Model predictive control algorithm is the heart of traditional advanced process control applications. It has been the decades now of its continuing industry implementations, bringing millions of dollars benefits to industries all over the world. However, the MPC applications had their peak in late 90s and early 00s when the major licensors were busy going all over the world and installing model predictive controllers to bring benefits to its clients as soon as possible. Today, existing applications are being revised, modernized and maintained, new applications are being installed on new units and more opportunities are being identified on less obvious locations and industries. Although, the root of all MPC algorithms known today were developed by quite small but highly skilled teams, lately, there are not that many licensors present on the market as the result of a quite significant merging process of proven MPC technologies. All those algorithms are today in the hands of corporations, mostly vendors of control systems and instrumentation.

But how did it all begin? To understand the present, let’s reveal some details from the past.

Early beginning

MPC was first implemented in industry – under various guises and names – long before a thorough understanding of its theoretical properties was available. Practitioners, mostly coming from the process side, had a more significant role in the development of MPC than the theorists. The theoretical explanations practically followed the practical applications installed on industrial units.
The development of MPC was, as many other things, conditioned by the development of the computers.
In the literature, the first use of computers to calculate an on-line economic optimal operating point for a process unit appears to have taken place in the late nineteen fifties. Åström and Wittenmark mention March 12, 1959 as the first day when a computer control system went online at a Texaco refinery in Port Arthur, Texas. It appears that computer control and on-line optimization were ideas which were developing together with the computers as they were becoming more powerful.

The principles of optimization concept can be found in the work of Kalman et al. in the early 1960s (Kalman, 1960a) and is known as a linear quadratic Gaussian controller (LQG) or Kalman filter. Control algorithm had integrated the concept of linear space and opened a vision for later algorithms. This algorithm had a large number of reported patents and a number of industrial applications. However, it did not reach a wider audience due to unresolved issues such as constraints, process nonlinearities, robustness. And the most important: the industrial community had no information about it or was not ready to accept new approach at that time.

First generation of MPC

However, this environment led to the development of a more general model based control methodology in which the dynamic optimization problem is solved on-line at each control execution. The most important influence had theories of state space and analysis of vectors and matrice system applied to control problems that were popular during 70s.
Also, with the computer development, control engineers started implementing more advanced regulations of single input single output systems,  such as based on feedback and feedforward type of control. Those kinds of advanced controls were being applied to solve more complex control problems such as heater controls and served as a solid ground to apply the same concept for multi-input multi-output systems.

During the end of seventies, practitioners of process control in the chemical industry capitalized on the increasing speed and storage capacity of computers, by expanding on-line optimization to process regulation through more frequent optimization.
Process inputs are computed so as to optimize future plant behavior over a time interval. This concept was presented by two independent teams during late 70s: IDCOM and DMC algorithms are the first generation of MPC as we know it today.

The first description of MPC control applications was presented by Richalet et al. in 1976 conference and later summarized in Automatica paper. They described their approach as model predictive heuristic control (MPHC) and the solution software IDCOM, an acronym for Identification and Command. In today’s context, the algorithm would be referred to as a linear MPC controller. They described the algorithm on the example of Fluid catalytic cracking unit main fractionator column and reported benefits of $150000/year.
In parallel, the other team of engineers at Shell Oil led by Cutler and Ramaker developed their own MPC technology with initial application of an unconstrained multivariable control algorithm which they named dynamic matrix control (DMC) on 1979 at the National AIChE meeting. Prett and Gillette (1980) described an application of DMC technology to FCCU reactor/regenerator control.

The initial IDCOM and DMC algorithms represent the first generation of MPC technology and had the enormous impact on industrial process control.

Next generation

During 80s MPC technology slowly started to prove the results to gain wider acceptance during 90s. During 80s, the algorithms had to be improved to be able to tackle larger and more complex problems of industry, especially in refining where they could gain the most benefits. Engineering teams continued the development of MPC algorithms and brought new implementations for improved handling. All groups were focusing how to improve handling of the constraints, fault tolerance, objective functions and degrees of freedom in their algorithms.
As the result of these improvements, the vendors presented upgraded technologies which were applied widely in industry during 90s:

• Setpoint presented improved IDCOM by the name IDCOM-M, which was later offered as SMCA (Single Multivariable Control Architecture),
• DMC group was separated from Shell Oil and developed improved DMC algorithm by the name of QDMC and was later bought by AspenTech,
• Shell Oil continued their work and developed SMOC (Shell Multivariable Optimizing Controller),
• Adersa presented nearly identical algorithm: HIECON (Hierarchical constraint control),
• Profimatics had their PCT algorithm, and
• Honeywell with RMPC.

Those are the algorithm which represent MPC technology generation of the 90s.

Merging and acquisitions during 90's

The late 90's were characteristic of MPC reaching its peak. In parallel with the market growth, the competition between the vendors was also reaching its peak during late 90's.
This was the time when major merging and acquisitions of companies started with the aim to control the market.
AspenTech and Honeywell got out as the winners of this phase.
ApenTech first bought DMC and later also bought Setpoint. DMC plus was the technology ApsenTech continue to develop.
Honeywell, on the other hand, purchased Profimatics, Inc. and formed Hi-Spec Solutions. The RMPC algorithm offered by Honeywell was merged with the Profimatics PCT controller to create Honewell RMPCT solution. Those two vendors took the most of the MPC golden days of the biggest growth.
During this period, other vendors of MPC occurred but could not jeopardize the leading role of AspenTech and Honeywell. However, those were later the subject of other acquisitions. APC applications present on the market during the 00s along with AspenTech and Honeywell were:

• APCS (Adaptive Predictive Control System): SCAP Europa,
• DeltaV MPC: Emerson Process Management,
• SMOC (Shell Multivariable Optimising Controller): Shell,
• Connoisseur (Control and Identification package): Invensys,
• MVC (Multivariate Control): Continental Controls Inc.,
• NOVA-NLC (NOVA Nonlinear Controller): DOT Products,
• Process Perfecter: Pavilion Technologies.

To support the market needs, some of these technologies started to include nonlinear MPC while most of them were still linear MPC.

More details about APC and MPC can be found in the article Overview of dynamic optimizing controllers.

The focus today

The consolidation of vendors continued over the last few years as well. AspenTech and Honeywell however still managed to preserve their leading role on the APC market. Today, we are witnessing a further technology development which is not so much focused on improving the algorithms, but to improve the development steps. The focus is put to make those steps smoother, faster and easier, both for the developer and for the client and do as much as possible remotely. A great amount of knowledge for on-line optimization has been gained over the decades, so the systems used for the development today are also smarter. However, shortening of time and resources during the development phases increases the risk to not define the "optimal" model and strategy.

Engineering work and knowledge in the definition of APC goals and the optimization strategy supported with the regular maintenance of developed APC applications are still the most important steps in the successful application of Advanced Process Control.

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