On the Role of Material Balances in the Synthesis of Overall Process Control Systems

The synthesis of control systems for overall processes remains a challenge. Whilst a number of automated approaches have been explored academically, in practice systems are mainly synthesised using experience and intuition in conjunction with dynamic simulation software. An approach is presented in this paper for the systematic synthesis of overall process control systems which is simple, practical and appropriate for use at the undergraduate teaching level. Many potential problems can be identified and avoided in the synthesis of process control systems by ensuring that the control system can maintain a steady-state control of the overall mass, the mass of the individual components and, where necessary, multiple phases. Processes with recycles are vulnerable to process control problems when the overall mass balance of the system containing the recycle is not correctly managed. This can be overcome by self-regulation (perhaps involving process design changes) or by changing the structure of the control system. Achieving and maintaining the material balance are the main purposes of the majority of controllers in most chemical processes. Without robust delivery of material balance control, higher level control objectives (such as quality controls) are unlikely to be met reliably. This paper presents a step-wise approach to the synthesis of overall process control systems that avoids many potential problems by identifying which process parameters can be manipulated to achieve the intended process mass balance and designing the control structure accordingly.


Introduction
Whereas a great emphasis in process control has traditionally been placed on the analysis or simulation of control systems, the creation or synthesis of control systems has by comparison received little attention.Historically, the focus of undergraduate process control courses has been on the use of Laplace-domain mathematics to analyse stability.More recently, dynamic simulation has been increasingly used as suitable software tools have become more accessible.However, practising engineers in the process industries rarely need or use either.Neither provide a means for systematic synthesis of process control schemes for chemical processes.Whilst the introduction of such software tools has increased the capability of analysing and simulating process control systems, the synthesis of the control systems to be analysed lacks systematic approaches, especially when considering the overall control systems for chemical processes.
Whilst the advent of new software tools has changed industrial practice, it has also prompted questions relating to the teaching of process control to chemical engineering undergraduates (Rossiter et. al. 2020).Ranade et al. (2012) suggested that the availability of such software tools should in principle has shifted the emphasis of learning in process control from "how" to "why".An international survey of Highlights • Synthesis of overall process control systems.
• Design of process control systems.
• The snowball effect in process recycle control.
• Overcoming the snowball effect through self-regulation and design changes.
• Avoiding process control problems through material balance considerations.
academics and industrialists highlighted the necessity of a change in emphasis in teaching process control away from traditional mathematical rigour to enabling students to understand the philosophy of control, concepts of analysis, design, feedback mitigations and uncertainty (Rossiter et al. 2020).This was supported by another survey which concluded that there was an overwhelming consensus that a first course in process control should focus more on concepts, case studies, motivation and context, rather than students becoming fully mathematically literate with a range of analysis and design tools (Rossiter et al. 2021).
In addressing how such changes can be introduced into the undergraduate curriculum, Udugama et al. (2020) suggested that the interdependency of the domains of process design, operations and control needed to be integrated more fully.It was highlighted that the current practice in process control education emphasised mathematical rigour first, whilst often neglecting the underlying process and any insights it may provide (Udugama et al. 2020).In a study of the renovation of undergraduate process control courses, it was emphasised by Edgar et al. (2006) that the new engineer should understand that process control is a natural extension of material and energy balances.In other words, dynamic loops are used to keep the material and energy balances in balance.
The traditional focus on theoretical process dynamics in the undergraduate curriculum differs greatly from the usual practice in the process industries, where the key issue is to understand the structure and purpose of the process and ensure that the controls are structured to deliver the process design intent.Indeed, an excessively theoretical approach can often obscure, rather than reveal, fundamental structural issues that can prevent the control system from working effectively.Undergraduate students should be introduced to authentic issues and challenges that will be encountered in industrial systems.
This paper investigates the early stages of the development of process control systems and how understanding the structure and purpose of the process can avoid control problems that might otherwise create major obstacles when considering the analysis and simulation of a chosen process control system.The approach is intended to be intuitive enough for introduction at an undergraduate level.

Synthesis of Overall Process Control Systems
Synthesis of process control systems requires the specification of measured and manipulated variables.Many techniques for choosing these sets of variables have been considered in the control literature.Industrially, a combination of experience and intuition are sufficient to achieve satisfactory control for the overwhelming majority of control loops in a process, with dynamic simulation typically being used to evaluate options for a small number of more challenging situations.The ultimate goal is not just to consider the control objectives of the individual process operations but the overall process and achieving the control objectives for the complete process.When considering the overall process, the problem has certain characteristics that do not necessarily feature in the design of control systems for single operations (Stephanopoulos and Ng 2000): 1.The variables to be controlled by an overall process are not as clearly or as easily defined as for single operations.2. Local control decisions, made within the context of single units, may have long-range effects throughout the process.3. The size of the control problem for the overall process is significantly larger than that for the individual operations, making its solution considerably more difficult.
There are many degrees of freedom to consider, and simultaneous consideration is required: 1.To maintain process variables within safe operating limits 2. To achieve and maintain material and energy balances 3. To maintain the products to be within specified quality standards 4. To maintain the required production rate 5. To ensure the stability of the process 6.To optimise the performance of the process commensurate with the other objectives The complexity of the problem has prompted many studies to investigate automated ways to synthesise process control systems (Umeda et al. 1978, Govind and Powers 1978, Manousiouthakis et al. 1986, Arkun and Ramakrishnan 1984, Lin et al., 1991, Mušic et al. 2000, Stephanopoulos and Ng 2000, Maga et al. 2002, Skogestad 2004, Zaytoon and Riera 2017, Hagglund and Guzman 2018).Even more ambitious studies have investigated systematic ways to synthesise simultaneously the process design and the process control system (Gill et al. 1998, Kookos and Perkins 2001, Ricardez Sandoval et al. 2007, Huusom 2015).Whilst these methods have achieved some success on smaller problems, there are no widely accepted methods to achieve the systematic synthesis of an overall process control system, especially one that could be practised at the undergraduate level.Before suggesting such an approach, it is worth highlighting the issues in a simple process.

