Model Predictive Control and the Future of Process Control

1 Motivation for improvement of process control

Chemical process industries will soon be facing a significant obstacle. They have to recognise that significant development and progress in their finances is imperative to engage capital investors. A slow decrease in the productivity of financed capital over approximately the past forty years has created an issue for chemical process industries. As a result, the financial health of chemical process industries has made it increasingly difficult to compete with booming industries such as the Information and Communication Technology (ICT) sector.

The consumer electronics and automotive industries financial position two decades ago is comparable to the chemical process industry’s current position. The former sector’s financial position rapidly declined despite restructuring to minimise expenditure. However, the sectors that survived the economic deterioration and are currently flourishing did so by revamping their operations to a supply-driven approach. The industries that failed to do this did not survive. (Backx et al., 2000).

2 Analysis of problems faced by industry

The solution for the chemical process industries cannot match the consumer electronics and automotive industries due to the intricate nature of a market-driven approach in the processing industry. Moreover, chemical process industries face additional problems such as limitations placed on production sites with regards to the reduction of energy consumption, natural resources and raw materials as well as minimising the impact that the industry has on the environment (Backx et al., 2000). Due to these restrictions and limitations, the chemical process industry requires more advanced operational system support which is needed to optimise productivity.

The problems that the industry faces can be summarised as follows: the plant needs to function so that it meets operating constraints linked to the lifetime of the plant as well as meeting safety and ecological constraints. Additionally, the plant needs to perform such that the plant economics are always satisfied. Furthermore, the plant needs to meet supply chain deadlines to optimise its performance and reputation. The plant needs to maximise capital productivity of the plant over its lifetime.

Chemical industries mainly operate production sites using a supply-driven approach. There is no direct link between true market demand and actual production. Products are manufactured in a pre-determined amount. Instead, production facilities should manufacture an amount of product that is directly proportional to the market demand or as close as realistically possible to the market demand.

Note that the total production costs will initially be high due to this new emphasis on flexibility. However, substantial investments will be necessary to adapt equipment and instrumentation to accommodate a more flexible approach. In the long run, companies will reap the rewards of the investment. They will benefit from the improved capital turnaround, improved margins, the capability to deliver to product requirements in the supply chain and the ability to satisfy fluctuating volumes of product that are required on demand (Backx et al., 2000).

3 Process control background

Three important types of variables exist in process control: Controlled Variables (CVs), Manipulated Variables (MVs) and Disturbance Variables (DVs). The specification of these parameters is essential when outlining a control strategy. The choice for which variables is controlled, manipulated or a disturbance is based on the control objectives, controller background and experience as well as information about the process (Seborg et al., 2011: 8 – 10).

3.1 Controlled variables

These are variables that are controlled. The specified value of a controlled variable is called a set point. Controlled variables tend to be the output of processes mainly.

3.2 Manipulated variables

These are the process variables which can be modified to keep the controlled variables near the set point. Examples of the most common type of manipulated variables are flow rates. Most manipulated variables are inputs to processes.

3.3 Disturbance variables

These are process variables that influence the controlled variable but cannot be adjusted. Examples of disturbance variables include conditions that affect the operating environment of the process, such as the ambient temperature or feed characteristics. Some disturbance variables cannot be measured online.

3.4 Feedback control

Feedback control is a control strategy where the controlled variable is measured, and that quantity is utilised to modify the manipulated variable. In feedback control, the disturbance variable is not measured. Two types of feedback exist, negative feedback and positive feedback.

Negative feedback refers to scenarios where rectification occurs by the controllers to ensure the controlled variable returns back to the set point. In the case of positive feedback, the controller exacerbates the situation by forcing the controller variable away from the set point.

A key point of feedback control is that corrective action occurs irrespective of the cause of the disturbance. The capability of this control strategy to handle disturbances despite their undetermined cause is a big reason why feedback control is an important process control strategy. However, feedback control has an important drawback in that corrective action only occurs after the disturbance has unsettled the process and the controlled variable has diverged away from the setpoint (Mokhatab & Poe, 2012: 473 – 509).

3.5  Feedforward control

In feedforward control, the key characteristic is that the disturbance variable and not the controlled variable is quantified by measuring devices. This provides the advantage that corrective action is taken before the controlled variable strays from the set point. In principle, the corrective action should counteract any consequences that the disturbance variable would have on the process. However, in reality, this will not be perfect, and instead, feedforward control will minimise the effect of the measured disturbances instead of eliminating them.

