Model predictive control

Model Predictive Control, or MPC, is an advanced method of process control that has been in use in the process industries such as chemical plants and oil refineries since the 1980s. Model predictive controllers rely on dynamic models of the process, most often linear empirical models obtained by system identification. The models are used to predict the behavior of dependent variables (ie., outputs) of a dynamical system with respect to changes in the process independent variables (ie., inputs). In chemical processes, independent variables are most often setpoints of regulatory controllers that govern valve movement (eg., valve positioners with or without flow, temperature or pressure controller cascades), while dependent variables are most often constraints in the process (eg., product purity, equipment safe operating limits). The model predictive controller uses the models and current plant measurements to calculate future moves in the independent variables that will result in operation that honors all independent and dependent variable constraints. The MPC then sends this set of independent variable moves to the corresponding regulatory controller setpoints to be implemented in the process.

Despite the fact that most real processes are approximately linear within only a limitted operating window, linear MPC approaches are used in the majority of applications with the feedback mechanism of the MPC compensating for prediction errors due to structural mismatch between the model and the plant. In model predictive controllers that consist only of linear models, the superposition principle of linear algebra enables the effect of changes in multiple independent variables to be added together to predict the response of the dependent variables. This simplifies the control problem to a series of direct matrix algrebra calculations that are fast and robust.

The major commercial suppliers of MPC software in the US are Honeywell, AspenTech, and Emerson.

Theory behind MPC

In principle a non-linear (or linear but state constrained) control problem could be handled by solving the Hamilton-Jacobi-Bellman equation in an offline mode (that is before the plant goes into operation). This would yield the optimal control for every possible state of the plant. In practice this approach is completely impractical from a mathematical, computational and data storage point of view for a high order plant. MPC gets around this problem by restricting attention to the current plant state and to a relatively short time horizon in the future: $[t,t+T]$; an online or on-the-fly calculation is used to explore state trajectories that emanate from the current state and find (via the solution of Euler-Lagrange equations) a cost-minimizing control strategy until time $t+T$. Before that time the plant state is sampled again and the calculations are repeated starting from the now current state, yielding a new control and new predicted state path. The prediction horizon keeps being shifted forward and for this reason MPC is also called receding horizon control. MPC gets around the massive computational requirements of a global HJB solution, but at the cost of requiring the calculations to be run live while the plant is operating. In practice, for those cases where such fast calculations are possible (including the linear case), MPC has given very good results. Much academic research has been done to find fast methods of solution of Euler-Lagrange type equations, to understand the global stability properties of MPC's local optimization, and in general to improve the MPC method. To some extent the theoreticians have been trying to catch up with the control engineers when it comes to MPC.

See also

• System identification
• Control theory
• Control engineering
• Feedforward

References

• Kwon, Bruckstein, Kailath: Stabilizing state feedback design via the moving horizon method, Intl. Journal of Control, 37, 1983, pp.631-643

• Garcia, Prett, Morari: Model predictive control: theory and practice, Automatica, 25, 1989, pp.335-348

• Mayne and Michalska: Receding horizon control of nonlinear systems, IEEE Transactions on Automatic Control, 35, 1990, pp.614-624

External link

• An Overview of Industrial Model Predictive Control Technology