This section of the paper will present a comprehensive summary of the subject under study, presenting details information on the Model Predictive Control System, Shell Control Problem, designing of the control system and the relevant parameters of the subject of study.

Incorporating an automated control strategy for anticipating and/or predicting into any process system is logical and systematic; hence Model Predictive Control (MPC) has undergone notable development in the course of the past twenty years, both inside the industry and in the research control group. Predictive control can be described as an approach rather than a specific algorithm, as its utilization is based upon interpreting an approach to define the algorithm that best suits the user requirements.

Before getting into detail, it is important to develop an understanding of why prediction is important. Prediction provides pivotal information on how the system is expected to respond when exposed to certain conditions. Humans have a natural prediction and response system which supports our day to day requirements, and in some way, PID can be deconstructed as a derivation of human technique for obtaining control of simple systems. A predictive control incorporates both measurement as well as decision made on the measurement via introducing the feedback loop. Therefore in order to automate predictions through measurement of the available data, a model is required.

As an example, a driver anticipates future demands, targets, distances and speeds of other vehicles/pedestrians etc. Therefore the driver anticipates / predicts, and responds with an effective control strategies in accordance with the given/assessed data in order to drive safely. This effective prediction provides us with the most desirable future outcome, and thus seems a logical concept. This logical concept can therefore be developed into automated strategies incorporating constraints explicitly enabling optimum constrained performances.

Model Predictive Control acts as the most general method for representing the process control problem in the time space. The primary concepts of the MPC are;

- Prediction
- Receding Horizon
- Modelling
- Performance Index
- Degree of freedom
- Constrain handling
- Multivariable

The integration and/or derivation of these primary components allows stochastic control, optimal control, multivariable control, dead time procedures control and references in the future. Due to its use of the finite control horizon, MPC offers another advantage of being able to handle constraints and non-linear processes in general.

Although it is true that MPC is considered to provide robust control in most common applications, proofs regarding its robustness and stability have been hard to collect due to its utilization of the finite horizon. This has proved to be a disadvantage for a more extensive spread of MPC with-in the control research group. There are some new results which are very promising about the expansion of MPC with-in this community in a brief span of time. On the contrary, despite the fact that various applications have been accounted for in both industry and research centers, MPC has not yet achieved its expected industrial application, as it still being developed for complex dynamic processes. One explanation behind this is that its usage obliges some numerical complexities, which are not an issue for the research control group, but which are a disadvantage with respect to the utilization of the technique by control engineers during practice.

The term Model Predictive Control does not assign a particular control method, rather a sufficient scope of control strategies which make express utilization of the process model to acquire the control signal by reducing an objective function. As a result of these methods of design, controllers are obtained which have basically the identical structure and which present satisfactory degrees of freedom. The ideas which show up in greater or lesser degree in the predictive control family are essentially:

- Explicit mode utilization to anticipate the output of the process at a time in the future (horizon)
- Estimation of a control arrangement to minimize an objective function, and
- Receding strategy, which ensure that at every moment the horizon is displaced in the future

The different MPC calculations (e.g. Receding Horizon Predictive Control (RHPC)) just vary from each other in the model used for process representation and minimization of noise and cost. This sort of control is of an open nature, in which numerous works have been produced and are generally welcomed by the industry and the academic world.

Numerous successful applications of predictive control currently exist, which are not only confined to the process industry, as its various applications to control different mechanical/other processes have succeeded in the recent decades. These include processes such as robot-engineering (Ortega and Camacho, 1996), clinical anesthesia (Linkers and Mahfonf, 1994) and many others. Its utilization in cement manufacturing, robot arms and drying towers are discussed in detail by Clarke in 1988, whereas potential improvements in the PVC plants, distillation columns, servos or steam generators have been outlined in the research conducted by Richalet in 1993.

The great execution that these applications display, demonstrates the potential of the MPC to accomplish exceedingly effective control systems designed to work for long-time durations with barely any intervention required.

