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23. Model Predictive Control


As mentioned in Chapter 11, all real world control problems are subject to constraints of various types. The most common constraints are actuator constraints (amplitude and slew rate limits). In addition, many problems also have constraints on state variables (e.g. maximal pressures that cannot be exceeded, minimum tank levels etc).

In many design problems, these constraints can be ignored, at least in the initial design phase. However, in other problems, these constraints are an inescapable part of the problem formulation since the system operates near a constraint boundary. Indeed, in many process control problems the optimal steady state operating point is frequently at a constraint boundary. In these cases, it is desirable to be able to carry out the design so as to include the constraints from the beginning.

Chapter 11 described methods for dealing with constraints based on anti-windup strategies. These are probably adequate for simple problems - especially SISO problems. Also, these methods can be extended to certain MIMO problems as we shall see later in Chapter 25. However, in more complex MIMO problems - especially those having both input and state constraints, it is desirable to have a more formal mechanism for dealing with constraints in MIMO control system design.

We describe one such mechanism here based on Model Predictive Control. This has actually been a major success story in the application of modern control. More than 2,000 applications of this method have been reported in the literature - predominantly in the petrochemical area. Also, the method is being increasingly used in electromechanical control problems as control systems push constraint boundaries. Its main advantages are:

  • it provides a "one-stop-shop" for MIMO control in the presence of constraints,
  • it is one of the few methods that allow one to treat state constraints, and
  • several commercial packages are available which give industrially robust versions of the algorithms aimed at chemical process control.

Here we will give a brief introduction to the method reflecting the authors' experience. One of us (Graebe) has considerable practical experience with mpc in his industry where it is credited with enabling very substantial annual financial savings through improved control performance.


  • MPC provides a systematic procedure for dealing with constraints (both input and state) in MIMO control problems
  • It has been widely used in industry.
  • Remarkable properties of the method can be established, e.g. global asymptotic stability.