An Illustrative Example for the Synthesis of Overall Process Control Systems
Figure 1 illustrates a simple example showing a process flow diagram for a reaction, separation and recycle system.In Fig. 1, the fresh Feed A, which is assumed to be pure, is mixed with recycled Component A, preheated and enters an adiabatic mixed flow reactor (continuous stirred tank reactor CSTR), where it is partially converted to Product B. The reactor is assumed to have a fixed volume and, to keep the case simple, is assumed to be operated adiabatically.The rate of reaction is given in this case by Rase (1977), Denbigh and Turner (1984) and Levenspiel (1999): The reaction rate constant k is typically characterised by the Arrhenius Law: The reactor temperature is assumed to be constant, and thus the reaction rate constant k is also fixed.The reactor effluent is cooled and separated in a distillation column.The relative volatility of Component A is greater than that of Component B. Thus, unconverted Component A is separated to the distillate and recycled to the reactor with Component B taken as product from the distillation bottoms.
Figure 2 shows a possible control system for the whole process that has been developed by considering the reactor, reactor effluent cooler and the distillation control systems in isolation.Figure 2 highlights the recycle path.The recycle stream between the reactor and distillation in (1) Fig. 2 potentially creates significant instability problems for the control arrangement when the control for the mass balance is considered.A problem can potentially arise if the flowrate of the fresh Feed A increases for some reason, then the level in the reactor increases temporarily until the reactor level controller increases the flowrate from the reactor.The increased flowrate from the reactor increases the flowrate to the distillation, which increases the level in the distillation reflux drum.The reflux level control increases the recycle flow, which in turn increases the flowrate to the reactor, which again temporarily increases the level in the reactor.This creates a positive feedback loop in which the flows throughout the recycle loop keep increasing.This phenomenon is known as the 'snowball' effect (Luyben 1994, Luyben et al. 1998).The basic problem with the control arrangement in Fig. 2 is that all flows in the recycle are set by level control, but the mass balance and total inventory in the recycle loop are not controlled (Luyben 1994, Luyben et al. 1998).This has the effect of creating a circuit of level controllers, each attempting to pass on unwanted extra inventory to each other.A small change in the feed can therefore in principle create a large change in the recycle flowrate, as there is no control on the overall inventory.The result is that any disturbance that tends to increase the total inventory (e.g. increase in fresh feed) in principle can create a large increase in all flowrates around the recycle, leading to an unstable operation (Luyben 1994, Luyben et al. 1998).
Accepting that there are potentially serious problems associated with control of the total material inventory in Fig. 2, consider now the inventory of the chemical components in the process.If there are no impurities in the feed and no by-products formed in the reactor, then only the inventory of Components A and B need to be controlled.For the recycle system in Fig. 2, Component B once formed can leave from the bottom of the distillation column as product under level control.The inventory of Component B in the process is therefore controlled.However, unreacted Component A cannot leave the process unless it reacts to Component B. The feed to the process is under flowrate control and not linked to the inventory of Component A in the process.
There is thus no control of the inventory of Component A in the overall process.Generally, there are two ways to solve these problems: 1. Allow the process to self-regulate if this is feasible, or modify the process design to allow self-regulation.2. Modify the control system to remove any potential for the snowball effect.
In the example in Fig. 2, at least some self-regulation of the inventory of Component A is possible.Selfregulation at constant reactor temperature can be created by change in the flowrate of the recycle changing the concentration in the reactor and thus changing the rate of reaction.If the flowrate of Feed A to the process increases, then this will lead to an increased concentration of Component A in the reactor, both from the fresh feed and then the recycle.The effect of this increase in concentration will depend on the parameters in the kinetic equation.Three cases can be distinguished, which can be illustrated by a simple quantitative analysis.