MPC offers a variety of advantages over the rest of the available methods, the most important of which are as follows:

- The staff with limited awareness of control is in particular attracted to this methodology, since the ideas are mainly intuitive and the tuning is also moderately simple.
- It can control a wide range of processes, ranging from the ones with moderately straightforward structure to more complex systems, incorporating those with long delays, continues and or with altering operational phase requirements
- It is easy to deal with the multi-variable case.
- Feed forward control is presented in a natural way to make up for measurable disturbances.
- It naturally recompense for dead times.
- Its augmentation to the treatment of constraints is reasonably straightforward, and these might be systematically included amid the design phase.
- The product is a controller which is a simple-to-execute control law.

However, it is important to highlight some of the disadvantages associated with the MPC. In spite of the fact that the application/utilization of control law is not difficult to implement and does not require performing many complex calculations, its formulation is more intricate than that of the conventional PID controllers. In the event that the process dynamic has no change, the formulation of the controller is possible in advance, but in the case of the adaptive control all the calculation must be completed at each testing time.

At the point when constraints are incorporated, the measure of processing needed is significantly higher. Despite the fact that this is not a key issue (considering the computing power available nowadays), it should always be under consideration that numerous industrial process control workstations are not in their perfect form of computing, data, and most importantly, that the majority of the accessible time at the process workstation must be utilized for tasks other than calculation on the control algorithm itself (recording, communication, alerts, and so on). Indeed, along these lines, the biggest disadvantage is the requirement for a proper model of the process to be accessible. Prior model knowledge is the base for the design algorithm, yet it is evident that the acquired benefits will be influenced by the differences existing between the real process and the model.

In the industry, MPC has established itself as being a sensible methodology for industrial control, despite the initial absence of theoretical results at some pivotal issues, for example in robustness and stability.

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In order to define the strategy of MPC, it is first important to highlight some of the basics of the MPC modelling. The simplest model to develop to provide accurate enough predictions is considered to be the best possible model, as excessive effort in improving the accuracy of the model may complicate the model with very little enhancement in efficiency. The MPC steady state simple models are objectively produced up to 80-100% accurate predictions with ability to capture the key dynamic changes during transients. It also important to note that the feedback’ normally corrects itself for small modelling errors.

The performance index can be defined as the accuracy to which the input trajectory behaves for a process in the automated predictive control strategy. The performance index is also designed to follow a simple set of conditions in order to obtain simple optimization. However for complex systems which require more measures of control and precision, the design of performance index becomes more demanding. High performance implies risk in terms ability to deal with uncertainly or robustness. The degree of freedom, which defined as complexity of input predictions, behaves in the same patter as performance index. The useful number of degree of freedom is associated with the prediction accuracy, and varying set-point or targets in a system requires higher number of degree of freedom. The simpler analogy is to define a model with a polynomial of first order, with data fit in a small domain. With low prediction horizon, it is not possible to compressively anticipate the outcomes of a process, which may lead to an ill-posed problem.

The predictive control has the ability to systematically embed constraints into the strategy development, as this is critical for obtaining effective and robust closed-loops behaviors. Embedding constraints, such as flow of water in process control, ensures that the integrated input strategies are optimized in accordance with operation set point and desired tuning requirements, incorporating a much more effective design as compared to a standard PI control.

All the controllers of the MPC family utilize the methodology which can be characterized by the following strategy, represented in the figure given as below;

The process model can be used to predict/anticipate the future values for a resolute horizon N (prediction-horizon) at each instant. These anticipated output values y (t+k | t) ^{1} for k equals to1 to N; depending upon the determined/know values up to the time t (past outputs and inputs) and also on the control signals in the future u (t+k | t), where k is between 0 and 1 less than N, which are the input values given/fed into the system of simulator to be calculated

By keeping the designed process closer to the reference trajectory w (t + k) through a determined criterion, the future control signal set is computed, which might be the set point itself or a close estimation. This determined criterion is usually in the form of a quadratic-function which outputs the error values between the predicted reference trajectory and the predicted output signal. The objective function incorporates the control effort under most circumstances. If the model is linear and the criterion is quadratic in nature, given that there are no constraints, an explicit result can be calculated, otherwise there is a need to use an iterative optimization method.

The process receives the control signal u(t | t) while the control signals being received after this time t are rejected, due to the fact that at the next sampling time y (t + 1) is known in advance and step 1 is now performed again with this new value, followed by the update of all the sequences. Hence the value of u (t + 1 | t + 1) is processed, which on a fundamental level will not be the same as the u(t + 1 | t) due to the new data access, utilizing the concept of receding horizon.

