Abstract
Since their inception in the early 1980s industrial model predictive controllers (MPC) rely on continuous quadratic programming (QP) formulations to derive their optimal solutions. More recent advances in mixed-integer programming (MIP) algorithms show that MIP formulations have the potential of being advantageously applied to the MPC problem. In this paper, we present an MIP formulation that can overcome difficulties faced in the practical implementation of MPCs. In particular, it is possible to set explicit priorities for inputs and outputs, define minimum moves to overcome hysteresis, and deal with digital or integer inputs. The proposed formulation is applied to simulated process systems and the results compared with those achieved by a traditional continuous MPC. The solutions of the resulting mixed-integer quadratic programming (MIQP) problems are derived by a computer implementation of the Outer Approximation method (OA) also developed as part of this work.
Highlights
Most industrial model predictive controllers currently in use are based on the algorithms developed in the early 1980’s (Qin and Badgwell, 2003)
In the following plots quadratic programming (QP) refers to the behavior of the variables when the traditional continuous Linear-model predictive controllers (MPC) is controlling the system, while mixed-integer quadratic programming (MIQP) refers to the situation when the proposed mixed-integer algorithm is in use
We have presented MIQP formulations for the steady state and dynamic layers of industrial MPCs
Summary
Most industrial model predictive controllers currently in use are based on the algorithms developed in the early 1980’s (Qin and Badgwell, 2003). The larger valve should only be used for larger flowrate changes, since smaller ones may not be implemented due to valve hysteresis Another characteristic, related to the multivariable nature of the controller, is the manipulation of independent variables that have only a small influence on an output, especially when this last variable hits a constraint. The algorithm proposed in this paper includes binary variables to represent the decisions to move the manipulated inputs during the control horizon, and these decisions can be penalized in the objective function or subjected to a priority sequence. This ensures that the available spans of the less important inputs are exhausted before the algorithm moves the more important ones.
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