Case 1
If an increase in the concentration of reactant in the reactor has no influence on the conversion to product, then there will be no self-regulation and no mitigation of the potential for the snowball effect.
Starting with the basic equation for the reactor conversion in the mixed-flow reactor (CSTR) in Fig. 2 (Rase 1977;Denbigh and Turner 1984;Levenspiel 1999): In an extreme case, somewhat unusual in practice, the kinetic equation in Equation 1 might have a = 0, a zeroorder reaction, in which case, Equation 3 becomes: For a zero-order reaction in which the feed concentration is fixed, the reaction rate is independent of the concentration of reactant in the reactor.Changing concentration in the reactor therefore has no effect on the rate of the reaction and therefore cannot prevent the potential for the snowball effect.The recycle rate would therefore increase (or in the case of decreasing feed reduce) inexorably until it reaches the limit of the process equipment in the recycle loop, typically either the maximum flow which can be delivered by a pump or admitted by a valve (or zero flow for reducing feed).
In summary, such a scenario has a fixed reaction rate, and any mismatch between the feed rate and this reaction (3) Water SP rate will inevitably cause an accumulation or diminution of inventory of the reactant in the entire process, which will not cease until some other process limit is reached-it is an open-loop unstable process.

Case 2
If increasing the recycle flowrate increases the rate of reaction, even at constant reactor temperature, this can create self-regulation and prevent the snowball effect.However, any self-regulation is limited by the maximum possible reaction rate that allows the reactor conversion to be increased to match the increase in the flowrate of fresh feed at steady state, beyond which point the snowball effect cannot be prevented.
It is clear from the above arguments that a zero-order reaction cannot self-regulate to prevent the snowball effect.Consider now the case when the reaction is not zero-order.Take as an example a first-order reaction: If it is assumed that the density is constant, then combining Equations 3 and 5: Rearranging: For the process in Fig. 2, a material balance around the reactor at steady state, assuming that both the fresh feed and the recycle are pure, gives: Substituting for X A from Equation 7gives: The volumetric flowrate can be written as: Recognising that an overall material balance for the process in Fig. 2 requires that at steady state F B = F A and substituting Equation 10 into Equation 9gives: Rearranging Equation 11gives: Defining the recycle ratio RR: Substituting Equation 13into Equation 12and rearranging finally gives: Consider now the consequence of Eq. 14 in terms of the control system in Fig. 2 and its ability to self-regulate.For a reactor with constant volume V and temperature, if the flowrate of fresh feed F A increases and the group F A A ∕kVM A increases, this means that from Eq. 14, the recycle ratio must increase to maintain the material balance and allow the process to self-regulate.As the flowrate of fresh feed F A increases, the concentration of the reactant in the reactor increases, and the concentration of the product decreases to maintain a constant reactor conversion.However, the increase in the concentration of Component A in the reactor is less than proportional to the increase in the feed rate, because of the increase in the recycle flowrate.This means that the increase in the rate of reaction is also less than proportional to the increase in the feed rate.If F A ρ A < < kVM A , a material balance can be maintained, and the process will self-regulate with a modest increase in the recycle rate, preventing the snowball effect.However, as F A ρ A increases, the extent of the increase in recycle rate needed becomes much larger, and as F A ρ A approaches kVM A , the group F A A ∕kVM A approaches unity and the recycle ratio from Eq. 14 tends to infinity.
Thus, as the flowrate of fresh Feed A in Fig. 2 increases, the process can initially self-regulate by increasing the recycle flowrate, which prevents the snowball effect.However, as F A ρ A approaches kVM A , the change in recycle, which follows a change in feed, becomes larger and tends towards infinity.Such a system therefore can accommodate some change in feed rate, but for larger changes will typically be constrained by some other process limit, as in Case 1.The ( 11) essentially a ratio of the feed rate to the maximum possible reaction rate.
In summary, provided it is possible to increase the recycle sufficiently for the resulting change in reactor composition to deliver an increase in conversion of Component A to Component B to match the increase in fresh Feed A flowrate at steady state, then the snowball effect will be prevented.But as the flowrate of Feed A starts to approach the maximum possible reaction rate, greater increases in recycle ratio result, such that ultimately the conversion of Component A to Component B cannot match the increase in fresh Feed A at steady-state and the snowball effect cannot be prevented.

