# What is MPC?

Model predictive control (MPC) refers to a class of control algorithms that compute a sequence of control moves based on an explicit prediction of outputs within some future horizon. The computed control moves are typically implemented in a receding horizon fashion, meaning only the moves for the current time are implemented and the whole calculation is repeated at the next sample time. In essence, MPC is a feedback control strategy based on repeated calculation of open-loop control trajectories.

In the process industries, serious applications and research on the subject began in the late 1970 for providing effective solutions to difficult process control problems. Owing to its unique ability to handle process interactions and constraints in a unified manner MPC become popular.

So why is MPC popular? MPC has some advantages:

+Straightforward formulation, based on well understood

concepts

+ Explicitly handles constraints

+ Explicit use of a model

+ Well understood tuning parameters; Prediction horizon and Optimization problem setup

+ Development time much shorter than for competing advanced control methods

+ Easier to maintain: changing model or specs does not require complete redesign, sometimes can be done on the fly.

There are differences between e.g. LQG and MPC. The latter could handle process interactions and constraints within it’s framework. One interesting feature is ”funneling technique”. Industrial MPC controllers use four basic options to

specify future CV behavior; a set-point, zone, reference trajectory or funnel. In the latter the reference trajectory is optimized, see here.

## What is explicit MPC?

A traditional model predictive controller solves a quadratic program (QP) at each control interval to determine the optimal manipulated variable (MV) adjustments. These adjustments are the solution of the implicit nonlinear function u=f(x).

Explicit model predictive control address the problem of removing the main drawbacks of MPC, namely the need to solve the mathematical program on line to compute the control action. The consequence of the computational constraint in MPC results in expensive hardware or limited bandwidth in the control loop.

Explicit model predictive control allows one to solve the optimization problem off-line for a given range of operating conditions of interest. In practice the control function are table lookups of linear gains.

This is a good overview of the field and a course is available here