Model Predictive Control

Model (Based) Predictive Control (MBPC or MPC) originated in the late seventies and has developed considerably since then. The term Model Predictive Control does not designate a specific control strategy but a very ample range of control methods which make an explicit use of a model of the process to obtain the control signal by minimizing an objective function. These design methods lead to linear controllers which have practically the same structure and present adequate degrees of freedom. The ideas appearing in greater or lesser degree in all the predictive control family are basically:

This chapter describes the elements that are common to all Model-Based Predictive controllers, showing the various alternatives that are used in the different implementations. Some of the most popular methods will later be reviewed in order to demonstrate their most outstanding characteristics.

As has been shown in previous chapters, there is a wide family of predictive controllers, each member of which being defined by the choice of the common elements such as the prediction model, the objective function and obtaining the control law.

This chapter describes one of the most popular predictive control algorithms: Generalized Predictive Control (GPC). The method is developed in detail, showing the general procedure to obtain the control law and its most outstanding characteristics. The original algorithm is extended to include the cases of measurable disturbances and change in the predictor. Close derivations of this controller as CRHPC and Stable GPC are also treated here, illustrating the way they can be implemented.

One of the reasons for the success of the traditional PID controllers in industry is that PID are very easy to implement and tune by using heuristic tuning rules such as the Ziegler-Nichols rules frequently used in practice. A Generalized Predictive Controller, as shown in the previous chapter, results in a linear control law which is very easy to implement once the controller parameters are known. The derivation of the GPC parameters requires, however, some mathematical complexities such as solving recursively the Diophantine equation, forming the matrices G, G′, f and then solving a set of linear equations. Although this is not a problem for people in the research control community where mathematical packages are normally available, it may be discouraging for those practitioners used to much simpler ways of implementing and tuning controllers.

Most industrial plants have many variables that have to be controlled (outputs) and many manipulated variables or variables used to control the plant (inputs). In certain cases a change in one of the manipulated variables mainly affects the corresponding controlled variable and each of the input-output pairs can be considered as a single-input single-output (SISO) plant and controlled by independent loops. In many cases, when one of the manipulated variables is changed, it not only affects the corresponding controlled variable but also upsets the other controlled variables. These interactions between process variables may result in poor performance of the control process or even instability. When the interactions are not negligible, the plant must be considered to be a process with multiple inputs and outputs (MIMO) instead of a set of SISO processes. The control of MIMO processes has been extensively treated in literature; perhaps the most popular way of controlling MIMO processes is by designing decoupling compensators to suppress or diminish the interactions and then designing multiple SISO controllers. This first requires determining how to pair the input and output variables, that is, which manipulated variable will be used to control each of the output variables, and also that the plant have the same number of manipulated and controlled variables. Total decoupling is very difficult to achieve for processes with complex dynamics or exhibiting dead times.

The control problem has been formulated in the previous chapters considering all signals to possess an unlimited range. This is not very realistic because in practice all processes are subject to constraints. Actuators have a limited range of action and a limited slew rate, as is the case of control valves which are limited by a fully closed and fully open position and a maximum slew rate. Constructive and/or safety reasons, as well as sensor range, cause bounds in process variables, as in the case of levels in tanks, flows in pipes and pressures in deposits. Furthermore, in practice, the operating points of plants are determined to satisfy economic goals and lie at the intersection of certain constraints. The control system normally operates close to the limits and constraint violations are likely to occur. The control system, especially for long-range predictive control, has to anticipate constraint violations and correct them in an appropriate way. Although input and output constraints are basically treated in the same way, as is shown in this chapter, the implications of the constraints differ. Output constraints are mainly due to safety reasons, and must be controlled in advance because output variables are affected by process dynamics. Input (or manipulated) variables can always be kept in bound by the controller by clipping the control action to a value satisfying amplitude and slew rate constraints.

Mathematical models of real processes cannot contemplate every aspect of reality. Simplifying assumptions have to be made, especially when the models are going to be used for control purposes, where models with simple structures (linear in most cases) and sufficiently small size have to be used due to available control techniques and real time considerations. Thus, mathematical models, and especially control models, can only describe the dynamics of the process in an approximative way.

This chapter is dedicated to presenting some MPC applications to the control of different real and simulated processes. The first application presented corresponds to a self-tuning and a gain scheduling GPC for a distributed collector field of a solar power plant. In order to illustrate how easily the control scheme shown in chapter 5 can be used in any commercial distributed control system, some applications concerning the control of typical variables such as flows, temperatures and levels of different processes of a pilot plant are presented. Finally the application of a GPC to a diffusion process of a sugar factory is presented.