Case 3
If increasing the recycle flowrate reaches the maximum possible reaction rate and does not allow the reactor conversion to match the increase in fresh feed at steady state, then the snowball effect can be prevented by increasing the reactor volume or increasing the reaction rate (for example, by increasing the reactor temperature).
The limit of increased reaction rate and therefore the limit for self-regulation can be increased if the volume in the reactor is increased by allowing the level in the reactor to increase, or changing to a larger reactor, or increasing the reactor temperature.Increasing the reactor volume V or increasing the reaction rate constant k (for example, by increasing the reaction temperature) allows the group F A A ∕kVM A to decrease.This allows an increase in the range over which the fresh feed flowrate can be increased and the process remain self-regulating.
The potential problems associated with the control system in Fig. 2 have been presented as a control problem, which is how it typically manifests itself.However, it reflects a more fundamental mass balance problem: the only way out of the process for the feed Component A is by reaction to Component B. The snowball effect arises because there is insufficient reaction capacity available to convert the feed to the product, a situation which should be apparent from analysis using a steady-state model.Indeed, the denominator term in Eq. ( 14), kVM A , can be seen as a representation of the maximum reaction capability, and the snowball effect results when the feed F A ρ A approaches that maximum.
If the process cannot self-regulate, it is also possible to change the design of the control system to remove the potential for such instability.This can, in principle, be achieved by ensuring there is a flowrate controller somewhere in the recycle (Luyben 1994, Luyben et al. 1998).Figure 3 shows an alternative control arrangement for the process in Fig. 2. In Fig. 3, the reactor effluent control has been changed to flowrate control.Inventory control for the reactor is now from the flowrate of fresh Feed A. The inclusion of reactor effluent flowrate control in the recycle loop prevents the snowball effect since the inventory of the Component A in the process is now being controlled by the flowrate of fresh Feed A to the process under level control into the reactor.This breaks the cycle by changing the overall mass balance in the process so as only to accept as much fresh feed as the reactor is capable of processing.It should be noted that in the control scheme in Fig. 3, the rate of production is now controlled by a combination of the reactor outlet flow controller, the level control in the reactor and the reactor temperature.How this works in practice depends on the degree of influence that concentration has on reaction rate.1.If there is no influence of concentration on reaction rate (as in case 1 above), then the production rate of Component B can only be influenced by changing the volume or temperature in the reactor.2. If there is an influence of concentration on reaction rate (as in case 2 above), then increasing the flowrate by changing the set point for the flowrate controller at the exit of the reactor will cause the reactor level to lower and the flowrate of fresh Feed A to increase to maintain the level.This will cause the concentration of Component A in the reactor to increase, both from the increased flowrate of fresh Feed A and unconverted Component A in the recycle, and the production of Component B will increase.Following the symbol definitions used under Case 2 above, if F A ρ A < < kVM A , the increase in production will be almost proportional to the increase in flowrate, but as F A ρ A approaches kVM A , smaller increases in production result from increases in the reactor exit flowrate.
In addition to the flowrate control of the reactor outlet, the reactor level can also be changed to adjust the residence time in the reactor and adjust the reactor conversion.
Yet another control system option to the one shown in Fig. 2 is shown in Fig. 4.This time the snowball effect is countered by measuring the combined feed to the reactor (fresh feed plus recycle) and using this to control the flowrate of the fresh Feed A. This means that there is flowrate control in the recycle, even though the control valve is outside the recycle loop, thus avoiding the snowball effect by admitting only as much feed to the process as can be reacted.Controlling the combined flowrate to the reactor within the recycle loop maintains the inventory of Component A in the process.The rate of production can be controlled by a combination of the combined flowrate of Component A to the reactor and the level in the reactor.
It should also be noted that the schemes in Figs. 2, 3, 4 would not be viable options if the flowrate of fresh Feed A was fixed by the outlet from an upstream process and the process subject to disturbances created by the upstream process.In this situation, some mechanism must be found to vary the overall reaction rate in order to consume the required amount of feed.This would typically require a composition measurement on the reactor outlet to manipulate either the reactor temperature (and hence the rate of reaction) or the level set point (and hence residence time in the reactor) to achieve the required reactor conversion.
Whilst the above simplified analysis is specific to a simple first-order single component reaction and process configuration, it nevertheless illustrates several important principles for the design of overall process control configurations and the link with the mass balance of the process.
The key is for the control designer to understand the overall mass balance of the process and what can practically be done to change it.For any recycle, there must be a route out of the loop for every component with enough capacity to maintain the mass balance, and the capacity of that route must be capable of adapting to amount of that component present.Fundamentally, the overall process control system should ensure that the process delivers the intended mass balance.It should also be noted that if self-regulation is not feasible, simply putting a flowrate controller somewhere in the recycle loop will not necessarily lead to a stable control system.