The fundamental basic structure of MPC can be demonstrated as in the figure presented below;

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The model is utilized to foresee the future outputs of the process/plant, depending on the past and current values and on the proposed ideal future control activities. This optimizations evaluates these activities considering the cost function, where the future tracking error is taken into account, and all the constraints. Hence the role of the process model in the controller is decisive. The model that is selected must have the capacity to capture the process dynamics to accurately predict the future values and also be easy to understand and implement. Since MPC is not a single method, rather a set of distinctive techniques, there can be numerous sorts of models which can effectively be utilized in different situations and conditions. The selection and designing of the model is based upon the user requirements.

A stand out amongst the most prevalent techniques used currently in the industry is the Truncated Impulse Response Model. This model is extremely easy to understand, as it just requires the calculation of the output when an impulse input excites the process. It is broadly acknowledged in industrial practice on the grounds that it is exceptionally intuitive and can likewise be utilized for multivariable processes; in spite of the fact that its primary disadvantages are the vast number of parameters required by it, and only the open-loop stable processes might be modelled along these lines. A similar model is the Step Response Model, derived when there is a step input.

Perhaps the State Space Model is more common in the academic research group, due to the simplicity of its derivation even for the multi-variable case. The state space description makes the robustness criteria and the stability expression much simpler. The Transfer Function Model is additionally utilized by the academic researchers and despite the fact that the controller derivation is more complex, it needs a lesser amount of parameters. It can handle dead time with much more ease compared to other models. Compared to state space, this model type is better understood in the industry, because a portion of the concepts utilized by its transfer function, for example, gains, time constants and dead time are generally utilized in industry. This description is common, to some degree, to both industry and academy.

Another major part of the MPC technique is the optimizer, which is the source of the control actions. In the event that a quadratic expression is obtained for the cost function, its minimum might be formulated as a linear function of past outputs, inputs and the future reference trajectory. In case of constraints such as inequality, the result must be calculated through the numerical algorithms which require more computations/simulations. The optimization problem complexity relies upon the amount of variables and the prediction horizons utilized. It generally ends up being a modest optimization problem which does not oblige complex computer codes being solved.

It is important to note that the measure of time required for the robust and constrained cases might be many times larger than the required for the unconstrained case, and the process bandwidth to which constrained MPC could be applied is considerably minimized.

Perceive that the MPC procedure is fundamentally the same as to the control system utilized when driving a car. The driver is aware of the coveted/perceived reference trajectory for a finite control horizon and by considering the attributes of the car. The driver selects/chooses one of the many control activities, such as brakes, accelerator, steering, in order follow the desired trajectory. Just the basic control actions are performed at every moment, and the method is repeated for the following control choice in a receding horizon style.

Recognize that when utilizing traditional control techniques, for example, PIDs, the past errors are the base for the future control actions. The analogy of driving a car, which was used in example earlier in this literature review, has also been carried out by one of the MPC vendor/designer know as SCAP (Martin and Rodellar, 1996), which states that the PID method for driving the car would be identical to driving it simply utilizing the mirror. This relationship is not completely reasonable with PIDs, in light of the fact that more data (the reference trajectory) is utilized by MPC. Recognize that if a future point in the reference trajectory that is desired has been utilized as the set-point for the PID, the contrasts between both control methods would not appear to be so abnormal.

The following section centers around those predictive control technologies that have considerable effect on the industry and are accessible in the commercial sector, also considering different topics such as short application summary and the constraints of the current technology. Despite the fact that there are organisations that limit the innovations created by them to their own usage only, the following companies might be viewed as illustrative of the current technology development of Model Predictive Control. Some of the names and acronyms of their products are: Adersa’s Hierarchical Constraint Control (HIECON) and Predictive Functional Control (PFC), AspenTech’s Dynamic Matrix Control (DMC), ABB’s 3d-MPC, Treiber Control’s Optimum Predictive Control (OPC) and many more. It must be noted that every product is not just the algorithm, but it also includes extra packages, normally plant test or identification packages.

There are a huge number of MPC-applications currently being applied in various industries. These application have previously reviewed by Qin and Badgwell in the late 20^{th} century. The petrochemical and chemical refining industry has been one of the oldest user of various application fields of MPC, as it enjoys a strong foundation in this field. Other considerable development territories incorporate pulp and paper, aerospace, food processing, and automotive enterprises. Different zones, for example, furnaces, gas, mining, utility, or mining likewise shows up in the report.

