Model predictive control
MPC is nearly universally implemented as a digital control, although there is research into achieving faster response times with specially designed analog circuitry.
[4] The models used in MPC are generally intended to represent the behavior of complex and simple dynamical systems.
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 algebra calculations that are fast and robust.
When linear models are not sufficiently accurate to represent the real process nonlinearities, several approaches can be used.
An algorithmic study by El-Gherwi, Budman, and El Kamel shows that utilizing a dual-mode approach can provide significant reduction in online computations while maintaining comparative performance to a non-altered implementation.
The proposed algorithm solves N convex optimization problems in parallel based on exchange of information among controllers.
As in linear MPC, NMPC requires the iterative solution of optimal control problems on a finite prediction horizon.
[9] NMPC algorithms typically exploit the fact that consecutive optimal control problems are similar to each other.
[11] While NMPC applications have in the past been mostly used in the process and chemical industries with comparatively slow sampling rates, NMPC is being increasingly applied, with advancements in controller hardware and computational algorithms, e.g., preconditioning,[12] to applications with high sampling rates, e.g., in the automotive industry, or even when the states are distributed in space (Distributed parameter systems).
Every region turns out to geometrically be a convex polytope for linear MPC, commonly parameterized by coefficients for its faces, requiring quantization accuracy analysis.
If the total number of the regions is small, the implementation of the eMPC does not require significant computational resources (compared to the online MPC) and is uniquely suited to control systems with fast dynamics.
Robust variants of model predictive control are able to account for set bounded disturbance while still ensuring state constraints are met.
Due to these fundamental differences, LQR has better global stability properties, but MPC often has more locally optimal[?]
Therefore, MPC typically solves the optimization problem in a smaller time window than the whole horizon and hence may obtain a suboptimal solution.
MPC can chart a path between these fixed points, but convergence of a solution is not guaranteed, especially if thought as to the convexity and complexity of the problem space has been neglected.