Synthesis of Overall Process Control Configurations
As pointed out previously, although different approaches for the automated synthesis of overall process control systems have achieved some success on smaller problems, there are no widely accepted methods to achieve the systematic synthesis of an overall process control system, especially one that could be practised at the undergraduate level.Stephanopoulos (1983Stephanopoulos ( , 1984) ) suggested a simple, yet practical, modular approach to the synthesis of control systems for overall processes.In this approach, the process is divided into a collection of operations or units.A control system for each operation is synthesised and the process operation control systems combined to give the overall process.Obvious conflicts between the control systems for the individual connecting operations are then resolved.Obvious conflicts arise when the output control of one operation clashes with the input control of the downstream operation.This typically manifests itself as two control valves in the same connecting stream, one from the upstream control system and one from the downstream control system.Such conflicts are readily resolved.However, this does nothing to reconcile long-range interactions throughout the process.The approach needs to be developed further to consider these more complex interactions.The approach suggested here has much in common with the modular approach of Stephanopoulos (1983Stephanopoulos ( , 1984) ) and includes the inventory control considerations of Aske and Skogestad (2009).However, it extends this to take into account of both the overall purpose of the flowsheet and the impact of recycles on control degrees of freedom.
1. First determine the overall objective of the process under consideration.There are two common cases.In one, the feed to the process under consideration is fixed upstream, and so the process must receive a flowrate of a feed that is determined elsewhere.In the second, the process is required to deliver a fixed amount of a product to a downstream process or meet a production target.2. Divide the process flow diagram into process nodes.
Each process node consists of one or more processing units, which together have a common goal, e.g., a reactor with its heating/cooling system to deal with the heat of reaction, or a distillation (including the reboiler, condenser and reflux drum), or heat exchange and so on.3. Starting from where the overall process flowrate (process throughput) is fixed, determine process control options by first assessing how a mass balance is to be achieved for each node of the process in isolation.If the process feed is fixed, start there and work forward downstream node-by-node through the process.Conversely, if the product rate is fixed, start there and work backwards upstream node-by-node through the process from where the flowrate is fixed.In both cases, treat flows from previously assessed nodes as having been fixed, and treat recycles at this stage as normally being manipulable only at their origin.For each node: a. Establish how the overall mass balance can be achieved.The total mass must either self-regulate (e.g.incompressible liquid flow through a closed vessel with no liquid interface, gas flow through a vessel driven by pressure difference and so on) or be controlled by manipulating at least one of its inflows or outflows.In the absence of self-regulation, the inventory must depend on at least one flow in or out of any part of the process node.Liquid inventory control should be in the direction of flow if downstream of flow control.Inventory control for multiple operations in series must operate consistently in the same direction relative to the point that fixes the flowrate (Buckley 1964;Aske and Skogestad 2009).This is illustrated in Fig. 5. b.Establish how the mass balance of each chemical component can be achieved.The mass balance of each chemical component must either self-regulate or be controlled by its inflows or outflows or chemical reactions.c.If more than one phase is present, the inventory of each phase must also either self-regulate or be regulated by its inflows or outflows or phase transition (e.g.having both a level controller and pressure controller or an interface controller for multiple phases).d.Once these mass balance considerations are established, modify the node control system to achieve the other control objectives.These would include temperature, pressure, pH, and other control objectives.For quality control, such as composition, the overall mass balance and the chemical component mass balances must be capable of being manipulated to achieve this (e.g. for distillation, increasing the reflux ratio either by increasing reflux flowrate or reducing top product flowrate).
4. Where a process contains recycles, for each recycle, repeat the sub-steps from Step 3 for all of the nodes connected together in the recycle as though it were a single node. 5. Dynamic simulation of parts, or all, of the process can now be carried out to allow the controller settings to be tuned, the stability and response of the process to disturbances to be checked and, if necessary, the design evolved to ensure that it achieves the overall process control objectives in a stable and optimal way (Luyben 2014).
Consider now the application of the procedure to a case study, chosen to exemplify the main features of the approach.

Application of the Synthesis Procedure
Consider the application of the approach to a process with two feeds (Tyreus andLuyben 1993, Luyben et al. 1998).
Figure 5 shows the process for the reaction between Feed A and Feed B to produce Product C according to the reaction: Whilst the main reaction is to Product C, some light (high volatility) by-products are also formed.The rate of reaction can be assumed to be represented by the rate equation: The reaction rate constant k can be assumed to follow the Arrhenius Law given by Eq. 2. There is some vaporisation of chemical components from the reactor.As much volatile material as possible is condensed using cooling water and returned to the reactor.The uncondensed light (noncondensable) by-products are vented.The flowrate of the vented non-condensable by-products can be used to control the pressure of the reactor.The reactor effluent is a mixture of Components A, B and C, which is first cooled using cooling water and then separated in a vacuum distillation column.The vacuum is created by a steam ejector.The order of relative volatility of the three components is α A > α B > α C .The unreacted Components A and B are separated as the distillation overhead and recycled to the reactor.The Product C is taken from the distillation column bottoms.There are two common scenarios found industrially where this flowsheet might be used and which result in quite different control designs.In one scenario, one of the feeds is set by an upstream process.In the second scenario, the process is required to deliver a fixed amount of product to downstream processes (or achieve a target production).

Control Based on a Fixed Feed Rate Requirement
Consider first the scenario where the flowrate of Feed A is fixed and the process must be operated so as to convert this into Product C. Following the above procedure, the scheme in Fig. 7 can be derived.The details of the step-by-step approach are given in Table 1.The process flow diagram in Fig. 6 is shown decomposed into 3 process nodes: the reactor, cooler and distillation nodes.Given that the feed is fixed in this case, the procedure is started from the reactor node and continues forward downstream.The resulting control system in Fig. 7 might in principle suffer from the snowball effect.Whilst the adjustment of conversion in the reactor should ensure that neither Feed A nor Feed B can accumulate and limit the extent of this, it will depend on the performance of the various control loops.The chemical analysis control of the reactor is likely to be slow compared with the level controllers, which might still allow the snowball effect.