Feedforward control has three main drawbacks:

1. The disturbance variable has to be measured or accurately estimated.
2. A process model has to be determined.
3. Unmeasured disturbances are not considered, and therefore no corrective action is taken for them. In industry, it is not cost-effective to measure every disturbance possible.

Consequently, some industrial processes make use of an integrated feedforward-feedback control strategy where feedback control allows for corrective action against unmeasured disturbances and feedforward control works to minimise measured disturbances to prevent the controlled variable from diverging away from the setpoint (Mokhatab & Poe, 2012: 473 – 509).

4 Ranking of process control operations

The main aim of process control as outlined below, is to sustain a process at the appropriate operating conditions whilst upholding safety, efficiency and quality standards. This hierarchy outlined below forms the backbone of determining a control strategy discussed later in the article (Seborg et al., 2011: 8 – 10).

It is not only vital to ensure that the controlled variables are maintained at the specified set points; other essential objectives need to be met in the hierarchy expressed below. The time scale is also depicted. The higher the activity is on the scale, the less often it needs to be conducted.

Figure 1: Ranking of process control operations (Seborg et al., 2011: 8).

Measurement and Actuation
Measurement instruments and actuation devices measure variables and action any control decisions. Examples of these instruments and devices include sensors, control valves and digital transmitters.

This level is essential in verifying the safety of the process as well as mitigating any hazards. It also ensures that the process operates sustainably and does not breach any environmental and safety regulations. Within the level, several layers exist including alarm management, instrumental safety systems and procedures for emergency shutdowns. The safety equipment and instruments must function separately from the day-to-day instrumentation and equipment used for control. Various methods, including sensor validation techniques, can be implemented to verify that the sensors operate up to standard.

Optimal operation of a plant needs process variables to operate within optimal ranges or at specified set points. Variables such as flow rates, compositions, temperatures and pressures can all be measured to maintain optimal process safety and operation. Therefore, regulatory control is employed by applying feedback and feedforward techniques. In more complex processes, advanced control techniques can be implemented, and advancements in technology have resulted in increased attention in monitory control system performance. Advanced control techniques such as model predictive control may be necessary depending on the safety, environmental and economic repercussions.

Numerous issues that are prevalent in process control arise from two primary sources:

1. Notable interactions between main process variables.
2. Upper and lower limit constraints that limit manipulated and controlled variables.

The system should be capable of operating close to the inequality constraints set out by the controller. For example, in the chemical process industry, the optimal operating conditions can occur at the upper or lower boundary in a range of values that the control equipment should be able to handle. In these scenarios, the setpoint is not the constraint number. This is because a process disturbance could drive the value away from the specified limit. As a result, the setpoint should be selected carefully, away from the boundary limits. It should be formulated from the capability of the control system to withstand the influence of disturbances. Basic control techniques of regulatory control, outlined above, may not be sufficient for complex control scenarios that have the potential to result in consequential circumstances and inequality constraints. In these scenarios, advanced control technique should be looked into, specifically model predictive control as it is capable of handle inequality constraints as well as process interaction.

In the process design phase, optimal operating conditions are outlined. However, these values tend to differ when the manufacturing process commences. This is due to a variety of factors including disturbances, economic causes such as the price of raw materials and product prices as well as equipment sizes differing from the pre-determined design size due to equipment availability. As a result, it is advised to re-evaluate and recalculate the optimal conditions frequently to ensure that the process is at peak performance. These new optimal setpoints become the new controlled variables.

The real-time optimisation computations are determined from a combination of data from the steady-state model of the plant and economic data such as income expected from product price estimations and expenses. A common objective for plant optimisation is to minimise the operating expenses or maximise financial gain. Furthermore, these real-time optimisation evaluations can be calculated for a remote process unit or on a plantwide scale.

Data reconciliation is another activity that is essential in the real-time optimisation phase of control activities. It is imperative to ensure that steady-state mass and energy balances are fulfilled.

The highest rank in process control activities relates to planning and scheduling exercises on a plantwide scale. If the plant production is continuous, the production rates of outputs of single units and the entire plant should be monitored and evaluated on the storage space available, equipment size restrictions and sales forecasts.

For batch and semi-batch production processes, the control issues are similar to the ones mentioned above. Still, planning and scheduling activities of the supply chain should be frequently evaluated. This makes the optimisation of the plant more challenging.

5 Control System Design Overview

Typically, control system design and the design of the process have been two separate and distinct engineering entities in the creation of a new process. Therefore, the typical approach is that the control system design does not commence until the plant design has been initiated, and the main equipment has been commissioned. This method has significant disadvantages as the plant design influences the process dynamics. The consequences of this approach are that the process may become unmanageable and turbulent despite the design appearing acceptable when operating at steady-state (Seborg et al., 2011:10 – 12).

