Model Identification and Data Analysis

8Predictive Control

8.1 Introduction

A control problem arises whenever we want to impose a behavior on a given system that is as close as possible to the behavior desired, by acting on quantities that can be manipulated. For example, in order to keep the temperature in a room as close as possible to a reference value (set point), we cannot act directly on the temperature, rather we modulate the amount of heat injected into the room. For an interesting entertaining introduction, we refer to Albertos and Mareels (2010).

In this chapter, we will see simple digital control methods based on black box models. For simplicity, we will make reference to single‐input single‐output systems, with denoting the control variable and the controlled variable. The desired behavior is denoted by and is called reference signal or set point.

The techniques we present are known as predictive control methods. The basic idea on which they rely on is to exploit the model of the system to be controlled in order to predict its response to a given input and choose the input in such a way that the predicted output be as close as possible to the desired output.

The simplest among such techniques is minimum variance ...