Abstract
We show that the open-loop transfer functions and the stability margins may be defined within the recent model-free control setting. Several convincing computer experiments are presented including one which studies the robustness with respect to delays.
Highlights
Stability margins are basic ingredients of control theory. They are widely taught and are quite often utilized in industry in order to check the control design of plants, or, more exactly, of their mathematical models. The importance of this topic is highlighted by the following fact: the literature on theoretical advances and on the connections with many case-studies contains several thousands of publications! This communication relates stability margins to the recent modelfree control and the corresponding intelligent PIDs [4], which were already illustrated by many concrete and varied applications
Our aims are the following ones: 1) Practitioners of stability margins and other frequency techniques will recognize that their expertise still makes sense within model-free control
4) iPID: It follows from Equation (17) that the stability margins necessitates here the famous Cardano formulae which give the roots of third degree algebraic equations
Summary
Stability margins are basic ingredients of control theory. They are widely taught (see, e.g., [1], [2], [9], [10], [11], [16], and the references therein) and are quite often utilized in industry in order to check the control design of plants, or, more exactly, of their mathematical models. Our aims are the following ones: 1) Practitioners of stability margins and other frequency techniques will recognize that their expertise still makes sense within model-free control. F represents the unknown structure of the control system as well as the perturbations
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