An improved, alternative approach is to contemplate and appraise the dynamics and concerns in the foundation stages of the process design.

There are two typical methods to go about the design of the control system:

1. Traditional Approach.

The control strategy and the hardware for the control system are determined based on information about the process, experience and intuition. Once the control system is installed, the controller settings are manipulated.

2. Model-Based Approach.

A dynamic model of the plant is first created, and this provides several advantages:

1. It can be utilised as the foundation for model-based controller design methods.
2. The dynamic model can be introduced into the control law, for example, in model predictive control.
3. The model can be used when simulating the process using computer software to assess various other control strategies to establish precursory parameters.

The ideology that a dynamic model of the process should be designed initially in complex processes is recommended. This helps ensure that the control system is meticulously designed. However, for more basic process control issues, the controller requirements are more elementary, and a model is unnecessary. For complex systems, a process model is essential in the comprehension of the design to be able to interpret the process and any upsets that may occur (Seborg et al., 2011:10 – 12).

The procedure with regards to the design and installation of the model-based approach is outlined in the figure below.

Figure 2: Main steps in the implementation of a control system using the model-based approach (Seborg et al., 2011 ).

6 Model Predictive Control

Model predictive control, as mentioned above, is an advanced control technique for complex multivariable control problems. It is a popular and widely used control strategy in the chemical process industry in the control of large-scale industries. The advantages that model predictive control provides over classic control such as feedback and feedforward is that it can optimally drive the process whilst taking into account the static and dynamic interactions between the inputs and outputs as well as any disturbances to the system (Huyck, 2013). Additionally, the control calculations can be interrelated with the computation of optimal set points. Furthermore, it considers multiple inputs and outputs concurrently and considers any constraints placed on the system. Lastly, when correct model predictions are made, these can alert the control room operators to any possible complications shortly (Seborg et al. 2011).

The success of model predictive control, as well as the numerous benefits it provides, are highly dependant on the accuracy of the model and the inaccuracy of the model can make the situation worse. This can result in economic as well as safety and environmental implications.

The aims of model predictive control are outlined below (Qin & Badgwell, 2003):

1. Ensure that the input and output variables remain within the boundary set-points.
2. Direct some controlled variables to the optimal set point and keep other controlled variables within pre-determined values.
3. Minimise unwarranted fluctuations of the manipulated variables.
4. Manage as many variables in the process as feasible where devices such as sensors and actuators are not present.

Figure 3: Block diagram of model predictive control (Seborg et al., 2011: 415)

The above figure illustrates a block diagram of model predictive control. The current output variables are determined from a process model. Residuals are the remaining balance between the actual output and the predicted output. This value becomes the feedback signal to the input of the Prediction block. The predicted outputs are used as the input to the set-point calculation and control calculation. The upper and lower boundaries for the input and output variables are considered in the computation. The model works in conjunction with the process and, as a result, the residuals are the feedback signal.

Figure 4: The idea behind Model Predictive Control (Seborg et al., 2011:415).

Figure 4 above illustrates the concept behind model predictive control, showing the output as the controlled variable(s) as well as the sampling points and control actions. The setpoint, or also commonly referred to as a target, can be identified in the above graph. It is determined from an objective function which and usually is linear but can also be quadratic.

The standard aims of an objective function are mainly economic optimisation. The objective function comprises of enhancing the rate of production and profit whilst minimising the expenditure.

The setpoint varies due to fluctuating circumstances regarding the sensors, devices, equipment as well as conditions including economic changes such as expenses. Environmental conditions may also contribute to fluctuating set points depending on the type of process. Model predictive control is unique in comparison to other types of advanced control methodologies in that the setpoints are computed every time the control calculations are determined.

Model predictive control computations are determined on present measurements and the predictions of future values of the controlled variables. The calculations direct the progression of control moves to achieve the anticipated response towards the set-point optimally as well as to minimise the movement of any control valves to maximise the longevity of the valves (Seborg et al., 2011:415 – 416).

Figure 5: Flow diagram for model predictive control calculations (Seborg et al., 2011: 423 – 424).

The first step in the model predictive control computation flow diagram depicted above is that the controller needs to acquire process data from the regulatory control system that is consolidated into the process. After that, the second step produces predictions that are computed using the process model and the new process data figures from step 1.