Control Based on a Fixed Product Demand
Consider now the scenario where the demand for Product C is fixed, and the process must be operated so as to manufacture sufficient Product C to meet that demand.Following the above procedure, the scheme in Fig. 8 can be derived.The details of the step-by-step approach are given in Table 2. Again, the process flow diagram in Fig. 6 is decomposed into 3 process nodes: the reactor, cooler and distillation nodes.This time the flowrate is fixed by the product flowrate from the distillation node, and the procedure starts from the distillation and moves backwards upstream.There could be concerns relating to the control of the distillation feed from level control of the bottoms, since this features a potentially significant time lag (depending on the number of trays and the type of column internals in the lower section of the column).It may be necessary or desirable to increase the capacity of the column sump to ensure that there is sufficient capacity to allow this level controller to work well despite the time lag.It should be noted that this concern is particular to the situation where a distillation column is used for the separation, especially if it has many stages The process flow diagram in Fig. 6 is shown decomposed into 3 process nodes: the reactor, cooler and distillation nodes.Given that the feed is fixed in this case, the procedure is started from the reactor node and continues forward downstream.A heat exchanger upstream of the reactor could be treated as a separate node.However, it self-regulates by continuity and the mass balance is therefore trivial Reactor 3a One feed (Feed A) to the reactor is fixed, the intent is to add Feed B in a stoichiometric ratio, and the recycle can only be manipulated at its origin, so none of these can be used to manage the liquid inventory of the reactor.The only practical option to deliver an overall liquid mass balance for the reactor is therefore by having a level controller manipulating the liquid outflow from the reactor

Reactor level controller 3b
Considering the reactor in isolation, the level control will also ensure that a mass balance of Components B and C is maintained across the reactor 3c The vapour mass balance is achieved by using a suitable pressure control Reactor pressure controller 3d The reactor temperature is controlled by manipulating steam flow to the reactor jacket Reactor temperature controller

Heat exchanger 3a/b/c
A mass balance of all components and phases will be achieved for the downstream of the heat exchanger by continuity 3d The heat exchanger outlet temperature is controlled by manipulating the flowrate of cooling water Distillation feed temperature controller

Distillation column 3a
Since the feed to the distillation column is fixed by the upstream parts of this process, one or both of the main product stream flows must be manipulated by an inventory controller to achieve a liquid mass balance.The vapour mass balance is delivered by the pressure control.Thus, there appear to be three available options: (i) the overhead level manipulates the reflux flowrate, and the sump level manipulates the flowrate of Product C; (ii) the overhead level manipulates the overhead product flowrate, and the sump level manipulates the reboil; and (iii) the overhead level manipulates the overhead product flowrate, and the sump level manipulates Product C flowrate.A control scheme where the overhead level manipulates reflux and sump level manipulates reboil is not viable because there is no variation of the outflow from the column to manage inventory 3b Considering the individual chemical components, assuming that an effective composition control scheme for the column will be implemented, noting that the purpose of the column is to separate the Product C (which leaves in the bottoms stream) from unreacted Components A and B (which leave in the overheads stream), there must therefore be an inventory control manipulating both product streams, and Option (iii) above is the most straightforward means of achieving this

Distillation reflux drum level controller Column sump level controller 3c
The vapour mass balance is achieved by using a suitable pressure control Column pressure controller 3d The distillation temperature profile can be controlled by manipulating either the steam flow to the reboiler or the reflux flowrate.Figure 7 shows the steam flow to the reboiler option

Whole process 4a
Considering the reactor, heat exchanger, distillation column and recycle as a single entity, distillation mass balance Option (iii) above delivers an overall process mass balance by manipulating the only significant route out of the process, the Product C stream below the feed.In another situation, for example, which features a flash separator rather than a distillation column, there would be no such concerns.

Evolution of the Control Design
Should the final step in the procedure highlight problems with the performance of the control system for either the fixed feed case or the fixed product case, then it might be necessary to evolve the control system.As an example, the control system in Fig. 9 avoids the potential for the snowball effect for the fixed feed case by placing a flow controller in the recycle.The reactor inventory is now controlled by the flowrate of fresh Feed A with the ratio of Feed A and Feed B controlled by the analysis of composition in the reactor.Figure 9 also avoids the potential problem with the time lag for the control of the distillation in Fig. 8 for the fixed product case.However, now Step Controllers 4b Consider the individual chemical components overall.If the quality controls for the distillation column function as required, then only the Product C stream can deliver an effective mass balance for Component C, but not either of the Components A and B. Since the feed flowrate of Feed A to the process is fixed, the only effective means of achieving a mass balance for Component A is to vary the consumption of Feed A in the reactor.The most straightforward way of achieving this is to analyse the reactor composition and manipulate either the reactor level set point (thereby increasing the residence time) or the temperature set point (thereby increasing the intrinsic reaction rate).Figure 7 shows analysis used to control the temperature.The mass balance for Component B needs also to be controlled.Like Component A, Component B can only leave the process by reacting to Component C. The consumption of Feed B is essentially equal to that of Feed A-it cannot be varied independently.In principle, matching the feed rate of Feed B to be exactly that for reaction with Feed A should be possible.However, in practice this approach is not feasible as the measurements will not be exact, and any difference in calibration between the two would lead to an accumulation of Component A or Component B. Depending on the size of the mismatch in flow, this may take place over hours, days or weeks (Luyben et al. 1998).A feedback control is thus required to manipulate the amount of Feed B fed to the process.The most natural approach is to introduce a scheme which feeds Feed B in ratio to Feed A but adjusts the ratio (which should always be close to one) using a feedback controller based on a reactor analysis of composition (such as mole fraction of Component B).This is shown in Fig. 7 Reactor analyser controllers 4c Since the recycle is liquid-only, there are no additional vapour inventory considerations across the process recycle 4d There are no additional temperature or quality control considerations across the process recycle.One possible concern with this scheme is that there is a closed loop of controlled inventories, comprising the reactor level, the distillation column reflux drum and the recycle stream.Such a closed loop can in principle suffer from the snowball effect.Whilst the adjustment of conversion in the reactor should ensure that neither Feed A nor Feed B can accumulate and limit the extent of this, it will depend on the performance of the various control loops.The chemical analysis control of the reactor is likely to be slow compared with the level controllers, which might still allow the snowball effect 5 Having identified a potentially viable control scheme for the overall process, dynamic simulation can now focus on resolving the remaining key questions 1.Which is the more effective option for controlling the reactor conversion (analysis of Feed A in the reactor), adjusting level or adjusting temperature?Fig. 7 shows temperature adjustment 2. Which is the more effective option for controlling the distillation separation, adjusting reflux flow or reboiler duty?Fig. 7 shows reboiler duty adjustment 3. How should the inventory controllers in the closed loop be tuned to avoid a problematic snowball effect?Dynamic simulation might also be used to determine controller tuning more generally and evaluate how effective the controls are against potential disturbances neither the feed flowrate nor the product flowrate can be controlled directly, but is implicitly fixed by the feed rate to the distillation column.A slow acting controller, manipulating this feed to achieve the desired long-term feed or product rate, could be used in conjunction with additional intermediate storage downstream to dampen out differences between the required flowrates and those achieved by the process control system.