A few applications in the cement business or pulp production lines, especially in United Kingdom, have been discussed in detail by the research conducted in 1996 by Martin and Rodellar. In spite of the fact that MPC innovation have not yet profoundly established its usage into territories where there are strong process non-linearities and frequent operational condition changes, the amount of non-linear MPC applications is now considered to be increasing in number.

Research completed by Muske and Rawlings (1993) indicated that there are various limitations of the MPC technology when employed in dynamics processes of industries. The most significant limitations, as highlighted in this research includes the over-parameterized models; as most of the commercial methods utilize the impulse or step response model of the plant, which are known to be over-parameterized. For example, a process which is of first-order might be modelled by a transfer function utilizing just three parameters (time constant, gain) to depict the same dynamics. Moreover, these models cannot be employed for unstable processes. These issues could be overcome through the use of an auto-regressive parametric model.

The tuning process is another parameter that is not well characterized since the trade-off between closed loop behaviors and tuning parameters is by and large not clear. In the presence of constraints, tuning may considerably be more troublesome, and it is not simple to ensure closed-loop stability, even for the cases which are nominal. This is the reason why so much exertion must be directed towards prior simulations. The problem feasibility is one of the most difficult areas of MPC, and therefore much of the research is being conducted in this field of study.

Dynamic optimization suboptimality: there are many packages available that offer suboptimal solution to minimize the cost function with a specific end goal to accelerate the time for results. It could be acknowledged in rapid applications (tracking systems), where tackling the issue at each sampling time may not be possible, however, it is hard to support for process control applications unless it might be demonstrated that the suboptimal result is constantly practically optimal.

Despite the fact that model identification packages provides assessments of model uncertainty, only one of these packages (RMPCT) utilizes this data within the control design. The rest of the controllers might be tuned again to enhance robustness, despite the fact that the connection between robustness and performance is still unclear. Sensible supposition would be to consider that the output disturbance will stay steady in the future, better feedback would be conceivable if the disturbance could be measured with more precision.

An efficient investigation of robustness and stability properties of MPC is impractical in its original finite horizon formulation. The control law is mostly time-varying and it is not possible to represent it in the standard closed-loop form, particularly when there are constraints. Moreover, the results acquired by the researchers about robustness and stability are limited to small-scale processes (limited control horizons and state space) only.

The engineering is consistently advancing and the new technology will need to face new difficulties in open topics, for example, identification of model, unmeasured disturbance forecast and estimation, modelling error treatment, and nonlinear model predictive control uncertainty. Despite critical progression in control algorithms and process control hardware, most process control problems nowadays are dealt with through sequencing, logic and PID controllers. There are however a few indications of change. Dynamic matrix control and similar algorithms are utilized on a couple of hundred frameworks typically in supervisory loops with essential control still with PID controllers. Primary control loops have also started to be affected by advanced control. It can be roughly approximated that in excess of 100000 loops use adaptation and automatic tuning. Despite 100000 being a large number, this is still just a little portion of the total quantity of industrial feedback loops.

Advances in computer technology and information infrastructure, request from clients, control theory and challenging problems are the drivers behind this development. Recent announcements by the makers are great evidences that the new innovations are having a huge effect.

In 1986, the Shell Company first published their benchmark control problem in the First Shell Process Control Workshop (Prett and Morari, 1987). It gave a realistic and standard testing ground for the assessment of new control theories and techniques.

The heavy oil fractionator process of Shell is multi-variable and has many constraints, with large dead-times and strong interactions. There is no doubt that the Shell benchmark control problem is a complex problem that needs efficient algorithms and control architectures to perform its desired control outputs.

Receding-horizon control (RHC), or model predictive control (MPC), or moving-horizon control (MHC) is a prominent method that has been effectively utilized as a part of the control of different linear and non-linear dynamic frameworks. Shell developed the quadratic dynamic matrix control algorithm (QDMC) for their Shell benchmark control problem. The principle advantage of QDMC is that the constraints and targets connected with the control problem are implanted into the control algorithm, which needs small and hoc controller modifications. But the downside of QDMC is that it is computational needs are intensive, bringing about the need for on-line computation. This is the fundamental detriment of MPC and limits its use to moderately quick and/or vast processes with larger number of inputs (Clark and Mohtadi, 1987; Richalet, 1993).

