Control of a grinding plant model using MPC and Dynamic Programming


  • Aalto University School of Science and Technology



Begin: 2008-02-01

End: 1900-01-01



Model predictive control is the only advanced control technique which has a significant and widespread impact on industrial process control. The development of the technique started from the Linear-Quadratic-Gaussian Control, which might be considered as a direct predecessor of modern MPC (so called ‘zero generation’ of MPC). However, the linear-quadratic regulator is limited by linear dynamics, quadratic objective function and absence of constraints, thus leaving many industrial problems out of its scope. Thus, the next generation of MPC appeared in the early 80’s having the following main features: linear process constraints, a linear process model, a quadratic objective and a finite time horizon. Thus, a finite horizon was used to approximate the infinite horizon problem, which hardly can be solved. Since even the solution of the finite horizon optimization problem can not be derived analytically in the presence of constraints, quadratic programming was employed to perform the optimization. At the same time, because of the finite horizon formulation, MPC faced stability problems. Attempts to achieve stability included different prediction and control horizon approaches and the introduction of a terminal cost to the MPC objective. The stability of MPC was studied actively during the early 90’s, and the value function of MPC is almost universally used as a natural Lyapunov function to establish stability. The computation requirements of MPCs are growing constantly due to many factors (more complex control systems involving more variables, nonlinearity of the models). As a result the computational requirements of MPCs are critical for many applications, especially for large and fast processes. Therefore many researchers have concentrated their efforts on reducing on-line computations. In contrast to computational requirements and stability, another important property of an MPC, namely, optimality did not attract so much attention in the literature. While the LQR provides the optimal solution of the problem, the later MPCs with finite horizon do not. In general, the researchers did not focus on exploration of optimality because of the idea that a close-to-optimal solution may be found through increasing the control horizon. However a longer control horizon also requires more computations to be done and a compromise must be made between the close-to-optimal properties of the controller and its computational demands.

The project develops a MPC controller with a two-phase control. In the first phase the control is chosen by optimization among the feasible controls like in the common MPC implementation and in the second phase the control is chosen among a predefined set of open-loop controls. The second phase estimates the value function of the infinite horizon problem relatively accurately and therefore the first phase requires only a short control horizon to achieve close-to-optimal performance of the controller. A comparison against traditional Quadratic Programming implementation of MPC is presented for the Grinding Plant control problem. A progress has been achieved in the trade-off between the close-to-optimal properties of MPC and its computational demands.



Alexey Zakharov


             This info last modified 2011-06-21 by Jukka Kortela