2Linear Identification of Closed-Loop Systems

This chapter introduces some closed-loop (CL) systems linear identification methods, taking the R (regulation), S (sensitivity) and T (tracking) (RST) type regulator as an example of an automatic controller. It concludes with an application of CL identification, in which another regulator is used (of the Youla–Koucera type).

2.1. Overview of system identification

One of the pillars supporting the Automatic Control domain is the field of System Identification (SI). This field includes quite a large set of techniques to define and estimate mathematical models associated with real systems/processes (whether they are linear or nonlinear). Usually, such models are digital and can be estimated by using measured data provided by the system/process under discussion. The Automatic Control and SI were actually developed at approximately the same time (at the end of the 1930s). They have been progressively developed alongside each other, as, traditionally, each identification model allowed for the creation of an automatic control law for the corresponding process.

Overall, there are two categories of SI techniques: for processes without automatic regulation (open loop [OL]) and for processes containing an integrated automatic controller (closed loop [CL]).

The main goal of open-loop SI (OLSI) is to provide a sufficiently accurate digital model from which an appropriate regulator can be designed. A range of linear identification methods in ...

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