In reality, there is a large number of complex high dimensional frameworks, in which the amount of constraints and variables is often as large as a few hundreds. Hence, it has become extremely critical to create a computationally efficient control algorithms and architectures with less burden of computations. Unfortunately, there are little references for this topic in open literature, however, influential research has been conducted in the last many decades, such as by Ricker and Lee, 1995, Xu, Xi, and Zhang, 1988, Zheng and Allgower, 1998, Katebi and Johnson, 1997, Van Antwerp and Braatz, 2000, and Zheng, 1999; to demonstrate the large scale nature of average industrial plants. This most likely is attributable to the natural troubles included in the complex computation for frameworks this large.

With the rapid and continues advancement of communication system and the field-bus engineering, control that is central in nature has not been an essential characteristic in applications and it is being slowly substituted by distributed control in large scale frameworks. Distributed control structure brings new prerequisites to the conventional control field and provides opportunity to solve new difficult control applications. In order to accommodate monetary issues and avoid degrading performance, it is a good idea to utilize a few economical microcomputers to replace an expensive high performance computer system within a control system. The advances in the fields of communication network and the field-bus technology has provided the opportunity for distributed control. A decentralized predictive control algorithm was proposed by Zheng and Allgower 1998 and Zheng 2000 who exhibited a one-stage estimation algorithm to decrease the amount of on-line computation by diminishing the amount of the choice variables. Van Antwerp and Braatz in the year 2000 created an iterative ellipsoid algorithm to enhance calculation of sub-optimal control moves in a short time interval. It ought to be brought up that these methodologies still work with a centralized computation arrangement, so they expand the computing load and thereby require high specification and expensive computers

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The Shell standard control problem was ﬁrst pub- lished by the company in 1986 in the First Shell Process Control Workshop (Prett & Morari, 1987), with the intention to provide a standard and realistic test bed for the evaluation of new control theories and technologies. It captures most of the relevant control issues while staying as realistic as possible. The full model of the process is given in the appendix, and can also be found in Prett and Morari (1987) and Prett, Garc!ıa and Morari (1990). The process is a multivariable (5-input, 7-output)

heavy oil fractionator, which is highly constrained, with very strong interactions and large dead times. The key elements of the Shell standard control problem are shown in Fig. 1. The problem is stated such that an inﬁnite number of scenarios can occur in controlling the unit. The process input/output relations are linearly modelled using a matrix of ﬁrst-order dead time transfer functions. Inputs u1; u2; and u3 can be used as manipulated variables to control the process, but are subject to saturation (70:5) and rate limit (70:05 per minute) actuator hard constraints, thus making the process non-linear. Inputs d1 and d2 are unmeasured but bounded disturbances entering the process, with jd1jp0:5 andjd2jp0:5: Furthermore, the process is subject to uncertainties in the gains of the model transfer functions. The main objective is to maintain process outputs y1 and y2 at speciﬁcation (0:070:005 in the steady state), while at the same time input u3 has to be minimised and output y7 has to be kept to values of at least 0:5 at all times. Furthermore, output y1 must be maintained within the maximum and minimum values of 0.5 and 0:5 at all times, and the unmeasured disturbances d1 and d2 have to be rejected even when the sensors of y1 and y2 fail. The closed-loop speed of response must be kept between 0.8 and 1.25 of the open-loop process bandwidth, and the fastest (minimum) permissible sample time is 1 min. It is apparent that the Shell standard control problem is an extremely diﬃcult problem which includes many possibly conﬂicting process requirements that are very diﬃcult to satisfy. A number of partial solutions to the problem have been proposed in the Second Shell Process Control Workshop (Prett et al., 1990) and it has been conjectured that a complete solution to the problem does not exist (Prett et al., 1990). In this work, the solution is also partial, but has the advantage that it achieves good results using a control strategy that is relatively simple and much easier to implement than most of the solutions available in the literature. Furthermore, it will be shown that the proposed approach is not limited to the Shell standard control problem and can be used in a wide range of real-world multivariable control problems.