Reflections on Application of Synthesis Approach
The examples above highlight several observations: 1.The approach of determining where the flowrate through the process is fixed and then working progressively through the process in the appropriate direction generally gives relatively few options for control structures.This makes it a relatively straightforward procedure to follow in order to generate an overall process control scheme.2. Considering the process nodes in a logical sequence ensures that potential conflicts (as found in the Stephanopoulos approach) are avoided.Once the flow of a stream linking nodes has been fixed in one node, it is simply not considered a candidate manipulated variable in any others.3. The step involving the whole of the recycle loop is analysed in a relatively simple additional check when recycles exist.It should be noted, however, that the approach of treating recycles as being manipulable only at their origins is not an "absolute" requirement.It is possible to modify a flowsheet to manipulate it as a result of measurements at either end.However, in most situations, manipulating recycles at their origin offers more logical control schemes.4. The same flowsheet, when controlled to achieve different purposes as in the two examples shown here, can give rise to markedly different control schemes.It is notable that the scheme for a fixed feed rate requires a controller which can vary the reaction rate (either by adjusting reactor temperature or level), whereas the scheme for a fixed product rate does not, since the natural variation in reactor composition achieves the necessary variation in reaction rate. 5. Schemes analogous to Fig. 7, where a main feed is fixed and other feeds are controlled on demand, are relatively common.The main challenge is ensuring that the analyser controllers are sufficiently reliable and act fast enough to avoid a snowball effect in the recycle.6. Schemes analogous to Fig. 8, are relatively rarely used, at least where a distillation column provides the separa-tion.This may reflect the preference for "fixed feed" control designs in chemical processes.7.This approach, by leading to a relatively small number of candidate control structures, enables a user to identify a correspondingly small number of dynamic simulations to perform in order to make the final control scheme design, including the tuning of the controls.

Process Dynamics
Of course, ensuring that the material balance and inventory control for the process can in principle be maintained does not remove the need to study the process dynamics.This is the final step in the above procedure.Indeed, the main benefit of the feed ratio scheme in Figs. 7, 8, and 9 lies in the dynamics of the control response.It ensures that the controls work with the natural requirements of the process, for example, that the two feeds are continuously supplied in proportion rather than allowing the reactor to become deficient or oversupplied in one and then using feedback to adjust retrospectively.Likewise, it may be useful to design controls that adjust the steam to the distillation column reboiler, or the reflux flowrate, in ratio to the column feed rate so that these variables respond in a timely fashion to process changes rather than solely by feedback.Control schemes which adopt this approach are generally more robust and work effectively even with relatively limited attention to the tuning of their feedback controllers.
Even when a process can in principle be self-regulating, the controller tuning is still important.If level controllers (other than for reactors) are tuned aggressively  Following the same logic as for the "fixed feed" case, it is desirable to ensure that the two feeds are maintained in ratio to each other and that the ratio is adjusted in order to ensure that the feed rates of Feeds A and B are precisely matched.The simplest way to achieve this is to use a level controller to manipulate the feed flowrate of Feed A, manipulate the feed rate of Feed B in ratio to the feed flowrate of Component A and adjust the ratio by composition analysis so as to achieve a target composition in the reactor 3c The vapour mass balance is achieved by using a suitable pressure control Reactor pressure controller 3d The reactor temperature is controlled by manipulating steam flow to the reactor jacket Reactor temperature controller