Before every control move, in the third step, it is imperative to decide which outputs or controlled variables, inputs or manipulated variables and disturbances are on hand for the model predictive control calculations. Step 3 closely relates to step 4; every input value has a similar consequence to both output values and, as a result, large input movements are necessary to manipulate these outputs separately. Therefore, it is essential to examine the model to investigate whether ill-conditioning occurs by determining the condition number of the process gain matrix for the present control model. The setpoint or target is then calculated from the optimisation function whilst considering inequality constraints to ensure health and safety standards are maintained. The control calculation is processed, and the final step is executing the computer control action, which is typically in the form of setpoints for regulatory control in control valves.

6.1 Model predictive control with inequality constraints

Inequality constraints placed on manipulated and controlled variables are an essential trait in model predictive control. The constraints on these variables were the main reason for the creation and growth of model predictive control. Constraints on manipulated variables or inputs are due to physical restrictions on plant equipment, for example, heat exchangers, reactors and valves. For example, the input flow rate could have a minimum boundary limit of 0 and maximum boundary range determined by a pump, valve and piping attributes (Seborg et al., 2011: 426).

6.2 Range Control

An attribute of a model predictive control application is that many controlled variables do not have targets. Instead, the aim is to keep the controlled variable within upper and lower limits; this technique is termed range control or zone control. It allows for more degrees of freedom to be created in control computations. Additionally, a large variety of controlled variables do not require a specific set point, for example, the volume in a surge tank. Therefore, in model predictive control, range control is the rule. Target values are only defined for controlled variables that need to be close to a specified amount in scenarios such as quality control or health and safety situations such as in maintaining the composition, pH or temperature.

Controlled variable constraints are an essential part of the plant operating plan. For example, a typical objective in distillation columns is to have a large output flow rate whilst meeting quality control standards and minimising weeping and flooding. In these scenarios, it is crucial to determine what hard constraints and soft constraints are in the plant operating strategy. A hard constraint cannot be breached at all. On the other hand, soft constraints can be infringed upon at the cost of adjusting the objective function towards a less desirable outcome. This technique permits some constraint infringements to be allowed but only for brief intervals (Seborg et al., 2011: 427).

6.3 Setpoint calculations

As mentioned in the model predictive flow diagram, setpoint computations are determined at the beginning of every control loop. The setpoint is obtained via two steps. Firstly, the optimal set point for the control computation is ascertained. After that, the first control move is executed. The setpoints are determined via objective functions that optimise the economic performance of the plant either on a single unit or plantwide scale. The objective function obtained from the steady-state model of the plant that features both the controlled variables and manipulated variables. The set-point computations are redone at every sampling point as the constraints vary. As a result, of the frequent sampling, the objective functions should be solved rapidly and adeptly (Seborg et al., 2011: 427).

6.4 Implementation of Model Predictive Control

When deciding whether or not to introduce model predictive control to a process, a cost/benefit analysis is beneficial and is recommended that this be carried out before the project proceeds.

The steps below outline the course of action to introduce model predictive control to a process (Hokanson and Gerstle, 1992; Qin and Badgwell, 2003):

1. Initial controller design
2. Pre-test activity
3. Plant tests
4. Model development
5. Control system design and simulation
6. Operator interface design and operator training
7. Installation and commissioning
8. Measuring results and monitoring performance

The first phase in the design process is to identify the input or manipulated variables, output or controlled variables and any disturbances. These decisions influence how the model predictive controller is organised and should be established on process information as well as the control aims. In practice, the model should have approximately 40 controlled variables and approximately 20 manipulated variables. These introductory decisions can be re-evaluated in phase 5 of the design process. The manipulated variable and disturbance variables should be selected in a discerning manner and are manipulated during phase 3 of the design process, which is the plant test phase.

During the second phase of the design process, all instrumentation in the plant should be inspected to ascertain whether they function accurately and precisely. Once examining the instrumentation and which variables are measured, an analysis can be done to ensure that instrumentation is situated in the correct locations to measure all the relevant variables for the model.

Phase 2 also requires trials to approximate the steady-state gains and settling times for every input and output pair. This data is utilised to programme phase 3 plantwide trials. The Distributed Control System (DCS) is a system of controllers, sensors and relevant computer software that is dispersed across the plant. Every part of the DCS provides a specific purpose, for example, data storage, data acquisition and process control. These individual components liaise with a centralised computer through the plant’s local area network which is also termed a control network. The DCS makes automatic decisions derived from production patterns which it obtains instantaneously from plant data. The DCS can make changes to each of a plant’s numerous interacting unit operations. (Control Station, 2018). Hence, all components of the DCS should be inspected to guarantee that the entire system functions well. A malfunctioning DCS will result in a futile model predictive control system.

