Process Control. Third Edition. Wiley.
REFERENCES Forsman, K (2016). Implementation of advanced control in the process industry without the use of MPC. Proc. 11th IFAC Symposium on Dynamics and Control of Process
Appendix A. COOLING SYSTEM FIGURES
Cooling machine
TC3
Pressure equalization vessel TC1
TC2
PC
VSD
Fig. 11: Cooling system: completely decentralized control.
Cooling machine
TC3
Pressure equalization vessel TC1
SR
TC2
PC
VSD
Fig. 12: Cooling system: SRC used for optimization.
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Cooling machine
TC3
Pressure equalization vessel TC1
SR VPC
MAX
TC2
MIN
PC
VSD
Fig. 13: Cooling system: SRC in combination with VPC and selectors, used for optimization.
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