Whole process 4a
Considering the reactor, heat exchanger, distillation column and recycle as a single entity, it can be seen that the reactor level control delivers an overall process mass balance by manipulating the feeds into the process 4b Similarly, the reactor composition control ensures that Feeds A and B are fed in the required proportions to deliver a mass balance of both.In this case, the variation in the outlet from the reactor will cause a change in the reactor composition, which automatically adjusts the composition to match the reaction rate with the removal of Component C

Reactor analyser controller 4c
Since the recycle is liquid-only, there are no additional vapour inventory considerations across the process with recycle 4d There are no additional temperature or quality control considerations across the process with recycle so that levels are relatively invariant, the recycle will increase rapidly, and the system will have very little capability to absorb disturbances in feed flowrate or reaction rate.However, if they are too slack, there is a danger that at least one level will exceed its design limits in the event of a disturbance (such as a temporary loss of feed).The aim of the controller tuning will normally be to provide a compromise between these extremes, making effective use of the available inventory in a process to absorb disturbances, whilst remaining within process limits.If no suitable compromise can be found, it may indicate that additional inventory is needed.Whilst suitable controller tuning can often be estimated relatively easily by experienced engineers, dynamic simulation either for parts of the process or the whole process can be used to evaluate the robustness of alternative schemes and tuning selections.Where no acceptable tuning can be found, it may imply that there is insufficient process inventory to accommodate the disturbances envisaged.

Conclusions
The synthesis of control systems for overall processes is a key activity in process design.Yet, whilst a number of automated approaches have been explored academically, in practice systems are usually synthesised intuitively using experience, with dynamic simulation software being typically used to validate designs for more complex situations.Teaching of process control at the undergraduate level remains largely focused on theoretical aspects of process dynamics, particularly system stability, with typically little guidance on synthesis.
An approach is presented in this paper for the synthesis of overall process control systems which is simple, practical and appropriate for use at the undergraduate teaching level.Step Controllers 5 Dynamic simulation can now be focused on determining which is the more effective option for controlling the distillation separation, either adjusting reflux flowrate or reboiler duty.It may also be used to determine controller tuning and evaluate how effective the controls are against potential disturbances.There could be concerns relating to the control of the distillation feed from level control of the bottoms, since this features a potentially significant time lag (depending on the number of trays and the type of column internals in the lower section of the column).It may be necessary or desirable to increase the capacity of the column sump to ensure that there is sufficient capacity to allow this level controller to work well despite the time lag It focuses on the purpose of the process and presents a series of steps to be applied in a prescribed order.The approach avoids many potential problems by identifying which process parameters can be manipulated to achieve the intended process mass balance and designing the control structure accordingly.
Processes with recycles are vulnerable to the snowball effect, which usually occurs due to the inability of a process to achieve a mass balance.The approach defined here avoids the effect by focusing on the need to establish a means by which each component and phase is mass balanced.In many cases, this will involve the inclusion of a flowrate controller somewhere in a recycle loop (Luyben 1994, Luyben et al. 1998), but other means of ensuring a mass balance, both of the individual operations and the overall process exist, as shown in the two examples here.
Following the synthesis of one or more candidate control structures, dynamic simulation of the whole process can be used to select the preferred structure, tune the controller settings, check the stability and response of the process to disturbances and evolve the design to ensure that it achieves the overall process control objectives in a stable and optimal way (Luyben 2014).
Achieving and maintaining the material balance are the main purposes of the majority of controllers in most processes.Without robust delivery of material balance control, higher level control objectives (such as quality controls) are unlikely to be met reliably.Undergraduate courses in process control for chemical engineers should therefore give a greater emphasis to the role of material balances and inventory control as the foundation of developing the control system design.

Fig
Fig. 1 A simple process with reaction, separation and recycle

Fig
Fig. 2 An overall control system for the simple process

Fig. 3
Fig.3Placing a flowrate controller on the reactor effluent in the recycle loop can avoid the snowball effect and maintain the inventory of the Feed A

Fig. 4
Fig.4Controlling the combined flowrate to the reactor within the recycle loop can also avoid the snowball effect and maintains the inventory of the Feed A

Fig
Fig. 5 Direction of liquid inventory control in relation to flowrate control

Fig. 6
Fig.6The process flow diagram for reaction of two feeds

Fig
Fig.8Control system with a fixed product flowrate

Fig. 9
Fig.9An alternative control system that does not allow the feed or product flowrate to be fixed directly

Table 1
Application of the synthesis procedure to the fixed feed case

Table 2
Application of the synthesis procedure to the fixed product case Again, the process flow diagram in Fig.6is shown decomposed into 3 process nodes: the reactor, cooler and distillation nodes.This time the flowrate is fixed by the product flowrate from the distillation node.The procedure starts from the distillation and moves backwards upstream Distillation column 3aSince the amount of Product C is fixed, in principle either the feed to the column or the overhead liquid product could be manipulated to achieve a mass balance 3bSince the feed composition entering the column is not being controlled, and the column is assumed to perform an effective separation of Components A and B from Component C, the inventory of Component C (the column sump level) can only be controlled in the column by manipulating the feed flow to the column.The inventory of Components A and B (represented by the reflux drum level) must be controlled by manipulating the overhead product flow (which forms the process recycle)