Pre-testing involves first changing the manipulated variable by introducing small step changes and after that stepping up the disturbance variable. By introducing step changes, this allows the gain and settling times to be estimated and therefore tuning the controllers accordingly. It is essential to benchmark the behaviour of the current control system to allow for comparison when the MPC system is introduced. Furthermore, a  benchmark of the economic performance of the DCS and model predictive control system should be done.

Plant testing is a lengthy process; the time for each plant trial is dependant on the settling times of the controlled variables and the number of manipulated variables and disturbance variables. The process involves varying a manipulated variable by introducing step changes with varying durations. Plant test trials should be executed in a similar method as those outlined for the pre-test trials in phase 2.

The dynamic model is obtained by combining the plant trial data and choosing a model structure as well as approximating the model parameters. It is also imperative that some test data be removed when developing the model. Any data that results in plant upsets or abnormal situations should be deleted by a controller observing the data trends during the trial. Examples of situations that are out of the ordinary include control valve saturation or when a  DCS control loop has been run in the manual mode.

In this phase, the preliminary design from phase 1 is analysed and amended accordingly. The model predictive control design parameters are determined. Examples of parameters that need to be finalised are the control and prediction horizon and the sampling period. The system is tested by simulating the closed-loop form using the specified process modal and a broad variety of process situations to appraise the system performance. Any parameters that need modifications are altered to secure a robust and superior model that can adapt to a wide variety of operating conditions.

Plant operators play an essential role in the process industry, and the model predictive control graphical user interface must be easy to use and understand. Operator training should be conducted as the theory behind model predictive control is different from regulatory control. In a basic control system, a single manipulated variable is adjusted per the effect it has on a single controlled variable. On the other hand, in model predictive control, every manipulated variable relies on all the controlled variables. As a result, comprehending why the model predictive control system behaves in the way it does, including in abnormal situations can be challenging to become accustomed to for operators and engineers who are new to the system.

Once the model predictive control system has been installed, it is tested in a setting termed “prediction mode”. In this setting, the DCS remains on and controls the plant, and the actual measurements are set alongside the model predictions for comparison.

The computed model predictive control moves are appraised to determine if they are sensible. Lastly,  the model predictive control results are reviewed during closed-loop operations with the computed control moves added as a set point to the DCS control loops. The model predictive control design parameters are tuned if required. Continuous assessment and adjustments may be necessary during the commissioning phase that may take a long time.

Phase 8: Measuring Results and Monitoring Performance

Assessing the model predictive control system is not simple and monitoring strategies for it is not readily available. Nonetheless, simple statistical data, averages and standard deviations for both measured variables and computed data, for example, control flaws and model residuals may be available. Other important information to have on hand is the duration that a manipulated variable is saturated, or a constraint is breached should be presented as a percentage of the total duration the model predictive control system operates. Another factor used to measure the performance of the system is whether or not the system is capable of coping with variables being close to the set point or upper and lower boundary of the limiting constraints. Performance benchmarks should be made before and after the system is introduced.

The system should be continually evaluated to ascertain it maintains a good standard, does not deteriorate due to faulty instrumentation and can still cope with disturbances. If the degradation of the system does occur, it may be necessary to retune the controller.

7 Final remarks

Despite oil refining and petrochemical industries using model predictive control as the control method of choice, other chemical process industries are forced to adapt and improve the way they operate due to varying market circumstances. Process operations need to be related much more closely to market demand to enhance capital productivity. Ultimately, a consistent model is essential in model predictive control to optimise the performance of the plant, which directly impacts the capital productivity, plant economics and can yield a more sustainable process.

8 References

Backx, T., Bosgra, O. and Marquardt, W. (2000), Integration of Model

Predictive Control and Optimisation of Processes, IFAC Symposium “Advanced Control of Chemical Processes“, ADCHEM 2000, Pisa, Italy, 249-260.

Control Station, (2018), What is a Distributed Control System, https://controlstation.com/what-is-a-distributed-control-system/, [2020, November 19]

Huyck, B., (2013), “Model Predictive Control in the Chemical Process Industry hosted by Industrial Controllers, ” Dissertation for Faculty of Engineering Science Kasteelpark Arenberg 10, Heverlee, Belgium.

Mokhatab, S. and Poe, W.A. (2012), Handbook of Natural Gas Transmission and Processing, 2^nd Edition, Elsevier.

Qin, S.J. and Badgwell, T.A. (2003), “A survey of industrial model predictive control technology, Control Engineering Practice, 11(7)”.

Seborg, D.E., Edgar, T.F., Mellicham, D.A. and Doyle, F.J. (2011), Process Dynamics and Control, John Wiley & Sons.